data mining introductory and advanced topics part i

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DATA MININGDATA MININGIntroductory and Advanced TopicsIntroductory and Advanced Topics

Part IPart I

Margaret H. DunhamMargaret H. DunhamDepartment of Computer Science and EngineeringDepartment of Computer Science and Engineering

Southern Methodist UniversitySouthern Methodist University

Companion slides for the text by Dr. M.H.Dunham, Companion slides for the text by Dr. M.H.Dunham, Data Mining, Data Mining, Introductory and Advanced TopicsIntroductory and Advanced Topics, Prentice Hall, 2002., Prentice Hall, 2002.

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Data Mining OutlineData Mining Outline PART IPART I

– IntroductionIntroduction– Related ConceptsRelated Concepts– Data Mining TechniquesData Mining Techniques

PART IIPART II– ClassificationClassification– ClusteringClustering– Association RulesAssociation Rules

PART IIIPART III– Web MiningWeb Mining– Spatial MiningSpatial Mining– Temporal MiningTemporal Mining

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Introduction OutlineIntroduction Outline

Define data miningDefine data mining Data mining vs. databasesData mining vs. databases Basic data mining tasksBasic data mining tasks Data mining developmentData mining development Data mining issuesData mining issues

Goal:Goal: Provide an overview of data mining. Provide an overview of data mining.

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IntroductionIntroduction

Data is growing at a phenomenal rateData is growing at a phenomenal rate Users expect more sophisticated Users expect more sophisticated

informationinformation How?How?

UNCOVER HIDDEN INFORMATIONUNCOVER HIDDEN INFORMATIONDATA MININGDATA MINING

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Data Mining DefinitionData Mining Definition

Finding hidden information in a Finding hidden information in a databasedatabase

Fit data to a modelFit data to a model Similar termsSimilar terms

– Exploratory data analysisExploratory data analysis– Data driven discoveryData driven discovery– Deductive learningDeductive learning

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Data Mining AlgorithmData Mining Algorithm

Objective: Fit Data to a ModelObjective: Fit Data to a Model– DescriptiveDescriptive– PredictivePredictive

Preference – Technique to choose the Preference – Technique to choose the best modelbest model

Search – Technique to search the dataSearch – Technique to search the data– ““Query”Query”

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Database Processing vs. Data Database Processing vs. Data Mining ProcessingMining Processing

QueryQuery– Well definedWell defined– SQLSQL

QueryQuery– Poorly definedPoorly defined– No precise query languageNo precise query language

DataData– Operational dataOperational data

OutputOutput– PrecisePrecise– Subset of databaseSubset of database

DataData– Not operational dataNot operational data

OutputOutput– FuzzyFuzzy– Not a subset of databaseNot a subset of database

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Query ExamplesQuery Examples DatabaseDatabase

Data MiningData Mining

– Find all customers who have purchased milkFind all customers who have purchased milk

– Find all items which are frequently purchased Find all items which are frequently purchased with milk. (association rules)with milk. (association rules)

– Find all credit applicants with last name of Smith.Find all credit applicants with last name of Smith.– Identify customers who have purchased more Identify customers who have purchased more than $10,000 in the last month.than $10,000 in the last month.

– Find all credit applicants who are poor credit Find all credit applicants who are poor credit risks. (classification)risks. (classification)– Identify customers with similar buying habits. Identify customers with similar buying habits. (Clustering)(Clustering)

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Data Mining Models and TasksData Mining Models and Tasks

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Basic Data Mining TasksBasic Data Mining Tasks Classification Classification maps data into predefined groups or maps data into predefined groups or

classesclasses– Supervised learningSupervised learning– Pattern recognitionPattern recognition– PredictionPrediction

RegressionRegression is used to map a data item to a real is used to map a data item to a real valued prediction variable.valued prediction variable.

Clustering Clustering groups similar data together into groups similar data together into clusters.clusters.– Unsupervised learningUnsupervised learning– SegmentationSegmentation– PartitioningPartitioning

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Basic Data Mining Tasks Basic Data Mining Tasks (cont’d)(cont’d)

Summarization Summarization maps data into subsets with maps data into subsets with associated simple descriptions.associated simple descriptions.– CharacterizationCharacterization– GeneralizationGeneralization

Link AnalysisLink Analysis uncovers relationships among uncovers relationships among data.data.– Affinity AnalysisAffinity Analysis– Association RulesAssociation Rules– Sequential Analysis determines sequential Sequential Analysis determines sequential

patterns.patterns.

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Ex: Time Series AnalysisEx: Time Series Analysis Example: Stock MarketExample: Stock Market Predict future valuesPredict future values Determine similar patterns over timeDetermine similar patterns over time Classify behaviorClassify behavior

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Data Mining vs. KDDData Mining vs. KDD

Knowledge Discovery in Databases Knowledge Discovery in Databases (KDD):(KDD): process of finding useful process of finding useful information and patterns in data.information and patterns in data.

Data Mining:Data Mining: Use of algorithms to Use of algorithms to extract the information and patterns extract the information and patterns derived by the KDD process. derived by the KDD process.

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KDD ProcessKDD Process

Selection:Selection: Obtain data from various sources. Obtain data from various sources. Preprocessing:Preprocessing: Cleanse data. Cleanse data. Transformation:Transformation: Convert to common format. Convert to common format.

Transform to new format.Transform to new format. Data Mining:Data Mining: Obtain desired results. Obtain desired results. Interpretation/Evaluation:Interpretation/Evaluation: Present results Present results

to user in meaningful manner.to user in meaningful manner.

Modified from [FPSS96C]

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KDD Process Ex: Web LogKDD Process Ex: Web Log Selection:Selection:

– Select log data (dates and locations) to useSelect log data (dates and locations) to use Preprocessing:Preprocessing:

– Remove identifying URLsRemove identifying URLs– Remove error logsRemove error logs

Transformation:Transformation: – Sessionize (sort and group)Sessionize (sort and group)

Data Mining:Data Mining: – Identify and count patternsIdentify and count patterns– Construct data structureConstruct data structure

Interpretation/Evaluation:Interpretation/Evaluation:– Identify and display frequently accessed sequences.Identify and display frequently accessed sequences.

Potential User Applications:Potential User Applications:– Cache predictionCache prediction– PersonalizationPersonalization

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Data Mining DevelopmentData Mining Development•Similarity Measures•Hierarchical Clustering•IR Systems•Imprecise Queries•Textual Data•Web Search Engines

•Bayes Theorem•Regression Analysis•EM Algorithm•K-Means Clustering•Time Series Analysis

•Neural Networks•Decision Tree Algorithms

•Algorithm Design Techniques•Algorithm Analysis•Data Structures

•Relational Data Model•SQL•Association Rule Algorithms•Data Warehousing•Scalability Techniques

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KDD IssuesKDD Issues

Human InteractionHuman Interaction OverfittingOverfitting OutliersOutliers InterpretationInterpretation Visualization Visualization Large DatasetsLarge Datasets High DimensionalityHigh Dimensionality

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KDD Issues (cont’d)KDD Issues (cont’d) Multimedia DataMultimedia Data Missing DataMissing Data Irrelevant DataIrrelevant Data Noisy DataNoisy Data Changing DataChanging Data IntegrationIntegration ApplicationApplication

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Social Implications of DMSocial Implications of DM

Privacy Privacy ProfilingProfiling Unauthorized useUnauthorized use

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Data Mining MetricsData Mining Metrics

UsefulnessUsefulness Return on Investment (ROI)Return on Investment (ROI) AccuracyAccuracy Space/TimeSpace/Time

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Database Perspective on Data Database Perspective on Data MiningMining

ScalabilityScalability Real World DataReal World Data UpdatesUpdates Ease of UseEase of Use

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Visualization TechniquesVisualization Techniques

GraphicalGraphical GeometricGeometric Icon-basedIcon-based Pixel-basedPixel-based HierarchicalHierarchical HybridHybrid

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Related Concepts OutlineRelated Concepts Outline

Database/OLTP SystemsDatabase/OLTP Systems Fuzzy Sets and LogicFuzzy Sets and Logic Information Retrieval(Web Search Engines)Information Retrieval(Web Search Engines) Dimensional ModelingDimensional Modeling Data WarehousingData Warehousing OLAP/DSSOLAP/DSS StatisticsStatistics Machine LearningMachine Learning Pattern MatchingPattern Matching

Goal:Goal: Examine some areas which are related to Examine some areas which are related to data mining.data mining.

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DB & OLTP SystemsDB & OLTP Systems SchemaSchema

– (ID,Name,Address,Salary,JobNo)(ID,Name,Address,Salary,JobNo) Data ModelData Model

– ERER– RelationalRelational

TransactionTransaction Query:Query:

SELECT NameSELECT NameFROM TFROM TWHERE Salary > 100000WHERE Salary > 100000

DM: Only imprecise queriesDM: Only imprecise queries

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Fuzzy Sets and LogicFuzzy Sets and Logic Fuzzy Set:Fuzzy Set: Set membership function is a real valued Set membership function is a real valued

function with output in the range [0,1].function with output in the range [0,1]. f(x): Probability x is in F.f(x): Probability x is in F. 1-f(x): Probability x is not in F.1-f(x): Probability x is not in F. EX:EX:

– T = {x | x is a person and x is tall}T = {x | x is a person and x is tall}– Let f(x) be the probability that x is tallLet f(x) be the probability that x is tall– Here f is the membership functionHere f is the membership function

DM: DM: Prediction and classification are fuzzy.Prediction and classification are fuzzy.

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Fuzzy SetsFuzzy Sets

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Classification/Prediction is Classification/Prediction is FuzzyFuzzy

Loan

Amnt

Simple Fuzzy

Accept Accept

RejectReject

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Information Retrieval Information Retrieval Information Retrieval (IR):Information Retrieval (IR): retrieving desired information retrieving desired information

from textual data.from textual data. Library ScienceLibrary Science Digital LibrariesDigital Libraries Web Search EnginesWeb Search Engines Traditionally keyword basedTraditionally keyword based Sample query:Sample query:

Find all documents about “data mining”.Find all documents about “data mining”.

DM: Similarity measures; DM: Similarity measures; Mine text/Web data.Mine text/Web data.

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Information Retrieval (cont’d)Information Retrieval (cont’d) Similarity:Similarity: measure of how close a measure of how close a

query is to a document.query is to a document. Documents which are “close enough” Documents which are “close enough”

are retrieved.are retrieved. Metrics:Metrics:

– PrecisionPrecision = |Relevant and Retrieved| = |Relevant and Retrieved| |Retrieved||Retrieved|

– RecallRecall = |Relevant and Retrieved|= |Relevant and Retrieved| |Relevant||Relevant|

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IR Query Result Measures IR Query Result Measures and Classificationand Classification

IR Classification

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Dimensional ModelingDimensional Modeling View data in a hierarchical manner more as View data in a hierarchical manner more as

business executives mightbusiness executives might Useful in decision support systems and miningUseful in decision support systems and mining Dimension:Dimension: collection of logically related collection of logically related

attributes; axis for modeling data.attributes; axis for modeling data. Facts:Facts: data stored data stored Ex: Dimensions – products, locations, dateEx: Dimensions – products, locations, date

Facts – quantity, unit priceFacts – quantity, unit price

DM: May view data as dimensional.DM: May view data as dimensional.

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Relational View of DataRelational View of Data

ProdID LocID Date Quantity UnitPrice 123 Dallas 022900 5 25 123 Houston 020100 10 20 150 Dallas 031500 1 100 150 Dallas 031500 5 95 150 Fort

Worth 021000 5 80

150 Chicago 012000 20 75 200 Seattle 030100 5 50 300 Rochester 021500 200 5 500 Bradenton 022000 15 20 500 Chicago 012000 10 25 1

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Dimensional Modeling QueriesDimensional Modeling Queries

Roll Up:Roll Up: more general dimension more general dimension Drill Down:Drill Down: more specific dimension more specific dimension Dimension (Aggregation) HierarchyDimension (Aggregation) Hierarchy SQL uses aggregationSQL uses aggregation Decision Support Systems (DSS):Decision Support Systems (DSS):

Computer systems and tools to assist Computer systems and tools to assist managers in making decisions and managers in making decisions and solving problems.solving problems.

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Cube view of DataCube view of Data

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Aggregation HierarchiesAggregation Hierarchies

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Star SchemaStar Schema

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Data WarehousingData Warehousing

““Subject-oriented, integrated, time-variant, nonvolatile” Subject-oriented, integrated, time-variant, nonvolatile” William InmonWilliam Inmon

Operational Data:Operational Data: Data used in day to day needs of Data used in day to day needs of company.company.

Informational Data:Informational Data: Supports other functions such as Supports other functions such as planning and forecasting.planning and forecasting.

Data mining tools often access data warehouses rather Data mining tools often access data warehouses rather than operational data.than operational data.

DM: May access data in warehouse.DM: May access data in warehouse.

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Operational vs. InformationalOperational vs. Informational Operational Data Data Warehouse

Application OLTP OLAPUse Precise Queries Ad HocTemporal Snapshot HistoricalModification Dynamic StaticOrientation Application BusinessData Operational Values IntegratedSize Gigabits TerabitsLevel Detailed SummarizedAccess Often Less OftenResponse Few Seconds MinutesData Schema Relational Star/Snowflake

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OLAPOLAP Online Analytic Processing (OLAP):Online Analytic Processing (OLAP): provides more provides more

complex queries than OLTP.complex queries than OLTP. OnLine Transaction Processing (OLTP):OnLine Transaction Processing (OLTP): traditional traditional

database/transaction processing.database/transaction processing. Dimensional data; cube view Dimensional data; cube view Visualization of operations:Visualization of operations:

– Slice:Slice: examine sub-cube. examine sub-cube.– Dice:Dice: rotate cube to look at another dimension. rotate cube to look at another dimension.– Roll Up/Drill DownRoll Up/Drill Down

DM: May use OLAP queries.DM: May use OLAP queries.

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OLAP OperationsOLAP Operations

Single Cell Multiple Cells Slice Dice

Roll Up

Drill Down

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StatisticsStatistics Simple descriptive modelsSimple descriptive models Statistical inference:Statistical inference: generalizing a model generalizing a model

created from a sample of the data to the entire created from a sample of the data to the entire dataset.dataset.

Exploratory Data Analysis:Exploratory Data Analysis: – Data can actually drive the creation of the Data can actually drive the creation of the

modelmodel– Opposite of traditional statistical view.Opposite of traditional statistical view.

Data mining targeted to business userData mining targeted to business user

DM: Many data mining methods come DM: Many data mining methods come from statistical techniques. from statistical techniques.

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Machine LearningMachine Learning Machine Learning:Machine Learning: area of AI that examines how to area of AI that examines how to

write programs that can learn.write programs that can learn. Often used in classification and prediction Often used in classification and prediction Supervised Learning:Supervised Learning: learns by example. learns by example. Unsupervised Learning: Unsupervised Learning: learns without knowledge of learns without knowledge of

correct answers.correct answers. Machine learning often deals with small static datasets. Machine learning often deals with small static datasets.

DM: Uses many machine learning DM: Uses many machine learning techniques.techniques.

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Pattern Matching Pattern Matching (Recognition)(Recognition)

Pattern Matching:Pattern Matching: finds occurrences of finds occurrences of a predefined pattern in the data.a predefined pattern in the data.

Applications include speech recognition, Applications include speech recognition, information retrieval, time series information retrieval, time series analysis.analysis.

DM: Type of classification.DM: Type of classification.

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DM vs. Related TopicsDM vs. Related TopicsArea Query Data Results Output

DB/OLTP Precise Database Precise DB Objects or Aggregation

IR Precise Documents Vague Documents OLAP Analysis Multidimensional Precise DB Objects

or Aggregation

DM Vague Preprocessed Vague KDD Objects

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Data Mining Techniques OutlineData Mining Techniques Outline

StatisticalStatistical– Point EstimationPoint Estimation– Models Based on SummarizationModels Based on Summarization– Bayes TheoremBayes Theorem– Hypothesis TestingHypothesis Testing– Regression and CorrelationRegression and Correlation

Similarity MeasuresSimilarity Measures Decision TreesDecision Trees Neural NetworksNeural Networks

– Activation FunctionsActivation Functions Genetic AlgorithmsGenetic Algorithms

Goal:Goal: Provide an overview of basic data Provide an overview of basic data mining techniquesmining techniques

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Point EstimationPoint Estimation Point Estimate:Point Estimate: estimate a population estimate a population

parameter.parameter. May be made by calculating the parameter for a May be made by calculating the parameter for a

sample.sample. May be used to predict value for missing data.May be used to predict value for missing data. Ex: Ex:

– R contains 100 employeesR contains 100 employees– 99 have salary information99 have salary information– Mean salary of these is $50,000Mean salary of these is $50,000– Use $50,000 as value of remaining employee’s Use $50,000 as value of remaining employee’s

salary. salary. Is this a good idea?Is this a good idea?

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Estimation ErrorEstimation Error Bias: Bias: Difference between expected value and Difference between expected value and

actual value.actual value.

Mean Squared Error (MSE):Mean Squared Error (MSE): expected value expected value of the squared difference between the of the squared difference between the estimate and the actual value:estimate and the actual value:

Why square?Why square? Root Mean Square Error (RMSE)Root Mean Square Error (RMSE)

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Jackknife EstimateJackknife Estimate Jackknife Estimate:Jackknife Estimate: estimate of parameter is estimate of parameter is

obtained by omitting one value from the set of obtained by omitting one value from the set of observed values.observed values.

Ex: estimate of mean for X={xEx: estimate of mean for X={x1, … , x, … , xn}}

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Maximum Likelihood Maximum Likelihood Estimate (MLE)Estimate (MLE)

Obtain parameter estimates that maximize Obtain parameter estimates that maximize the probability that the sample data occurs for the probability that the sample data occurs for the specific model.the specific model.

Joint probability for observing the sample Joint probability for observing the sample data by multiplying the individual probabilities. data by multiplying the individual probabilities. Likelihood function: Likelihood function:

Maximize L.Maximize L.

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MLE ExampleMLE Example

Coin toss five times: {H,H,H,H,T}Coin toss five times: {H,H,H,H,T} Assuming a perfect coin with H and T equally Assuming a perfect coin with H and T equally

likely, the likelihood of this sequence is: likely, the likelihood of this sequence is:

However if the probability of a H is 0.8 then:However if the probability of a H is 0.8 then:

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MLE Example (cont’d)MLE Example (cont’d) General likelihood formula:General likelihood formula:

Estimate for p is then 4/5 = 0.8Estimate for p is then 4/5 = 0.8

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Expectation-Maximization Expectation-Maximization (EM)(EM)

Solves estimation with incomplete data.Solves estimation with incomplete data. Obtain initial estimates for parameters.Obtain initial estimates for parameters. Iteratively use estimates for missing Iteratively use estimates for missing

data and continue until convergence.data and continue until convergence.

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EM ExampleEM Example

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EM AlgorithmEM Algorithm

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Models Based on SummarizationModels Based on Summarization Visualization:Visualization: Frequency distribution, mean, variance, Frequency distribution, mean, variance,

median, mode, etc.median, mode, etc. Box Plot:Box Plot:

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Scatter DiagramScatter Diagram

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Bayes TheoremBayes Theorem Posterior Probability:Posterior Probability: P(hP(h1|x|xi)) Prior Probability:Prior Probability: P(h P(h1)) Bayes Theorem:Bayes Theorem:

Assign probabilities of hypotheses given a data Assign probabilities of hypotheses given a data value.value.

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Bayes Theorem ExampleBayes Theorem Example Credit authorizations (hypotheses): Credit authorizations (hypotheses):

hh11=authorize purchase, h=authorize purchase, h2 = authorize after = authorize after further identification, hfurther identification, h3=do not authorize, =do not authorize, hh4= do not authorize but contact police= do not authorize but contact police

Assign twelve data values for all Assign twelve data values for all combinations of credit and income:combinations of credit and income:

From training data: P(hFrom training data: P(h11) = 60%; P(h) = 60%; P(h22)=20%; )=20%;

P(h P(h33)=10%; P(h)=10%; P(h44)=10%.)=10%.

1 2 3 4 Excellent x1 x2 x3 x4 Good x5 x6 x7 x8 Bad x9 x10 x11 x12

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Bayes Example(cont’d)Bayes Example(cont’d) Training Data:Training Data:

ID Income Credit Class xi 1 4 Excellent h1 x4 2 3 Good h1 x7 3 2 Excellent h1 x2 4 3 Good h1 x7 5 4 Good h1 x8 6 2 Excellent h1 x2 7 3 Bad h2 x11 8 2 Bad h2 x10 9 3 Bad h3 x11 10 1 Bad h4 x9

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Bayes Example(cont’d)Bayes Example(cont’d) Calculate P(xCalculate P(xii|h|hjj) and P(x) and P(xii)) Ex: P(xEx: P(x77|h|h11)=2/6; P(x)=2/6; P(x44|h|h11)=1/6; P(x)=1/6; P(x22|h|h11)=2/6; P(x)=2/6; P(x88||

hh11)=1/6; P(x)=1/6; P(xii|h|h11)=0 for all other x)=0 for all other xii.. Predict the class for xPredict the class for x44::

– Calculate P(hCalculate P(hjj|x|x44) for all h) for all hjj. . – Place xPlace x4 4 in class with largest value.in class with largest value.– Ex: Ex:

»P(hP(h11|x|x44)=(P(x)=(P(x44|h|h11)(P(h)(P(h11))/P(x))/P(x44)) =(1/6)(0.6)/0.1=1. =(1/6)(0.6)/0.1=1.

»xx4 4 in class hin class h11..

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Hypothesis TestingHypothesis Testing

Find model to explain behavior by Find model to explain behavior by creating and then testing a hypothesis creating and then testing a hypothesis about the data.about the data.

Exact opposite of usual DM approach.Exact opposite of usual DM approach. HH0 0 – Null hypothesis; Hypothesis to be – Null hypothesis; Hypothesis to be

tested.tested. HH1 1 – Alternative hypothesis– Alternative hypothesis

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Chi Squared StatisticChi Squared Statistic

O – observed valueO – observed value E – Expected value based on hypothesis.E – Expected value based on hypothesis.

Ex: Ex: – O={50,93,67,78,87}O={50,93,67,78,87}– E=75E=75– 22=15.55 and therefore significant=15.55 and therefore significant

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RegressionRegression

Predict future values based on past Predict future values based on past valuesvalues

Linear RegressionLinear Regression assumes linear assumes linear relationship exists.relationship exists.

y = cy = c00 + c + c11 x x11 + … + c + … + cnn x xnn

Find values to best fit the dataFind values to best fit the data

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Linear RegressionLinear Regression

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CorrelationCorrelation

Examine the degree to which the values Examine the degree to which the values for two variables behave similarly.for two variables behave similarly.

Correlation coefficient r:Correlation coefficient r:• 1 = perfect correlation1 = perfect correlation• -1 = perfect but opposite correlation-1 = perfect but opposite correlation• 0 = no correlation0 = no correlation

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Similarity MeasuresSimilarity Measures Determine similarity between two objects.Determine similarity between two objects. Similarity characteristics:Similarity characteristics:

Alternatively, distance measure measure how Alternatively, distance measure measure how unlike or dissimilar objects are.unlike or dissimilar objects are.

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Similarity MeasuresSimilarity Measures

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Distance MeasuresDistance Measures

Measure dissimilarity between objectsMeasure dissimilarity between objects

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Twenty Questions GameTwenty Questions Game

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Decision TreesDecision Trees Decision Tree (DT):Decision Tree (DT):

– Tree where the root and each internal node is Tree where the root and each internal node is labeled with a question. labeled with a question.

– The arcs represent each possible answer to The arcs represent each possible answer to the associated question. the associated question.

– Each leaf node represents a prediction of a Each leaf node represents a prediction of a solution to the problem.solution to the problem.

Popular technique for classification; Leaf Popular technique for classification; Leaf node indicates class to which the node indicates class to which the corresponding tuple belongs.corresponding tuple belongs.

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Decision Tree ExampleDecision Tree Example

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Decision TreesDecision Trees

AA Decision Tree Model Decision Tree Model is a computational is a computational model consisting of three parts:model consisting of three parts:– Decision TreeDecision Tree– Algorithm to create the treeAlgorithm to create the tree– Algorithm that applies the tree to data Algorithm that applies the tree to data

Creation of the tree is the most difficult part.Creation of the tree is the most difficult part. Processing is basically a search similar to Processing is basically a search similar to

that in a binary search tree (although DT may that in a binary search tree (although DT may not be binary).not be binary).

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Decision Tree AlgorithmDecision Tree Algorithm

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DT DT Advantages/DisadvantagesAdvantages/Disadvantages

Advantages:Advantages:– Easy to understand. Easy to understand. – Easy to generate rulesEasy to generate rules

Disadvantages:Disadvantages:– May suffer from overfitting.May suffer from overfitting.– Classifies by rectangular partitioning.Classifies by rectangular partitioning.– Does not easily handle nonnumeric data.Does not easily handle nonnumeric data.– Can be quite large – pruning is necessary.Can be quite large – pruning is necessary.

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Neural Networks Neural Networks Based on observed functioning of human Based on observed functioning of human

brain. brain. (Artificial Neural Networks (ANN)(Artificial Neural Networks (ANN) Our view of neural networks is very simplistic. Our view of neural networks is very simplistic. We view a neural network (NN) from a We view a neural network (NN) from a

graphical viewpoint.graphical viewpoint. Alternatively, a NN may be viewed from the Alternatively, a NN may be viewed from the

perspective of matrices.perspective of matrices. Used in pattern recognition, speech Used in pattern recognition, speech

recognition, computer vision, and recognition, computer vision, and classification.classification.

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Neural NetworksNeural Networks Neural Network (NN)Neural Network (NN) is a directed graph is a directed graph

F=<V,A> with vertices V={1,2,…,n} and arcs F=<V,A> with vertices V={1,2,…,n} and arcs A={<i,j>|1<=i,j<=n}, with the following A={<i,j>|1<=i,j<=n}, with the following restrictions:restrictions:– V is partitioned into a set of input nodes, VV is partitioned into a set of input nodes, V II, ,

hidden nodes, Vhidden nodes, VHH, and output nodes, V, and output nodes, VOO..– The vertices are also partitioned into layers The vertices are also partitioned into layers – Any arc <i,j> must have node i in layer h-1 Any arc <i,j> must have node i in layer h-1

and node j in layer h.and node j in layer h.– Arc <i,j> is labeled with a numeric value wArc <i,j> is labeled with a numeric value w ijij..– Node i is labeled with a function fNode i is labeled with a function f ii..

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Neural Network ExampleNeural Network Example

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NN NodeNN Node

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NN Activation FunctionsNN Activation Functions

Functions associated with nodes in Functions associated with nodes in graph.graph.

Output may be in range [-1,1] or [0,1]Output may be in range [-1,1] or [0,1]

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NN Activation FunctionsNN Activation Functions

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NN LearningNN Learning

Propagate input values through graph.Propagate input values through graph. Compare output to desired output.Compare output to desired output. Adjust weights in graph accordingly.Adjust weights in graph accordingly.

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Neural NetworksNeural Networks

A A Neural Network ModelNeural Network Model is a computational is a computational model consisting of three parts:model consisting of three parts:– Neural Network graph Neural Network graph – Learning algorithm that indicates how Learning algorithm that indicates how

learning takes place.learning takes place.– Recall techniques that determine hew Recall techniques that determine hew

information is obtained from the network. information is obtained from the network. We will look at propagation as the recall We will look at propagation as the recall

technique.technique.

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NN AdvantagesNN Advantages

LearningLearning Can continue learning even after Can continue learning even after

training set has been applied.training set has been applied. Easy parallelizationEasy parallelization Solves many problemsSolves many problems

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NN DisadvantagesNN Disadvantages

Difficult to understandDifficult to understand May suffer from overfittingMay suffer from overfitting Structure of graph must be determined Structure of graph must be determined

a priori.a priori. Input values must be numeric.Input values must be numeric. Verification difficult.Verification difficult.

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Genetic AlgorithmsGenetic Algorithms Optimization search type algorithms. Optimization search type algorithms. Creates an initial feasible solution and Creates an initial feasible solution and

iteratively creates new “better” solutions.iteratively creates new “better” solutions. Based on human evolution and survival of the Based on human evolution and survival of the

fittest.fittest. Must represent a solution as an individual.Must represent a solution as an individual. Individual:Individual: string I=I string I=I11,I,I22,…,I,…,Inn where I where Ijj is in given is in given

alphabet A. alphabet A. Each character IEach character Ij j is called a is called a genegene.. Population:Population: set of individuals. set of individuals.

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Genetic AlgorithmsGenetic Algorithms A A Genetic Algorithm (GA)Genetic Algorithm (GA) is a is a

computational model consisting of five parts:computational model consisting of five parts:– A starting set of individuals, P.A starting set of individuals, P.– CrossoverCrossover:: technique to combine two technique to combine two

parents to create offspring.parents to create offspring.– Mutation: Mutation: randomly change an individual.randomly change an individual.– Fitness: Fitness: determine the best individuals.determine the best individuals.– Algorithm which applies the crossover and Algorithm which applies the crossover and

mutation techniques to P iteratively using mutation techniques to P iteratively using the fitness function to determine the best the fitness function to determine the best individuals in P to keep. individuals in P to keep.

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Crossover ExamplesCrossover Examples

111 111

000 000

Parents Children

111 000

000 111

a) Single Crossover

111 111

Parents Children

111 000

000

a) Single Crossover

111 111

000 000

Parents

a) Multiple Crossover

111 111

000

Parents Children

111 000

000 111

Children

111 000

000 11100

11

00

11

© Prentice Hall 88

Genetic AlgorithmGenetic Algorithm

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GA Advantages/DisadvantagesGA Advantages/Disadvantages AdvantagesAdvantages

– Easily parallelizedEasily parallelized DisadvantagesDisadvantages

– Difficult to understand and explain to end Difficult to understand and explain to end users.users.

– Abstraction of the problem and method to Abstraction of the problem and method to represent individuals is quite difficult.represent individuals is quite difficult.

– Determining fitness function is difficult.Determining fitness function is difficult.– Determining how to perform crossover and Determining how to perform crossover and

mutation is difficult.mutation is difficult.

© Prentice Hall 90


Part II Part II




© Prentice Hall 92

Classification OutlineClassification Outline

Classification Problem OverviewClassification Problem Overview Classification TechniquesClassification Techniques

– RegressionRegression– DistanceDistance– Decision TreesDecision Trees– RulesRules– Neural NetworksNeural Networks

Goal:Goal: Provide an overview of the classification Provide an overview of the classification problem and introduce some of the basic problem and introduce some of the basic algorithmsalgorithms

© Prentice Hall 93

Classification ProblemClassification Problem Given a database D={tGiven a database D={t11,t,t22,…,t,…,tnn} and a set } and a set

of classes C={Cof classes C={C11,…,C,…,Cmm}, the }, the Classification ProblemClassification Problem is to define a is to define a mapping f:Dmapping f:DC where each tC where each tii is assigned is assigned to one class.to one class.

Actually divides D into Actually divides D into equivalence equivalence classesclasses..

PredictionPrediction isis similar, but may be viewed similar, but may be viewed as having infinite number of classes.as having infinite number of classes.

© Prentice Hall 94

Classification ExamplesClassification Examples Teachers classify students’ grades as Teachers classify students’ grades as

A, B, C, D, or F. A, B, C, D, or F. Identify mushrooms as poisonous or Identify mushrooms as poisonous or

edible.edible. Predict when a river will flood.Predict when a river will flood. Identify individuals with credit risks. Identify individuals with credit risks. Speech recognitionSpeech recognition Pattern recognitionPattern recognition

© Prentice Hall 95

Classification Ex: GradingClassification Ex: Grading

If x >= 90 then grade If x >= 90 then grade =A.=A.

If 80<=x<90 then If 80<=x<90 then grade =B.grade =B.

If 70<=x<80 then If 70<=x<80 then grade =C.grade =C.

If 60<=x<70 then If 60<=x<70 then grade =D.grade =D.

If x<50 then grade =F.If x<50 then grade =F.

>=90<90

x

>=80<80

x

>=70<70

x

F

B

A

>=60<50

x C

D

© Prentice Hall 96

Classification Ex: Letter Classification Ex: Letter RecognitionRecognition

View letters as constructed from 5 components:

Letter C

Letter E

Letter A

Letter D

Letter F

Letter B

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Classification TechniquesClassification Techniques Approach:Approach:

1.1. Create specific model by evaluating Create specific model by evaluating training data (or using domain training data (or using domain experts’ knowledge).experts’ knowledge).

2.2. Apply model developed to new data.Apply model developed to new data. Classes must be predefinedClasses must be predefined Most common techniques use DTs, Most common techniques use DTs,

NNs, or are based on distances or NNs, or are based on distances or statistical methods.statistical methods.

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Defining ClassesDefining Classes

Partitioning Based

Distance Based

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Issues in ClassificationIssues in Classification

Missing DataMissing Data– IgnoreIgnore– Replace with assumed valueReplace with assumed value

Measuring PerformanceMeasuring Performance– Classification accuracy on test dataClassification accuracy on test data– Confusion matrixConfusion matrix– OC CurveOC Curve

© Prentice Hall 100

Height Example DataHeight Example DataName Gender Height Output1 Output2 Kristina F 1.6m Short Medium Jim M 2m Tall Medium Maggie F 1.9m Medium Tall Martha F 1.88m Medium Tall Stephanie F 1.7m Short Medium Bob M 1.85m Medium Medium Kathy F 1.6m Short Medium Dave M 1.7m Short Medium Worth M 2.2m Tall Tall Steven M 2.1m Tall Tall Debbie F 1.8m Medium Medium Todd M 1.95m Medium Medium Kim F 1.9m Medium Tall Amy F 1.8m Medium Medium Wynette F 1.75m Medium Medium


Classification PerformanceClassification Performance

True Positive

True NegativeFalse Positive

False Negative


Confusion Matrix ExampleConfusion Matrix Example

Using height data example with Output1 Using height data example with Output1 correct and Output2 actual assignmentcorrect and Output2 actual assignment

Actual Assignment Membership Short Medium Tall Short 0 4 0 Medium 0 5 3 Tall 0 1 2


Operating Characteristic CurveOperating Characteristic Curve


RegressionRegression Assume data fits a predefined functionAssume data fits a predefined function Determine best values for Determine best values for regression regression

coefficientscoefficients cc00,c,c11,…,c,…,cnn.. Assume an error: y = cAssume an error: y = c00+c+c11xx11+…+c+…+cnnxxnn+ Estimate error using mean squared error for

training set:


Linear Regression Poor FitLinear Regression Poor Fit


Classification Using RegressionClassification Using Regression

Division:Division: Use regression function to Use regression function to divide area into regions. divide area into regions.

PredictionPrediction: Use regression function to : Use regression function to predict a class membership function. predict a class membership function. Input includes desired class.Input includes desired class.


DivisionDivision


PredictionPrediction


Classification Using DistanceClassification Using Distance Place items in class to which they are Place items in class to which they are

“closest”.“closest”. Must determine distance between an item Must determine distance between an item

and a class.and a class. Classes represented byClasses represented by

– Centroid:Centroid: Central value. Central value.– Medoid:Medoid: Representative point. Representative point.– Individual pointsIndividual points

Algorithm: KNNAlgorithm: KNN


K Nearest Neighbor (KNN):K Nearest Neighbor (KNN): Training set includes classes.Training set includes classes. Examine K items near item to be Examine K items near item to be

classified.classified. New item placed in class with the most New item placed in class with the most

number of close items.number of close items. O(q) for each tuple to be classified. O(q) for each tuple to be classified.

(Here q is the size of the training set.)(Here q is the size of the training set.)


KNNKNN


KNN AlgorithmKNN Algorithm


Classification Using Decision Classification Using Decision TreesTrees

Partitioning based:Partitioning based: Divide search Divide search space into rectangular regions.space into rectangular regions.

Tuple placed into class based on the Tuple placed into class based on the region within which it falls.region within which it falls.

DT approaches differ in how the tree is DT approaches differ in how the tree is built: built: DT InductionDT Induction

Internal nodes associated with attribute Internal nodes associated with attribute and arcs with values for that attribute.and arcs with values for that attribute.

Algorithms: ID3, C4.5, CARTAlgorithms: ID3, C4.5, CART


Decision TreeDecision TreeGiven: Given:

– D = {tD = {t11, …, t, …, tnn} where t} where tii=<t=<ti1i1, …, t, …, tihih> > – Database schema contains {ADatabase schema contains {A11, A, A22, …, A, …, Ahh}}– Classes C={CClasses C={C11, …., C, …., Cmm}}

Decision or Classification TreeDecision or Classification Tree is is a tree associated a tree associated with D such thatwith D such that– Each internal node is labeled with attribute, AEach internal node is labeled with attribute, Aii

– Each arc is labeled with predicate which can be Each arc is labeled with predicate which can be applied to attribute at parentapplied to attribute at parent

– Each leaf node is labeled with a class, CEach leaf node is labeled with a class, Cjj


DT InductionDT Induction


DT Splits Area DT Splits Area

Gender

Height

M

F


Comparing DTsComparing DTs

BalancedDeep


DT IssuesDT Issues

Choosing Splitting AttributesChoosing Splitting Attributes Ordering of Splitting AttributesOrdering of Splitting Attributes SplitsSplits Tree StructureTree Structure Stopping CriteriaStopping Criteria Training DataTraining Data PruningPruning


Decision Tree Induction is often based on Decision Tree Induction is often based on Information TheoryInformation Theory

SoSo


InformationInformation


DT Induction DT Induction

When all the marbles in the bowl are When all the marbles in the bowl are mixed up, little information is given. mixed up, little information is given.

When the marbles in the bowl are all When the marbles in the bowl are all from one class and those in the other from one class and those in the other two classes are on either side, more two classes are on either side, more information is given.information is given.

Use this approach with DT Induction !Use this approach with DT Induction !


Information/EntropyInformation/Entropy Given probabilitites pGiven probabilitites p11, p, p22, .., p, .., pss whose sum is whose sum is

1, 1, EntropyEntropy is defined as:is defined as:

Entropy measures the amount of randomness Entropy measures the amount of randomness or surprise or uncertainty.or surprise or uncertainty.

Goal in classificationGoal in classification– no surpriseno surprise– entropy = 0entropy = 0


EntropyEntropy

log (1/p) H(p,1-p)


ID3ID3 Creates tree using information theory Creates tree using information theory

concepts and tries to reduce expected concepts and tries to reduce expected number of comparison..number of comparison..

ID3 chooses split attribute with the highest ID3 chooses split attribute with the highest information gain:information gain:


ID3 Example (Output1)ID3 Example (Output1) Starting state entropy:Starting state entropy:4/15 log(15/4) + 8/15 log(15/8) + 3/15 log(15/3) = 0.43844/15 log(15/4) + 8/15 log(15/8) + 3/15 log(15/3) = 0.4384 Gain using gender:Gain using gender:

– Female: 3/9 log(9/3)+6/9 log(9/6)=0.2764Female: 3/9 log(9/3)+6/9 log(9/6)=0.2764– Male: 1/6 (log 6/1) + 2/6 log(6/2) + 3/6 log(6/3) = Male: 1/6 (log 6/1) + 2/6 log(6/2) + 3/6 log(6/3) =

0.43920.4392– Weighted sum: (9/15)(0.2764) + (6/15)(0.4392) = Weighted sum: (9/15)(0.2764) + (6/15)(0.4392) =

0.341520.34152– Gain: 0.4384 – 0.34152 = 0.09688Gain: 0.4384 – 0.34152 = 0.09688

Gain using height:Gain using height:0.4384 – (2/15)(0.301) = 0.39830.4384 – (2/15)(0.301) = 0.3983

Choose height as first splitting attributeChoose height as first splitting attribute


C4.5C4.5 ID3 ID3 favors attributes with large number of favors attributes with large number of

divisionsdivisions Improved version of ID3:Improved version of ID3:

– Missing DataMissing Data– Continuous DataContinuous Data– PruningPruning– RulesRules– GainRatio:GainRatio:


CARTCART

Create Binary TreeCreate Binary Tree Uses entropyUses entropy Formula to choose split point, s, for node t:Formula to choose split point, s, for node t:

PPLL,P,PRR probability that a tuple in the training set probability that a tuple in the training set will be on the left or right side of the tree.will be on the left or right side of the tree.


CART ExampleCART Example At the start, there are six choices for At the start, there are six choices for

split point split point (right branch on equality):(right branch on equality):– P(Gender)=P(Gender)=2(6/15)(9/15)(2/15 + 4/15 + 3/15)=0.2242(6/15)(9/15)(2/15 + 4/15 + 3/15)=0.224– P(1.6) = 0P(1.6) = 0– P(1.7) = P(1.7) = 2(2/15)(13/15)(0 + 8/15 + 3/15) = 0.1692(2/15)(13/15)(0 + 8/15 + 3/15) = 0.169– P(1.8) = P(1.8) = 2(5/15)(10/15)(4/15 + 6/15 + 3/15) = 0.3852(5/15)(10/15)(4/15 + 6/15 + 3/15) = 0.385– P(1.9) = P(1.9) = 2(9/15)(6/15)(4/15 + 2/15 + 3/15) = 0.2562(9/15)(6/15)(4/15 + 2/15 + 3/15) = 0.256– P(2.0) = P(2.0) = 2(12/15)(3/15)(4/15 + 8/15 + 3/15) = 0.322(12/15)(3/15)(4/15 + 8/15 + 3/15) = 0.32

Split at 1.8Split at 1.8


Classification Using Neural Classification Using Neural NetworksNetworks

Typical NN structure for classification:Typical NN structure for classification:– One output node per classOne output node per class– Output value is class membership function valueOutput value is class membership function value

Supervised learning Supervised learning For each tuple in training set, propagate it For each tuple in training set, propagate it

through NN. Adjust weights on edges to through NN. Adjust weights on edges to improve future classification. improve future classification.

Algorithms: Propagation, Backpropagation, Algorithms: Propagation, Backpropagation, Gradient DescentGradient Descent


NN Issues NN Issues Number of source nodesNumber of source nodes Number of hidden layersNumber of hidden layers Training dataTraining data Number of sinksNumber of sinks InterconnectionsInterconnections WeightsWeights Activation FunctionsActivation Functions Learning TechniqueLearning Technique When to stop learningWhen to stop learning


Decision Tree vs. Neural Decision Tree vs. Neural NetworkNetwork


PropagationPropagation

Tuple Input

Output


NN Propagation AlgorithmNN Propagation Algorithm


Example PropagationExample Propagation

© Prentie Hall


NN LearningNN Learning

Adjust weights to perform better with the Adjust weights to perform better with the associated test data.associated test data.

Supervised:Supervised: Use feedback from Use feedback from knowledge of correct classification.knowledge of correct classification.

Unsupervised:Unsupervised: No knowledge of No knowledge of correct classification needed.correct classification needed.


NN Supervised LearningNN Supervised Learning


Supervised LearningSupervised Learning Possible error values assuming output from Possible error values assuming output from

node i is ynode i is yii but should be d but should be dii::

Change weights on arcs based on estimated Change weights on arcs based on estimated errorerror


NN BackpropagationNN Backpropagation

Propagate changes to weights Propagate changes to weights backward from output layer to input backward from output layer to input layer.layer.

Delta Rule:Delta Rule: w wijij= c x= c xijij (d (dj j – y– yjj)) Gradient Descent:Gradient Descent: technique to modify technique to modify

the weights in the graph.the weights in the graph.


BackpropagationBackpropagation

Error


Backpropagation AlgorithmBackpropagation Algorithm


Gradient DescentGradient Descent


Gradient Descent AlgorithmGradient Descent Algorithm


Output Layer LearningOutput Layer Learning


Hidden Layer LearningHidden Layer Learning


Types of NNsTypes of NNs

Different NN structures used for Different NN structures used for different problems.different problems.

PerceptronPerceptron Self Organizing Feature MapSelf Organizing Feature Map Radial Basis Function NetworkRadial Basis Function Network


PerceptronPerceptron

Perceptron is one of the simplest NNs.Perceptron is one of the simplest NNs. No hidden layers.No hidden layers.


Perceptron ExamplePerceptron Example

Suppose:Suppose:– Summation: S=3xSummation: S=3x11+2x+2x22-6-6– Activation: if S>0 then 1 else 0Activation: if S>0 then 1 else 0


Self Organizing Feature Map Self Organizing Feature Map (SOFM)(SOFM)

Competitive Unsupervised LearningCompetitive Unsupervised Learning Observe how neurons work in brain:Observe how neurons work in brain:

– Firing impacts firing of those nearFiring impacts firing of those near– Neurons far apart inhibit each otherNeurons far apart inhibit each other– Neurons have specific nonoverlapping Neurons have specific nonoverlapping

taskstasks Ex: Kohonen NetworkEx: Kohonen Network


Kohonen NetworkKohonen Network


Kohonen NetworkKohonen Network

Competitive Layer – viewed as 2D gridCompetitive Layer – viewed as 2D grid Similarity between competitive nodes and Similarity between competitive nodes and

input nodes:input nodes:– Input: X = <xInput: X = <x11, …, x, …, xhh>>

– Weights: <wWeights: <w1i1i, … , w, … , whihi>>– Similarity defined based on dot productSimilarity defined based on dot product

Competitive node most similar to input “wins”Competitive node most similar to input “wins” Winning node weights (as well as Winning node weights (as well as

surrounding node weights) increased.surrounding node weights) increased.


Radial Basis Function NetworkRadial Basis Function Network

RBF function has Gaussian shapeRBF function has Gaussian shape RBF NetworksRBF Networks

– Three LayersThree Layers– Hidden layer – Gaussian activation Hidden layer – Gaussian activation

functionfunction– Output layer – Linear activation functionOutput layer – Linear activation function


Radial Basis Function NetworkRadial Basis Function Network


Classification Using RulesClassification Using Rules Perform classification using If-Then Perform classification using If-Then

rulesrules Classification Rule:Classification Rule: r = <a,c> r = <a,c>

Antecedent, ConsequentAntecedent, Consequent May generate from from other May generate from from other

techniques (DT, NN) or generate techniques (DT, NN) or generate directly.directly.

Algorithms: Gen, RX, 1R, PRISMAlgorithms: Gen, RX, 1R, PRISM


Generating Rules from DTsGenerating Rules from DTs


Generating Rules ExampleGenerating Rules Example


Generating Rules from NNsGenerating Rules from NNs


1R Algorithm1R Algorithm


1R Example1R Example


PRISM AlgorithmPRISM Algorithm


PRISM ExamplePRISM Example


Decision Tree vs. Rules Decision Tree vs. Rules

Tree has implied Tree has implied order in which order in which splitting is splitting is performed.performed.

Tree created based Tree created based on looking at all on looking at all classes.classes.

Rules have no Rules have no ordering of ordering of predicates.predicates.

Only need to look at Only need to look at one class to one class to generate its rules.generate its rules.


Clustering OutlineClustering Outline

Clustering Problem OverviewClustering Problem Overview Clustering TechniquesClustering Techniques

– Hierarchical AlgorithmsHierarchical Algorithms– Partitional AlgorithmsPartitional Algorithms– Genetic AlgorithmGenetic Algorithm– Clustering Large DatabasesClustering Large Databases

Goal:Goal: Provide an overview of the clustering Provide an overview of the clustering problem and introduce some of the basic problem and introduce some of the basic algorithmsalgorithms


Clustering ExamplesClustering Examples

SegmentSegment customer database based on customer database based on similar buying patterns.similar buying patterns.

Group houses in a town into Group houses in a town into neighborhoods based on similar neighborhoods based on similar features.features.

Identify new plant speciesIdentify new plant species Identify similar Web usage patternsIdentify similar Web usage patterns


Clustering ExampleClustering Example


Clustering HousesClustering Houses

Size BasedGeographic Distance Based


Clustering vs. ClassificationClustering vs. Classification

No prior knowledgeNo prior knowledge– Number of clustersNumber of clusters– Meaning of clustersMeaning of clusters

Unsupervised learningUnsupervised learning


Clustering IssuesClustering Issues

Outlier handlingOutlier handling Dynamic dataDynamic data Interpreting resultsInterpreting results Evaluating resultsEvaluating results Number of clustersNumber of clusters Data to be usedData to be used ScalabilityScalability


Impact of Outliers on Impact of Outliers on ClusteringClustering


Clustering ProblemClustering Problem

Given a database D={tGiven a database D={t11,t,t22,…,t,…,tnn} of tuples } of tuples and an integer value k, the and an integer value k, the Clustering Clustering ProblemProblem is to define a mapping is to define a mapping f:Df:D{1,..,k} where each t{1,..,k} where each t ii is assigned to is assigned to one cluster Kone cluster Kjj, 1<=j<=k., 1<=j<=k.

A A ClusterCluster, K, Kjj, contains precisely those , contains precisely those tuples mapped to it.tuples mapped to it.

Unlike classification problem, clusters Unlike classification problem, clusters are not known a priori.are not known a priori.


Types of Clustering Types of Clustering HierarchicalHierarchical – Nested set of clusters – Nested set of clusters

created.created. Partitional Partitional – One set of clusters – One set of clusters

created.created. Incremental Incremental – Each element handled – Each element handled

one at a time.one at a time. SimultaneousSimultaneous – All elements handled – All elements handled

together.together. Overlapping/Non-overlappingOverlapping/Non-overlapping


Clustering ApproachesClustering Approaches

Clustering

Hierarchical Partitional Categorical Large DB

Agglomerative Divisive Sampling Compression


Cluster ParametersCluster Parameters


Distance Between ClustersDistance Between Clusters Single LinkSingle Link: smallest distance between points: smallest distance between points Complete Link:Complete Link: largest distance between points largest distance between points Average Link:Average Link: average distance between pointsaverage distance between points Centroid:Centroid: distance between centroidsdistance between centroids


Hierarchical ClusteringHierarchical Clustering Clusters are created in levels actually Clusters are created in levels actually

creating sets of clusters at each level.creating sets of clusters at each level. AgglomerativeAgglomerative

– Initially each item in its own clusterInitially each item in its own cluster– Iteratively clusters are merged togetherIteratively clusters are merged together– Bottom UpBottom Up

DivisiveDivisive– Initially all items in one clusterInitially all items in one cluster– Large clusters are successively dividedLarge clusters are successively divided– Top DownTop Down


Hierarchical AlgorithmsHierarchical Algorithms

Single LinkSingle Link MST Single LinkMST Single Link Complete LinkComplete Link Average LinkAverage Link


DendrogramDendrogram Dendrogram:Dendrogram: a tree data a tree data

structure which illustrates structure which illustrates hierarchical clustering hierarchical clustering techniques.techniques.

Each level shows clusters Each level shows clusters for that level.for that level.– Leaf – individual clustersLeaf – individual clusters– Root – one clusterRoot – one cluster

A cluster at level i is the A cluster at level i is the union of its children clusters union of its children clusters at level i+1.at level i+1.


Levels of ClusteringLevels of Clustering


Agglomerative ExampleAgglomerative ExampleAA BB CC DD EE

AA 00 11 22 22 33

BB 11 00 22 44 33

CC 22 22 00 11 55

DD 22 44 11 00 33

EE 33 33 55 33 00

BA

E C

D

4

Threshold of

2 3 51

A B C D E


MST ExampleMST Example

AA BB CC DD EE

AA 00 11 22 22 33

BB 11 00 22 44 33

CC 22 22 00 11 55

DD 22 44 11 00 33

EE 33 33 55 33 00

BA

E C

D


Agglomerative AlgorithmAgglomerative Algorithm


Single LinkSingle Link View all items with links (distances) View all items with links (distances)

between them.between them. Finds maximal connected components Finds maximal connected components

in this graph.in this graph. Two clusters are merged if there is at Two clusters are merged if there is at

least one edge which connects them.least one edge which connects them. Uses threshold distances at each level.Uses threshold distances at each level. Could be agglomerative or divisive.Could be agglomerative or divisive.


MST Single Link AlgorithmMST Single Link Algorithm


Single Link ClusteringSingle Link Clustering


Partitional ClusteringPartitional Clustering

NonhierarchicalNonhierarchical Creates clusters in one step as Creates clusters in one step as

opposed to several steps.opposed to several steps. Since only one set of clusters is output, Since only one set of clusters is output,

the user normally has to input the the user normally has to input the desired number of clusters, k.desired number of clusters, k.

Usually deals with static sets.Usually deals with static sets.


Partitional AlgorithmsPartitional Algorithms

MSTMST Squared ErrorSquared Error K-MeansK-Means Nearest NeighborNearest Neighbor PAMPAM BEABEA GAGA


MST AlgorithmMST Algorithm


Squared ErrorSquared Error

Minimized squared errorMinimized squared error


Squared Error AlgorithmSquared Error Algorithm


K-MeansK-Means Initial set of clusters randomly chosen.Initial set of clusters randomly chosen. Iteratively, items are moved among sets Iteratively, items are moved among sets

of clusters until the desired set is of clusters until the desired set is reached.reached.

High degree of similarity among High degree of similarity among elements in a cluster is obtained.elements in a cluster is obtained.

Given a cluster KGiven a cluster Kii={t={ti1i1,t,ti2i2,…,t,…,timim}, the }, the cluster meancluster mean is m is mii = (1/m)(t = (1/m)(ti1i1 + … + t + … + timim))


K-Means ExampleK-Means Example Given: {2,4,10,12,3,20,30,11,25}, k=2Given: {2,4,10,12,3,20,30,11,25}, k=2 Randomly assign means: mRandomly assign means: m11=3,m=3,m22=4=4 KK11={2,3}, K={2,3}, K22={4,10,12,20,30,11,25}, ={4,10,12,20,30,11,25},

mm11=2.5,m=2.5,m22=16=16 KK11={2,3,4},K={2,3,4},K22={10,12,20,30,11,25}, m={10,12,20,30,11,25}, m11=3,m=3,m22=18=18 KK11={2,3,4,10},K={2,3,4,10},K22={12,20,30,11,25}, ={12,20,30,11,25},

mm11=4.75,m=4.75,m22=19.6=19.6 KK11={2,3,4,10,11,12},K={2,3,4,10,11,12},K22={20,30,25}, m={20,30,25}, m11=7,m=7,m22=25=25 Stop as the clusters with these means are the Stop as the clusters with these means are the

same.same.


K-Means AlgorithmK-Means Algorithm


Nearest NeighborNearest Neighbor

Items are iteratively merged into the Items are iteratively merged into the existing clusters that are closest.existing clusters that are closest.

IncrementalIncremental Threshold, t, used to determine if items Threshold, t, used to determine if items

are added to existing clusters or a new are added to existing clusters or a new cluster is created.cluster is created.


Nearest Neighbor AlgorithmNearest Neighbor Algorithm


PAMPAM Partitioning Around Medoids (PAM) Partitioning Around Medoids (PAM)

(K-Medoids)(K-Medoids) Handles outliers well.Handles outliers well. Ordering of input does not impact results.Ordering of input does not impact results. Does not scale well.Does not scale well. Each cluster represented by one item, Each cluster represented by one item,

called the called the medoid.medoid. Initial set of k medoids randomly chosen.Initial set of k medoids randomly chosen.


PAMPAM


PAM Cost CalculationPAM Cost Calculation At each step in algorithm, medoids are changed At each step in algorithm, medoids are changed

if the overall cost is improved.if the overall cost is improved. CCjihjih – cost change for an item t – cost change for an item tjj associated with associated with

swapping medoid tswapping medoid tii with non-medoid t with non-medoid thh..


PAM AlgorithmPAM Algorithm


BEABEA Bond Energy AlgorithmBond Energy Algorithm Database design (physical and logical)Database design (physical and logical) Vertical fragmentationVertical fragmentation Determine affinity (bond) between attributes Determine affinity (bond) between attributes

based on common usage.based on common usage. Algorithm outline:Algorithm outline:

1.1. Create affinity matrixCreate affinity matrix2.2. Convert to BOND matrix Convert to BOND matrix 3.3. Create regions of close bondingCreate regions of close bonding


BEABEA

Modified from [OV99]


Genetic Algorithm ExampleGenetic Algorithm Example

{{A,B,C,D,E,F,G,H}A,B,C,D,E,F,G,H} Randomly choose initial solution:Randomly choose initial solution:

{A,C,E} {B,F} {D,G,H} or{A,C,E} {B,F} {D,G,H} or10101000, 01000100, 0001001110101000, 01000100, 00010011

Suppose crossover at point four and Suppose crossover at point four and choose 1choose 1stst and 3 and 3rdrd individuals: individuals:10100011, 01000100, 0001100010100011, 01000100, 00011000

What should termination criteria be?What should termination criteria be?


GA AlgorithmGA Algorithm


Clustering Large DatabasesClustering Large Databases Most clustering algorithms assume a large Most clustering algorithms assume a large

data structure which is memory resident.data structure which is memory resident. Clustering may be performed first on a Clustering may be performed first on a

sample of the database then applied to the sample of the database then applied to the entire database.entire database.

AlgorithmsAlgorithms– BIRCHBIRCH– DBSCANDBSCAN– CURECURE


Desired Features for Large Desired Features for Large DatabasesDatabases

One scan (or less) of DBOne scan (or less) of DB OnlineOnline Suspendable, stoppable, resumableSuspendable, stoppable, resumable IncrementalIncremental Work with limited main memoryWork with limited main memory Different techniques to scan (e.g. Different techniques to scan (e.g.

sampling)sampling) Process each tuple onceProcess each tuple once


BIRCHBIRCH Balanced Iterative Reducing and Balanced Iterative Reducing and

Clustering using HierarchiesClustering using Hierarchies Incremental, hierarchical, one scanIncremental, hierarchical, one scan Save clustering information in a tree Save clustering information in a tree Each entry in the tree contains Each entry in the tree contains

information about one clusterinformation about one cluster New nodes inserted in closest entry in New nodes inserted in closest entry in

treetree


Clustering FeatureClustering Feature CT Triple: (N,LS,SS)CT Triple: (N,LS,SS)

– N: Number of points in clusterN: Number of points in cluster– LS: Sum of points in the clusterLS: Sum of points in the cluster– SS: Sum of squares of points in the clusterSS: Sum of squares of points in the cluster

CF TreeCF Tree– Balanced search treeBalanced search tree– Node has CF triple for each childNode has CF triple for each child– Leaf node represents cluster and has CF value Leaf node represents cluster and has CF value

for each subcluster in it.for each subcluster in it.– Subcluster has maximum diameterSubcluster has maximum diameter


BIRCH AlgorithmBIRCH Algorithm


Improve ClustersImprove Clusters


DBSCANDBSCAN Density Based Spatial Clustering of Density Based Spatial Clustering of

Applications with NoiseApplications with Noise Outliers will not effect creation of cluster.Outliers will not effect creation of cluster. InputInput

– MinPts MinPts – minimum number of points in – minimum number of points in clustercluster

– EpsEps – for each point in cluster there must – for each point in cluster there must be another point in it less than this distance be another point in it less than this distance away.away.


DBSCAN Density ConceptsDBSCAN Density Concepts Eps-neighborhood:Eps-neighborhood: Points within Eps distance Points within Eps distance

of a point.of a point. Core point:Core point: Eps-neighborhood dense enough Eps-neighborhood dense enough

(MinPts)(MinPts) Directly density-reachable:Directly density-reachable: A point p is directly A point p is directly

density-reachable from a point q if the distance density-reachable from a point q if the distance is small (Eps) and q is a core point.is small (Eps) and q is a core point.

Density-reachable:Density-reachable: A point si density- A point si density-reachable form another point if there is a path reachable form another point if there is a path from one to the other consisting of only core from one to the other consisting of only core points.points.


Density ConceptsDensity Concepts


DBSCAN AlgorithmDBSCAN Algorithm


CURECURE

Clustering Using RepresentativesClustering Using Representatives Use many points to represent a cluster Use many points to represent a cluster

instead of only oneinstead of only one Points will be well scatteredPoints will be well scattered


CURE ApproachCURE Approach


CURE AlgorithmCURE Algorithm


CURE for Large DatabasesCURE for Large Databases


Comparison of Clustering Comparison of Clustering TechniquesTechniques


Association Rules OutlineAssociation Rules OutlineGoal: Provide an overview of basic Association Provide an overview of basic Association

Rule mining techniquesRule mining techniques Association Rules Problem OverviewAssociation Rules Problem Overview

– Large itemsetsLarge itemsets Association Rules AlgorithmsAssociation Rules Algorithms

– AprioriApriori– SamplingSampling– PartitioningPartitioning– Parallel AlgorithmsParallel Algorithms

Comparing TechniquesComparing Techniques Incremental AlgorithmsIncremental Algorithms Advanced AR TechniquesAdvanced AR Techniques


Example: Market Basket DataExample: Market Basket Data Items frequently purchased together:Items frequently purchased together:

Bread Bread PeanutButterPeanutButter Uses:Uses:

– Placement Placement – AdvertisingAdvertising– SalesSales– CouponsCoupons

Objective: increase sales and reduce Objective: increase sales and reduce costscosts


Association Rule DefinitionsAssociation Rule Definitions

Set of items:Set of items: I={I I={I11,I,I22,…,I,…,Imm}} Transactions:Transactions: D={t D={t11,t,t22, …, t, …, tnn}, t}, tjj I I Itemset:Itemset: {I {Ii1i1,I,Ii2i2, …, I, …, Iikik} } I I Support of an itemset:Support of an itemset: Percentage of Percentage of

transactions which contain that itemset.transactions which contain that itemset. Large (Frequent) itemset:Large (Frequent) itemset: Itemset Itemset

whose number of occurrences is above a whose number of occurrences is above a threshold.threshold.


Association Rules ExampleAssociation Rules Example

I = { Beer, Bread, Jelly, Milk, PeanutButter}Support of {Bread,PeanutButter} is 60%


Association Rule DefinitionsAssociation Rule Definitions

Association Rule (AR): Association Rule (AR): implication X implication X Y where X,Y Y where X,Y I and X I and X Y = Y = ;;

Support of AR (s) X Support of AR (s) X YY: : Percentage of transactions that Percentage of transactions that contain X contain X YY

Confidence of AR (Confidence of AR () X ) X Y: Y: Ratio of Ratio of number of transactions that contain X number of transactions that contain X Y to the number that contain X Y to the number that contain X


Association Rules Ex (cont’d)Association Rules Ex (cont’d)


Association Rule ProblemAssociation Rule Problem Given a set of items I={IGiven a set of items I={I11,I,I22,…,I,…,Imm} and a } and a

database of transactions D={tdatabase of transactions D={t11,t,t22, …, t, …, tnn} } where twhere tii={I={Ii1i1,I,Ii2i2, …, I, …, Iikik} and I} and Iijij I, the I, the Association Rule ProblemAssociation Rule Problem is to is to identify all association rulesidentify all association rules X X Y Y with with a minimum support and confidence.a minimum support and confidence.

Link AnalysisLink Analysis NOTE:NOTE: Support of Support of X X Y Y is same as is same as

support of X support of X Y. Y.


Association Rule TechniquesAssociation Rule Techniques

1.1. Find Large Itemsets.Find Large Itemsets.2.2. Generate rules from frequent itemsets.Generate rules from frequent itemsets.


Algorithm to Generate ARsAlgorithm to Generate ARs


AprioriApriori

Large Itemset Property:Large Itemset Property:Any subset of a large itemset is large.Any subset of a large itemset is large. Contrapositive:Contrapositive:

If an itemset is not large, If an itemset is not large, none of its supersets are large.none of its supersets are large.


Large Itemset PropertyLarge Itemset Property


Apriori Ex (cont’d)Apriori Ex (cont’d)

s=30% = 50%


Apriori AlgorithmApriori Algorithm

1.1. CC11 = Itemsets of size one in I; = Itemsets of size one in I;

2.2. Determine all large itemsets of size 1, LDetermine all large itemsets of size 1, L1;1;

3. i = 1;4.4. RepeatRepeat5.5. i = i + 1;i = i + 1;6.6. CCi i = Apriori-Gen(L= Apriori-Gen(Li-1i-1););

7.7. Count CCount Cii to determine L to determine Li;i;

8.8. until no more large itemsets found;until no more large itemsets found;


Apriori-GenApriori-Gen

Generate candidates of size i+1 from Generate candidates of size i+1 from large itemsets of size i.large itemsets of size i.

Approach used: join large itemsets of Approach used: join large itemsets of size i if they agree on i-1 size i if they agree on i-1

May also prune candidates who have May also prune candidates who have subsets that are not large.subsets that are not large.


Apriori-Gen ExampleApriori-Gen Example


Apriori-Gen Example (cont’d)Apriori-Gen Example (cont’d)


Apriori Adv/DisadvApriori Adv/Disadv

Advantages:Advantages:– Uses large itemset property.Uses large itemset property.– Easily parallelizedEasily parallelized– Easy to implement.Easy to implement.

Disadvantages:Disadvantages:– Assumes transaction database is memory Assumes transaction database is memory

resident.resident.– Requires up to m database scans.Requires up to m database scans.


SamplingSampling Large databasesLarge databases Sample the database and apply Apriori to the Sample the database and apply Apriori to the

sample. sample. Potentially Large Itemsets (PL):Potentially Large Itemsets (PL): Large Large

itemsets from sampleitemsets from sample Negative Border (BD Negative Border (BD -- ): ):

– Generalization of Apriori-Gen applied to Generalization of Apriori-Gen applied to itemsets of varying sizes.itemsets of varying sizes.

– Minimal set of itemsets which are not in PL, Minimal set of itemsets which are not in PL, butbut whose subsets are all in PL. whose subsets are all in PL.


Negative Border ExampleNegative Border Example

PL PL BD-(PL)


Sampling AlgorithmSampling Algorithm

1.1. DDss = sample of Database D; = sample of Database D;2.2. PL = Large itemsets in DPL = Large itemsets in Dss using smalls; using smalls;3.3. C = PL C = PL BDBD--(PL);(PL);4.4. Count C in Database using s;Count C in Database using s;5.5. ML = large itemsets in BDML = large itemsets in BD--(PL);(PL);6.6. If ML = If ML = then donethen done7.7. else C = repeated application of BDelse C = repeated application of BD-;-;

8.8. Count C in Database;Count C in Database;


Sampling ExampleSampling Example Find AR assuming s = 20%Find AR assuming s = 20% DDss = { t = { t11,t,t22}} Smalls = 10%Smalls = 10% PL = {{Bread}, {Jelly}, {PeanutButter}, PL = {{Bread}, {Jelly}, {PeanutButter},

{Bread,Jelly}, {Bread,PeanutButter}, {Jelly, {Bread,Jelly}, {Bread,PeanutButter}, {Jelly, PeanutButter}, {Bread,Jelly,PeanutButter}}PeanutButter}, {Bread,Jelly,PeanutButter}}

BDBD--(PL)={{Beer},{Milk}}(PL)={{Beer},{Milk}} ML = {{Beer}, {Milk}} ML = {{Beer}, {Milk}} Repeated application of BDRepeated application of BD- - generates all generates all

remaining itemsetsremaining itemsets


Sampling Adv/DisadvSampling Adv/Disadv

Advantages:Advantages:– Reduces number of database scans to one Reduces number of database scans to one

in the best case and two in worst.in the best case and two in worst.– Scales better.Scales better.

Disadvantages:Disadvantages:– Potentially large number of candidates in Potentially large number of candidates in

second passsecond pass


PartitioningPartitioning

Divide database into partitions DDivide database into partitions D11,D,D22,,…,D…,Dpp

Apply Apriori to each partitionApply Apriori to each partition Any large itemset must be large in at Any large itemset must be large in at

least one partition.least one partition.


Partitioning AlgorithmPartitioning Algorithm

1.1. Divide D into partitions DDivide D into partitions D11,D,D22,…,D,…,Dp;p;

2. For I = 1 to p do3.3. LLii = Apriori(D = Apriori(Dii););4.4. C = LC = L11 … … L Lpp;;5.5. Count C on D to generate L;Count C on D to generate L;


Partitioning ExamplePartitioning Example

D1

D2

S=10%

L1 ={{Bread}, {Jelly}, {Bread}, {Jelly}, {PeanutButter}, {PeanutButter}, {Bread,Jelly}, {Bread,Jelly}, {Bread,PeanutButter}, {Bread,PeanutButter}, {Jelly, PeanutButter}, {Jelly, PeanutButter}, {Bread,Jelly,PeanutButter}}{Bread,Jelly,PeanutButter}}

L2 ={{Bread}, {Milk}, {Bread}, {Milk}, {PeanutButter}, {Bread,Milk}, {PeanutButter}, {Bread,Milk}, {Bread,PeanutButter}, {Milk, {Bread,PeanutButter}, {Milk, PeanutButter}, PeanutButter}, {Bread,Milk,PeanutButter}, {Bread,Milk,PeanutButter}, {Beer}, {Beer,Bread}, {Beer}, {Beer,Bread}, {Beer,Milk}}{Beer,Milk}}


Partitioning Adv/DisadvPartitioning Adv/Disadv

Advantages:Advantages:– Adapts to available main memoryAdapts to available main memory– Easily parallelizedEasily parallelized– Maximum number of database scans is Maximum number of database scans is

two.two. Disadvantages:Disadvantages:

– May have many candidates during second May have many candidates during second scan.scan.


Parallelizing AR AlgorithmsParallelizing AR Algorithms Based on AprioriBased on Apriori Techniques differ:Techniques differ:

– What is counted at each siteWhat is counted at each site– How data (transactions) are distributedHow data (transactions) are distributed

Data ParallelismData Parallelism– Data partitionedData partitioned– Count Distribution AlgorithmCount Distribution Algorithm

Task ParallelismTask Parallelism– Data and candidates partitionedData and candidates partitioned– Data Distribution AlgorithmData Distribution Algorithm


Count Distribution Algorithm(CDA)Count Distribution Algorithm(CDA)1.1. Place data partition at each site.Place data partition at each site.2.2. In Parallel at each site doIn Parallel at each site do3.3. CC11 = Itemsets of size one in I; = Itemsets of size one in I;4.4. Count CCount C1;1;

5.5. Broadcast counts to all sites;Broadcast counts to all sites;6.6. Determine global large itemsets of size 1, LDetermine global large itemsets of size 1, L11;;7. i = 1; 8.8. RepeatRepeat9.9. i = i + 1;i = i + 1;10.10. CCi i = Apriori-Gen(L= Apriori-Gen(L i-1i-1););11.11. Count CCount Ci;i;

12.12. Broadcast counts to all sites;Broadcast counts to all sites;13.13. Determine global large itemsets of size i, LDetermine global large itemsets of size i, L ii;;14.14. until no more large itemsets found;until no more large itemsets found;


CDA ExampleCDA Example


Data Distribution Algorithm(DDA)Data Distribution Algorithm(DDA)1.1. Place data partition at each site.Place data partition at each site.2.2. In Parallel at each site doIn Parallel at each site do3.3. Determine local candidates of size 1 to count;Determine local candidates of size 1 to count;4.4. Broadcast local transactions to other sites;Broadcast local transactions to other sites;5.5. Count local candidates of size 1 on all data;Count local candidates of size 1 on all data;6.6. Determine large itemsets of size 1 for local Determine large itemsets of size 1 for local

candidates; candidates; 7.7. Broadcast large itemsets to all sites;Broadcast large itemsets to all sites;8.8. Determine LDetermine L11;;9. i = 1; 10.10. RepeatRepeat11.11. i = i + 1;i = i + 1;12.12. CCi i = Apriori-Gen(L= Apriori-Gen(Li-1i-1););13.13. Determine local candidates of size i to count;Determine local candidates of size i to count;14.14. Count, broadcast, and find LCount, broadcast, and find L ii;;15.15. until no more large itemsets found;until no more large itemsets found;


DDA ExampleDDA Example


Comparing AR TechniquesComparing AR Techniques TargetTarget TypeType Data TypeData Type Data SourceData Source TechniqueTechnique Itemset Strategy and Data StructureItemset Strategy and Data Structure Transaction Strategy and Data StructureTransaction Strategy and Data Structure OptimizationOptimization ArchitectureArchitecture Parallelism StrategyParallelism Strategy


Comparison of AR TechniquesComparison of AR Techniques


Hash TreeHash Tree


Incremental Association RulesIncremental Association Rules Generate ARs in a dynamic database.Generate ARs in a dynamic database. Problem: algorithms assume static Problem: algorithms assume static

databasedatabase Objective: Objective:

– Know large itemsets for DKnow large itemsets for D– Find large itemsets for D Find large itemsets for D { { D} D}

Must be large in either D or Must be large in either D or D D Save LSave Li i and counts and counts


Note on ARsNote on ARs Many applications outside market basket Many applications outside market basket

data analysisdata analysis– Prediction (telecom switch failure)Prediction (telecom switch failure)– Web usage miningWeb usage mining

Many different types of association rulesMany different types of association rules– TemporalTemporal– SpatialSpatial– CausalCausal


Advanced AR TechniquesAdvanced AR Techniques

Generalized Association RulesGeneralized Association Rules Multiple-Level Association RulesMultiple-Level Association Rules Quantitative Association RulesQuantitative Association Rules Using multiple minimum supportsUsing multiple minimum supports Correlation RulesCorrelation Rules


Measuring Quality of RulesMeasuring Quality of Rules

SupportSupport ConfidenceConfidence InterestInterest ConvictionConviction Chi Squared TestChi Squared Test



Part III Part III





Web Mining OutlineWeb Mining Outline

Goal:Goal: Examine the use of data mining on Examine the use of data mining on the World Wide Webthe World Wide Web

IntroductionIntroduction Web Content MiningWeb Content Mining Web Structure MiningWeb Structure Mining Web Usage MiningWeb Usage Mining


Web Mining IssuesWeb Mining Issues

SizeSize– >350 million pages (1999) >350 million pages (1999) – Grows at about 1 million pages a dayGrows at about 1 million pages a day– Google indexes 3 billion documentsGoogle indexes 3 billion documents

Diverse types of dataDiverse types of data


Web DataWeb Data

Web pagesWeb pages Intra-page structuresIntra-page structures Inter-page structuresInter-page structures Usage dataUsage data Supplemental dataSupplemental data

– ProfilesProfiles– Registration informationRegistration information– CookiesCookies


Web Mining TaxonomyWeb Mining Taxonomy

Modified from [zai01]


Web Content MiningWeb Content Mining Extends work of basic search enginesExtends work of basic search engines Search EnginesSearch Engines

– IR applicationIR application– Keyword basedKeyword based– Similarity between query and documentSimilarity between query and document– CrawlersCrawlers– IndexingIndexing– ProfilesProfiles– Link analysisLink analysis


CrawlersCrawlers Robot (spider)Robot (spider) traverses the hypertext sructure in the traverses the hypertext sructure in the

Web.Web. Collect information from visited pagesCollect information from visited pages Used to construct indexes for search enginesUsed to construct indexes for search engines Traditional CrawlerTraditional Crawler – visits entire Web (?) and – visits entire Web (?) and

replaces indexreplaces index Periodic CrawlerPeriodic Crawler – visits portions of the Web and – visits portions of the Web and

updates subset of indexupdates subset of index Incremental CrawlerIncremental Crawler – selectively searches the Web – selectively searches the Web

and incrementally modifies indexand incrementally modifies index Focused CrawlerFocused Crawler – visits pages related to a particular – visits pages related to a particular

subjectsubject


Focused CrawlerFocused Crawler Only visit links from a page if that page Only visit links from a page if that page

is determined to be relevant.is determined to be relevant. Classifier is static after learning phase.Classifier is static after learning phase. Components:Components:

– Classifier which assigns relevance score to Classifier which assigns relevance score to each page based on crawl topic.each page based on crawl topic.

– Distiller to identify Distiller to identify hub pages.hub pages.– Crawler visits pages to based on crawler Crawler visits pages to based on crawler

and distiller scores.and distiller scores.


Focused CrawlerFocused Crawler

Classifier to related documents to topicsClassifier to related documents to topics Classifier also determines how useful Classifier also determines how useful

outgoing links areoutgoing links are Hub PagesHub Pages contain links to many contain links to many

relevant pages. Must be visited even if relevant pages. Must be visited even if not high relevance score.not high relevance score.


Focused CrawlerFocused Crawler


Context Focused CrawlerContext Focused Crawler Context Graph:Context Graph:

– Context graph created for each seed document .Context graph created for each seed document .– Root is the sedd document.Root is the sedd document.– Nodes at each level show documents with links Nodes at each level show documents with links

to documents at next higher level. to documents at next higher level. – Updated during crawl itself .Updated during crawl itself .

Approach:Approach:1.1. Construct context graph and classifiers using Construct context graph and classifiers using

seed documents as training data.seed documents as training data.2.2. Perform crawling using classifiers and context Perform crawling using classifiers and context

graph created.graph created.


Context GraphContext Graph


Virtual Web ViewVirtual Web View Multiple Layered DataBase (MLDB)Multiple Layered DataBase (MLDB) built on top of built on top of

the Web.the Web. Each layer of the database is more generalized (and Each layer of the database is more generalized (and

smaller) and centralized than the one beneath it.smaller) and centralized than the one beneath it. Upper layers of MLDB are structured and can be Upper layers of MLDB are structured and can be

accessed with SQL type queries.accessed with SQL type queries. Translation tools convert Web documents to XML.Translation tools convert Web documents to XML. Extraction tools extract desired information to place in Extraction tools extract desired information to place in

first layer of MLDB.first layer of MLDB. Higher levels contain more summarized data obtained Higher levels contain more summarized data obtained

through generalizations of the lower levels.through generalizations of the lower levels.


PersonalizationPersonalization Web access or contents tuned to better fit the Web access or contents tuned to better fit the

desires of each user.desires of each user. Manual techniques identify user’s preferences Manual techniques identify user’s preferences

based on profiles or demographics.based on profiles or demographics. Collaborative filteringCollaborative filtering identifies preferences identifies preferences

based on ratings from similar users.based on ratings from similar users. Content based filteringContent based filtering retrieves pages retrieves pages

based on similarity between pages and user based on similarity between pages and user profiles.profiles.


Web Structure MiningWeb Structure Mining

Mine structure (links, graph) of the WebMine structure (links, graph) of the Web TechniquesTechniques

– PageRankPageRank– CLEVERCLEVER

Create a model of the Web organization.Create a model of the Web organization. May be combined with content mining to May be combined with content mining to

more effectively retrieve important pages.more effectively retrieve important pages.


PageRankPageRank Used by GoogleUsed by Google Prioritize pages returned from search by Prioritize pages returned from search by

looking at Web structure.looking at Web structure. Importance of page is calculated based Importance of page is calculated based

on number of pages which point to it – on number of pages which point to it – BacklinksBacklinks..

Weighting is used to provide more Weighting is used to provide more importance to backlinks coming form importance to backlinks coming form important pages.important pages.


PageRank (cont’d)PageRank (cont’d)

PR(p) = c (PR(1)/NPR(p) = c (PR(1)/N11 + … + PR(n)/N + … + PR(n)/Nnn))– PR(i): PageRank for a page i which points PR(i): PageRank for a page i which points

to target page p.to target page p.– NNii: number of links coming out of page i: number of links coming out of page i


CLEVERCLEVER

Identify authoritative and hub pages.Identify authoritative and hub pages. Authoritative PagesAuthoritative Pages : :

– Highly important pages.Highly important pages.– Best source for requested information.Best source for requested information.

Hub PagesHub Pages : :– Contain links to highly important pages.Contain links to highly important pages.


HITSHITS Hyperlink-Induces Topic SearchHyperlink-Induces Topic Search Based on a set of keywords, find set of Based on a set of keywords, find set of

relevant pages – R.relevant pages – R. Identify hub and authority pages for these.Identify hub and authority pages for these.

– Expand R to a base set, B, of pages linked to or Expand R to a base set, B, of pages linked to or from R.from R.

– Calculate weights for authorities and hubs.Calculate weights for authorities and hubs. Pages with highest ranks in R are returned.Pages with highest ranks in R are returned.


HITS AlgorithmHITS Algorithm


Web Usage MiningWeb Usage Mining Extends work of basic search enginesExtends work of basic search engines Search EnginesSearch Engines

– IR applicationIR application– Keyword basedKeyword based– Similarity between query and documentSimilarity between query and document– CrawlersCrawlers– IndexingIndexing– ProfilesProfiles– Link analysisLink analysis


Web Usage Mining ApplicationsWeb Usage Mining Applications

PersonalizationPersonalization Improve structure of a site’s Web pagesImprove structure of a site’s Web pages Aid in caching and prediction of future Aid in caching and prediction of future

page referencespage references Improve design of individual pagesImprove design of individual pages Improve effectiveness of e-commerce Improve effectiveness of e-commerce

(sales and advertising)(sales and advertising)


Web Usage Mining ActivitiesWeb Usage Mining Activities Preprocessing Web logPreprocessing Web log

– Cleanse Cleanse – Remove extraneous informationRemove extraneous information– SessionizeSessionize

Session:Session: Sequence of pages referenced by one user at a sitting. Sequence of pages referenced by one user at a sitting. Pattern DiscoveryPattern Discovery

– Count patterns that occur in sessionsCount patterns that occur in sessions– Pattern Pattern is sequence of pages references in session.is sequence of pages references in session.– Similar to association rulesSimilar to association rules

» Transaction: sessionTransaction: session» Itemset: pattern (or subset)Itemset: pattern (or subset)» Order is importantOrder is important

Pattern AnalysisPattern Analysis


ARs in Web MiningARs in Web Mining Web Mining:Web Mining:

– ContentContent– StructureStructure– UsageUsage

Frequent patterns of sequential page references Frequent patterns of sequential page references in Web searching.in Web searching.

Uses:Uses:– CachingCaching– Clustering usersClustering users– Develop user profilesDevelop user profiles– Identify important pagesIdentify important pages


Web Usage Mining IssuesWeb Usage Mining Issues

Identification of exact user not possible.Identification of exact user not possible. Exact sequence of pages referenced by Exact sequence of pages referenced by

a user not possible due to caching.a user not possible due to caching. Session not well definedSession not well defined Security, privacy, and legal issuesSecurity, privacy, and legal issues


Web Log CleansingWeb Log Cleansing

Replace source IP address with unique Replace source IP address with unique but non-identifying ID.but non-identifying ID.

Replace exact URL of pages referenced Replace exact URL of pages referenced with unique but non-identifying ID.with unique but non-identifying ID.

Delete error records and records Delete error records and records containing not page data (such as containing not page data (such as figures and code)figures and code)


SessionizingSessionizing

Divide Web log into sessions.Divide Web log into sessions. Two common techniques:Two common techniques:

– Number of consecutive page references Number of consecutive page references from a source IP address occurring within from a source IP address occurring within a predefined time interval (e.g. 25 a predefined time interval (e.g. 25 minutes).minutes).

– All consecutive page references from a All consecutive page references from a source IP address where the interclick time source IP address where the interclick time is less than a predefined threshold.is less than a predefined threshold.


Data Structures Data Structures

Keep track of patterns identified during Keep track of patterns identified during Web usage mining processWeb usage mining process

Common techniques:Common techniques:– Trie Trie – Suffix TreeSuffix Tree– Generalized Suffix TreeGeneralized Suffix Tree– WAP TreeWAP Tree


Trie vs. Suffix TreeTrie vs. Suffix Tree

Trie:Trie:– Rooted treeRooted tree– Edges labeled which character (page) from Edges labeled which character (page) from

patternpattern– Path from root to leaf represents pattern.Path from root to leaf represents pattern.

Suffix Tree:Suffix Tree:– Single child collapsed with parent. Edge Single child collapsed with parent. Edge

contains labels of both prior edges.contains labels of both prior edges.


Trie and Suffix TreeTrie and Suffix Tree


Generalized Suffix TreeGeneralized Suffix Tree

Suffix tree for multiple sessions. Suffix tree for multiple sessions. Contains patterns from all sessions.Contains patterns from all sessions. Maintains count of frequency of Maintains count of frequency of

occurrence of a pattern in the node.occurrence of a pattern in the node. WAP Tree:WAP Tree:

Compressed version of generalized suffix Compressed version of generalized suffix treetree


Types of PatternsTypes of Patterns

Algorithms have been developed to discover Algorithms have been developed to discover different types of patterns.different types of patterns.

Properties:Properties:– Ordered Ordered – Characters (pages) must occur in the – Characters (pages) must occur in the

exact order in the original session.exact order in the original session.– Duplicates Duplicates – Duplicate characters are allowed in – Duplicate characters are allowed in

the pattern.the pattern.– ConsecutiveConsecutive – All characters in pattern must – All characters in pattern must

occur consecutive in given session.occur consecutive in given session.– Maximal Maximal – Not subsequence of another pattern.– Not subsequence of another pattern.


Pattern TypesPattern Types Association RulesAssociation Rules

None of the properties holdNone of the properties hold EpisodesEpisodes

Only ordering holdsOnly ordering holds Sequential PatternsSequential Patterns

Ordered and maximalOrdered and maximal Forward SequencesForward Sequences

Ordered, consecutive, and maximalOrdered, consecutive, and maximal Maximal Frequent SequencesMaximal Frequent Sequences

All properties holdAll properties hold


EpisodesEpisodes

Partially ordered set of pagesPartially ordered set of pages Serial episodeSerial episode – totally ordered with – totally ordered with

time constrainttime constraint Parallel episodeParallel episode – partial ordered with – partial ordered with

time constrainttime constraint General episodeGeneral episode – partial ordered with – partial ordered with

no time constraintno time constraint


DAG for EpisodeDAG for Episode


Spatial Mining OutlineSpatial Mining OutlineGoal:Goal: Provide an introduction to some spatial Provide an introduction to some spatial

mining techniques.mining techniques. IntroductionIntroduction Spatial Data Overview Spatial Data Overview Spatial Data Mining PrimitivesSpatial Data Mining Primitives Generalization/SpecializationGeneralization/Specialization Spatial RulesSpatial Rules Spatial ClassificationSpatial Classification Spatial ClusteringSpatial Clustering


Spatial ObjectSpatial Object

Contains both spatial and nonspatial Contains both spatial and nonspatial attributes.attributes.

Must have a location type attributes:Must have a location type attributes:– Latitude/longitudeLatitude/longitude– Zip codeZip code– Street addressStreet address

May retrieve object using either (or May retrieve object using either (or both) spatial or nonspatial attributes.both) spatial or nonspatial attributes.


Spatial Data Mining ApplicationsSpatial Data Mining Applications GeologyGeology GIS SystemsGIS Systems Environmental ScienceEnvironmental Science AgricultureAgriculture MedicineMedicine RoboticsRobotics May involved both spatial and temporal May involved both spatial and temporal

aspectsaspects


Spatial QueriesSpatial Queries Spatial selection may involve specialized selection Spatial selection may involve specialized selection

comparison operations:comparison operations:– NearNear– North, South, East, WestNorth, South, East, West– Contained inContained in– Overlap/intersectOverlap/intersect

Region (Range) QueryRegion (Range) Query – find objects that intersect a given – find objects that intersect a given region.region.

Nearest Neighbor QueryNearest Neighbor Query – find object close to identified – find object close to identified object.object.

Distance ScanDistance Scan – find object within a certain distance of an – find object within a certain distance of an identified object where distance is made increasingly larger.identified object where distance is made increasingly larger.


Spatial Data StructuresSpatial Data Structures Data structures designed specifically to store or Data structures designed specifically to store or

index spatial data.index spatial data. Often based on B-tree or Binary Search TreeOften based on B-tree or Binary Search Tree Cluster data on disk basked on geographic location.Cluster data on disk basked on geographic location. May represent complex spatial structure by placing May represent complex spatial structure by placing

the spatial object in a containing structure of a the spatial object in a containing structure of a specific geographic shape.specific geographic shape.

Techniques:Techniques:– Quad TreeQuad Tree– R-TreeR-Tree– k-D Treek-D Tree


MBRMBR

Minimum Bounding RectangleMinimum Bounding Rectangle Smallest rectangle that completely Smallest rectangle that completely

contains the objectcontains the object


MBR ExamplesMBR Examples


Quad TreeQuad Tree Hierarchical decomposition of the space Hierarchical decomposition of the space

into quadrants (MBRs)into quadrants (MBRs) Each level in the tree represents the Each level in the tree represents the

object as the set of quadrants which object as the set of quadrants which contain any portion of the object.contain any portion of the object.

Each level is a more exact representation Each level is a more exact representation of the object.of the object.

The number of levels is determined by The number of levels is determined by the degree of accuracy desired.the degree of accuracy desired.


Quad Tree ExampleQuad Tree Example


R-TreeR-Tree As with Quad Tree the region is divided As with Quad Tree the region is divided

into successively smaller rectangles into successively smaller rectangles (MBRs).(MBRs).

Rectangles need not be of the same Rectangles need not be of the same size or number at each level.size or number at each level.

Rectangles may actually overlap.Rectangles may actually overlap. Lowest level cell has only one object.Lowest level cell has only one object. Tree maintenance algorithms similar to Tree maintenance algorithms similar to

those for B-trees.those for B-trees.


R-Tree ExampleR-Tree Example


K-D TreeK-D Tree Designed for multi-attribute data, not Designed for multi-attribute data, not

necessarily spatialnecessarily spatial Variation of binary search treeVariation of binary search tree Each level is used to index one of the Each level is used to index one of the

dimensions of the spatial object.dimensions of the spatial object. Lowest level cell has only one objectLowest level cell has only one object Divisions not based on MBRs but Divisions not based on MBRs but

successive divisions of the dimension successive divisions of the dimension range.range.


k-D Tree Examplek-D Tree Example


Topological RelationshipsTopological Relationships

DisjointDisjoint Overlaps or IntersectsOverlaps or Intersects EqualsEquals Covered by or inside or contained inCovered by or inside or contained in Covers or containsCovers or contains


Distance Between ObjectsDistance Between Objects EuclideanEuclidean ManhattanManhattan Extensions:Extensions:


Progressive RefinementProgressive Refinement

Make approximate answers prior to Make approximate answers prior to more accurate ones.more accurate ones.

Filter out data not part of answerFilter out data not part of answer Hierarchical view of data based on Hierarchical view of data based on

spatial relationshipsspatial relationships Coarse predicate recursively refinedCoarse predicate recursively refined


Progressive RefinementProgressive Refinement


Spatial Data Dominant AlgorithmSpatial Data Dominant Algorithm


STINGSTING

STatistical Information Grid-basedSTatistical Information Grid-based Hierarchical technique to divide area Hierarchical technique to divide area

into rectangular cellsinto rectangular cells Grid data structure contains summary Grid data structure contains summary

information about each cellinformation about each cell Hierarchical clustering Hierarchical clustering Similar to quad treeSimilar to quad tree


STINGSTING


STING Build AlgorithmSTING Build Algorithm


STING AlgorithmSTING Algorithm


Spatial RulesSpatial Rules Characteristic RuleCharacteristic Rule

The average family income in Dallas is $50,000.The average family income in Dallas is $50,000. Discriminant RuleDiscriminant Rule

The average family income in Dallas is $50,000, The average family income in Dallas is $50,000, while in Plano the average income is $75,000.while in Plano the average income is $75,000.

Association RuleAssociation RuleThe average family income in Dallas for families The average family income in Dallas for families living near White Rock Lake is $100,000.living near White Rock Lake is $100,000.


Spatial Association RulesSpatial Association Rules

Either antecedent or consequent must Either antecedent or consequent must contain spatial predicates.contain spatial predicates.

View underlying database as set of View underlying database as set of spatial objects.spatial objects.

May create using a type of progressive May create using a type of progressive refinementrefinement


Spatial Association Rule AlgorithmSpatial Association Rule Algorithm


Spatial ClassificationSpatial Classification

Partition spatial objectsPartition spatial objects May use nonspatial attributes and/or May use nonspatial attributes and/or

spatial attributesspatial attributes Generalization and progressive Generalization and progressive

refinement may be used.refinement may be used.


ID3 ExtensionID3 Extension

Neighborhood GraphNeighborhood Graph– Nodes – objectsNodes – objects– Edges – connects neighborsEdges – connects neighbors

Definition of neighborhood variesDefinition of neighborhood varies ID3 considers nonspatial attributes of all ID3 considers nonspatial attributes of all

objects in a neighborhood (not just one) objects in a neighborhood (not just one) for classification.for classification.


Spatial Decision TreeSpatial Decision Tree

Approach similar to that used for spatial Approach similar to that used for spatial association rules.association rules.

Spatial objects can be described based Spatial objects can be described based on objects close to them – on objects close to them – Buffer.Buffer.

Description of class based on Description of class based on aggregation of nearby objects.aggregation of nearby objects.


Spatial Decision Tree AlgorithmSpatial Decision Tree Algorithm


Spatial ClusteringSpatial Clustering

Detect clusters of irregular shapesDetect clusters of irregular shapes Use of centroids and simple distance Use of centroids and simple distance

approaches may not work well.approaches may not work well. Clusters should be independent of order Clusters should be independent of order

of input.of input.


Spatial ClusteringSpatial Clustering


CLARANS ExtensionsCLARANS Extensions

Remove main memory assumption of Remove main memory assumption of CLARANS.CLARANS.

Use spatial index techniques.Use spatial index techniques. Use sampling and R*-tree to identify Use sampling and R*-tree to identify

central objects.central objects. Change cost calculations by reducing Change cost calculations by reducing

the number of objects examined.the number of objects examined. Voronoi DiagramVoronoi Diagram


VoronoiVoronoi


SD(CLARANS)SD(CLARANS)

Spatial DominantSpatial Dominant First clusters spatial components using First clusters spatial components using

CLARANSCLARANS Then iteratively replaces medoids, but Then iteratively replaces medoids, but

limits number of pairs to be searched.limits number of pairs to be searched. Uses generalizationUses generalization Uses a learning to to derive description Uses a learning to to derive description

of cluster.of cluster.


SD(CLARANS) AlgorithmSD(CLARANS) Algorithm


DBCLASDDBCLASD

Extension of DBSCANExtension of DBSCAN Distribution Based Clustering of LArge Distribution Based Clustering of LArge

Spatial DatabasesSpatial Databases Assumes items in cluster are uniformly Assumes items in cluster are uniformly

distributed.distributed. Identifies distribution satisfied by Identifies distribution satisfied by

distances between nearest neighbors.distances between nearest neighbors. Objects added if distribution is uniform.Objects added if distribution is uniform.


DBCLASD AlgorithmDBCLASD Algorithm


Aggregate ProximityAggregate Proximity

Aggregate ProximityAggregate Proximity – measure of how – measure of how close a cluster is to a feature.close a cluster is to a feature.

Aggregate proximity relationship finds the Aggregate proximity relationship finds the k closest features to a cluster.k closest features to a cluster.

CRH AlgorithmCRH Algorithm – uses different shapes: – uses different shapes:– Encompassing CircleEncompassing Circle– Isothetic RectangleIsothetic Rectangle– Convex HullConvex Hull


CRHCRH


Temporal Mining OutlineTemporal Mining OutlineGoal:Goal: Examine some temporal data Examine some temporal data

mining issues and approaches.mining issues and approaches. IntroductionIntroduction Modeling Temporal EventsModeling Temporal Events Time SeriesTime Series Pattern DetectionPattern Detection SequencesSequences Temporal Association RulesTemporal Association Rules


Temporal DatabaseTemporal Database Snapshot Snapshot – Traditional database– Traditional database TemporalTemporal – Multiple time points – Multiple time points Ex:Ex:


Temporal QueriesTemporal Queries QueryQuery

DatabaseDatabase

Intersection QueryIntersection Query

Inclusion QueryInclusion Query

Containment QueryContainment Query

Point Query – Tuple retrieved is valid at a particular point in time.Point Query – Tuple retrieved is valid at a particular point in time.

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Types of DatabasesTypes of Databases

Snapshot – No temporal supportSnapshot – No temporal support Transaction Time – Supports time when Transaction Time – Supports time when

transaction inserted datatransaction inserted data– TimestampTimestamp– RangeRange

Valid Time – Supports time range when Valid Time – Supports time range when data values are validdata values are valid

Bitemporal – Supports both transaction Bitemporal – Supports both transaction and valid time.and valid time.


Modeling Temporal EventsModeling Temporal Events Techniques to model temporal events.Techniques to model temporal events. Often based on earlier approachesOften based on earlier approaches Finite State Recognizer (Machine) (FSR)Finite State Recognizer (Machine) (FSR)

– Each event recognizes one characterEach event recognizes one character– Temporal ordering indicated by arcsTemporal ordering indicated by arcs– May recognize a sequenceMay recognize a sequence– Require precisely defined transitions between statesRequire precisely defined transitions between states

ApproachesApproaches– Markov ModelMarkov Model– Hidden Markov ModelHidden Markov Model– Recurrent Neural NetworkRecurrent Neural Network


FSRFSR


Markov Model (MM)Markov Model (MM) Directed graphDirected graph

– Vertices represent statesVertices represent states– Arcs show transitions between statesArcs show transitions between states– Arc has probability of transitionArc has probability of transition– At any time one state is designated as current At any time one state is designated as current

state.state. Markov PropertyMarkov Property – Given a current state, the – Given a current state, the

transition probability is independent of any transition probability is independent of any previous states.previous states.

Applications: speech recognition, natural Applications: speech recognition, natural language processinglanguage processing


Markov ModelMarkov Model


Hidden Markov Model (HMM)Hidden Markov Model (HMM) Like HMM, but states need not correspond to Like HMM, but states need not correspond to

observable states.observable states. HMM models process that produces as HMM models process that produces as

output a sequence of observable symbols.output a sequence of observable symbols. HMM will actually output these symbols.HMM will actually output these symbols. Associated with each node is the probability Associated with each node is the probability

of the observation of an event.of the observation of an event. Train HMM to recognize a sequence.Train HMM to recognize a sequence. Transition and observation probabilities Transition and observation probabilities

learned from training set.learned from training set.


Hidden Markov ModelHidden Markov Model

Modified from [RJ86]


HMM AlgorithmHMM Algorithm


HMM ApplicationsHMM Applications

Given a sequence of events and an Given a sequence of events and an HMM, what is the probability that the HMM, what is the probability that the HMM produced the sequence?HMM produced the sequence?

Given a sequence and an HMM, what is Given a sequence and an HMM, what is the most likely state sequence which the most likely state sequence which produced this sequence?produced this sequence?


Recurrent Neural Network (RNN)Recurrent Neural Network (RNN)

Extension to basic NNExtension to basic NN Neuron can obtian input form any other Neuron can obtian input form any other

neuron (including output layer).neuron (including output layer). Can be used for both recognition and Can be used for both recognition and

prediction applications.prediction applications. Time to produce output unknownTime to produce output unknown Temporal aspect added by backlinks.Temporal aspect added by backlinks.


RNNRNN


Time SeriesTime Series

Set of attribute values over timeSet of attribute values over time Time Series Analysis – finding patterns Time Series Analysis – finding patterns

in the values.in the values.– TrendsTrends– CyclesCycles– SeasonalSeasonal– OutliersOutliers


Analysis TechniquesAnalysis Techniques Smoothing Smoothing – Moving average of attribute – Moving average of attribute

values.values. Autocorrelation Autocorrelation – relationships between – relationships between

different subseriesdifferent subseries– Yearly, seasonalYearly, seasonal– LagLag – Time difference between related items. – Time difference between related items.– Correlation Coefficient rCorrelation Coefficient r


SmoothingSmoothing


Correlation with Lag of 3Correlation with Lag of 3


SimilaritySimilarity Determine similarity between a target pattern, X, Determine similarity between a target pattern, X,

and sequence, Y: sim(X,Y)and sequence, Y: sim(X,Y) Similar to Web usage miningSimilar to Web usage mining Similar to earlier word processing and spelling Similar to earlier word processing and spelling

corrector applications.corrector applications. Issues:Issues:

– LengthLength– ScaleScale– GapsGaps– OutliersOutliers– BaselineBaseline


Longest Common SubseriesLongest Common Subseries

Find longest subseries they have in Find longest subseries they have in common.common.

Ex:Ex:– X = <10,5,6,9,22,15,4,2>X = <10,5,6,9,22,15,4,2>– Y = <6,9,10,5,6,22,15,4,2>Y = <6,9,10,5,6,22,15,4,2>– Output: <22,15,4,2>Output: <22,15,4,2>– Sim(X,Y) = l/n = 4/9Sim(X,Y) = l/n = 4/9


Similarity based on Linear Similarity based on Linear TransformationTransformation

Linear transformation function fLinear transformation function f– Convert a value form one series to a value Convert a value form one series to a value

in the secondin the second ff – tolerated difference in results – tolerated difference in results – – time value difference allowedtime value difference allowed


PredictionPrediction

Predict future value for time seriesPredict future value for time series Regression may not be sufficientRegression may not be sufficient Statistical TechniquesStatistical Techniques

– ARMAARMA– ARIMAARIMA

NNNN


Pattern DetectionPattern Detection

Identify patterns of behavior in time Identify patterns of behavior in time seriesseries

Speech recognition, signal processingSpeech recognition, signal processing FSR, MM, HMMFSR, MM, HMM


String MatchingString Matching

Find given pattern in sequenceFind given pattern in sequence Knuth-Morris-Pratt:Knuth-Morris-Pratt: Construct FSM Construct FSM Boyer-Moore:Boyer-Moore: Construct FSM Construct FSM


Distance between StringsDistance between Strings

Cost to convert one to the otherCost to convert one to the other TransformationsTransformations

– Match: Current characters in both strings Match: Current characters in both strings are the sameare the same

– Delete: Delete current character in input Delete: Delete current character in input stringstring

– Insert: Insert current character in target Insert: Insert current character in target string into stringstring into string


Distance between StringsDistance between Strings


Frequent SequenceFrequent Sequence


Frequent Sequence ExampleFrequent Sequence Example

Purchases made by Purchases made by customerscustomers

s(<{A},{C}>) = 1/3s(<{A},{C}>) = 1/3 s(<{A},{D}>) = 2/3s(<{A},{D}>) = 2/3 s(<{B,C},{D}>) = 2/3s(<{B,C},{D}>) = 2/3


Frequent Sequence LatticeFrequent Sequence Lattice


SPADESPADE

Sequential Pattern Discovery using Sequential Pattern Discovery using Equivalence classesEquivalence classes

Identifies patterns by traversing lattice Identifies patterns by traversing lattice in a top down manner.in a top down manner.

Divides lattice into equivalent classes Divides lattice into equivalent classes and searches each separately.and searches each separately.

ID-List:ID-List: Associates customers and Associates customers and transactions with each item.transactions with each item.


SPADE ExampleSPADE Example

ID-List for Sequences of length 1:ID-List for Sequences of length 1:

Count for <{A}> is 3Count for <{A}> is 3 Count for <{A},{D}> is 2Count for <{A},{D}> is 2


Equivalence ClassesEquivalence Classes


SPADE AlgorithmSPADE Algorithm


Temporal Association RulesTemporal Association Rules

Transaction has time:Transaction has time:<TID,CID,I<TID,CID,I11,I,I22, …, I, …, Imm,t,tss,t,tee>>

[t[tss,t,tee] is range of time the transaction is active.] is range of time the transaction is active. Types:Types:

– Inter-transaction rulesInter-transaction rules– Episode rulesEpisode rules– Trend dependenciesTrend dependencies– Sequence association rulesSequence association rules– Calendric association rulesCalendric association rules


Inter-transaction RulesInter-transaction Rules

Intra-transaction association rulesIntra-transaction association rulesTraditional association RulesTraditional association Rules

Inter-transaction association rulesInter-transaction association rules– Rules across transactionsRules across transactions– Sliding windowSliding window – How far apart (time or – How far apart (time or

number of transactions) to look for related number of transactions) to look for related itemsets.itemsets.


Episode RulesEpisode Rules

Association rules applied to sequences Association rules applied to sequences of events.of events.

EpisodeEpisode – set of event predicates and – set of event predicates and partial ordering on thempartial ordering on them


Trend DependenciesTrend Dependencies Association rules across two database Association rules across two database

states based on time.states based on time. Ex: (SSN,=) Ex: (SSN,=) (Salary, (Salary, ))

Confidence=4/5Confidence=4/5Support=4/36Support=4/36


Sequence Association RulesSequence Association Rules Association rules involving sequencesAssociation rules involving sequences Ex:Ex:

<{A},{C}> <{A},{C}> <{A},{D}> <{A},{D}>Support = 1/3Support = 1/3Confidence 1Confidence 1


Calendric Association RulesCalendric Association Rules

Each transaction has a unique Each transaction has a unique timestamp.timestamp.

Group transactions based on time Group transactions based on time interval within which they occur.interval within which they occur.

Identify large itemsets by looking at Identify large itemsets by looking at transactions only in this predefined transactions only in this predefined interval.interval.