Spring 2003 Data Mining by H. Liu, ASU 1

3. Classification Methods

Patterns and Models

Regression, NBC

k-Nearest Neighbors

Decision Trees and Rules

Large size data

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Models and Patterns

• A model is a global description of data, or an abstract representation of a real-world process– Estimating parameters of a model

– Data-driven model building

– Examples: Regression, Graphical model (BN), HMM

• A pattern is about some local aspects of data– Patterns in data matrices

• Predicates (age < 40) ^ (income < 10)

– Patterns for strings (ASCII characters, DNA alphabet)

– Pattern discovery: rules

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Performance Measures

• Generality– How many instances are covered

• Applicability– Or is it useful? All husbands are male.

• Accuracy– Is it always correct? If not, how often?

• Comprehensibility– Is it easy to understand? (a subjective measure)

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Forms of Knowledge

• Concepts– Probabilistic, logical (proposition/predicate), functional

• Rules• Taxonomies and Hierarchies

– Dendrograms, decision trees

• Clusters• Structures and Weights/Probabilities

– ANN, BN

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Induction from Data

• Inferring knowledge from data - generalization• Supervised vs. unsupervised learning

– Some graphical illustrations of learning tasks (regression, classification, clustering)

– Any other types of learning?

• The task of deduction– infer information that is a logical consequence of

querying a database• Who conducted this class before?

• Which courses are attended by Mary?

– Deductive databases: extending the RDBMS

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What is a bad classifier?

• Some simplest classifiers– Table-Lookup

• What if x cannot be found in the training data?

• We give up!?

– Or, we can …

• A simple classifier Cs can be built as a reference– If it can be found in the table (training data), return its

class; otherwise, what should it return?

• A bad classifier is one that does worse than Cs.• Do we need to learn a classifier for data of one class?

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Many Techniques

• Decision trees• Linear regression• Neural networks• k-nearest neighbour• Naïve Bayesian classifiers• Support Vector Machines• and many more ...

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Regression for Numeric Prediction• Linear regression is a statistical technique when

class and all the attributes are numeric. • y = α + βx, where α and β are regression

coefficients• We need to use instances <xi,y> to find α and β

– by minimizing SSE (least squares)– SSE = Σ(yi-yi’)2 = Σ(yi- α + βxi)2

• Extensions– Multiple regression – Piecewise linear regression– Polynomial regression

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Nearest Neighbor

• Also called instance based learning• Algorithm

– Given a new instance x,

– find its nearest neighbor <x’,y’>

– Return y’ as the class of x

• Distance measures– Normalization?!

• Some interesting questions– What’s its time complexity?

– Does it learn?

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Nearest Neighbor (2)

• Dealing with noise – k-nearest neighbor– Use more than 1 neighbors

– How many neighbors?

– Weighted nearest neighbors

• How to speed up?– Huge storage

– Use representatives (a problem of instance selection)• Sampling

• Grid

• Clustering

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Naïve Bayes Classification

• This is a direct application of Bayes’ rule• P(C|x) = P(x|C)P(C)/P(x)

x - a vector of x1,x2,…,xn

• That’s the best classifier you can ever build– You don’t even need to select features, it takes care of

it automatically

• But, there are problems– There are a limited number of instances

– How to estimate P(x|C)

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NBC (2)

• Assume conditional independence between xi’s

• We have P(C|x) ≈ P(x1|C) P(xi|C) (xn|C)P(C)

• How good is it in reality?• Let’s build one NBC for a very simple data set

– Estimate the priors and conditional probabilities with the training data

– P(C=1) = ? P(C=2) =?

– What is the class for (1,2,1)?P(1|x) ≈ P(1|1) P(2|1) (1|1)P(1), P(2|x) ≈

– What is the class for (1,2,2)?

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Example of NBC

C 1 2

7 = 4 3

A1 0 2 0

A1 1 2 1

A1 2 0 2

A2 0

A2 1

A2 2

A3 1

A3 2

A1 A2 A3 C

1 2 1 1

0 0 1 1

2 1 2 2

1 2 1 2

0 1 2 1

2 2 2 2

1 0 1 1

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Golf Data

Outlook Temp Humidity Windy ClassSunny Hot High No YesSunny Hot High Yes YesO’cast Hot High No NoRain Mild Normal No NoRain Cool Normal No NoRain Cool Normal Yes YesO’cast Cool Normal Yes NoSunny Mild High No YesSunny Cool Normal No NoRain Mild Normal No NoSunny Mild Normal Yes NoO’cast Mild High Yes NoO’cast Hot Normal No NoRain Mild High Yes Yes

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Decision Trees

• A decision tree

Outlook

Humidity Wind

sunny overcast rain

YES

high normal strong weak

NO YES NO YES

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How to `grow’ a tree?

• Randomly Random Forests (Breiman, 2001)• What are the criteria to build a tree?

– Accurate

– Compact

• A straightforward way to grow is– Pick an attribute

– Split data according to its values

– Recursively do the first two steps until• No data left

• No feature left

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Discussion

• There are many possible trees– let’s try it on the golf data

• How to find the most compact one – that is consistent with the data?

• Why the most compact?– Occam’s razor principle

• Issue of efficiency w.r.t. optimality– One attribute at a time or …

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Grow a good tree efficiently

• The heuristic – to find commonality in feature values associated with class values– To build a compact tree generalized from the data

• It means for each feature, we check whose splits can lead to pure leaf nodes.

• Is it a good heuristic?– What do you think?

– How to judge it?

– Is it really efficient?

– How to implement it?

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• Measuring the purity of a data set – Entropy• Information gain (see the brief review)• Choose the feature with max gain

Let’s grow one

Outlook (7,7)

Sun (5)

Rain (5)

OCa (4)

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Different numbers of values

• Different attributes can have varied numbers of values

• Some treatments– Removing useless attributes before learning

– Binarization

– Discretization

• Gain-ratio is another practical solution– Gain = root-Info – InfoAttribute(i)

– Split-Info = -((|Ti|/|T|)log2 (|Ti|/|T|))

– Gain-ratio = Gain / Split-Info

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Another kind of problems

• A difficulty problem. Why is it difficulty?• Similar ones are Parity, Majority problems.

XOR problem

0 0 0 0 1 1 1 0 1 1 1 0

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Tree Pruning

• An effective approach to avoid overfitting data and for a more compact tree (easy to understand)

• Two general ways to prune– Pre-pruning to stop splitting further

• Any significant difference in classification accuracy before and after division

– Post-pruning to trim back

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Rules from Decision Trees

• Two types of rules– Order sensitive (more compact, less efficient)– Order insensitive

• The most straightforward way is …• Class-based method

– Group rules according to classes– Select most general rules (or remove redundant ones)

• Data-based method– Select one rule at a time (keep the most general one)– Work on the remaining data until all data is covered

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Variants of Decision Trees and Rules

• Tree stumps• Holte’s 1R rules (1992)

– For each attribute• Sort according to its values v

• Find the most frequent class value c for each v

– Breaking tie with coin flipping

• Output the most accurate rule as if v then c

– An example (the Golf data)

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Handling Large Size Data

• When data simply cannot fit in memory …– Is it a big problem?

• Three representative approaches– Smart data structures to avoid unnecessary recalculation

• Hash trees• SPRINT

– Sufficient statistics• AVC-set (Attribute-Value, Class label) to summarize the class

distribution for each attribute• Example: RainForest

– Parallel processing• Make data parallelizable

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Ensemble Methods

• A group of classifiers– Hybrid (Stacking)– Single type

• Strong vs. weak learners• A good ensemble

– Accuracy– Diversity

• Some major approaches form ensembles– Bagging– Boosting

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Bibliography

• I.H. Witten and E. Frank. Data Mining – Practical Machine Learning Tools and Techniques with Java Implementations. 2000. Morgan Kaufmann.

• M. Kantardzic. Data Mining – Concepts, Models, Methods, and Algorithms. 2003. IEEE.

• J. Han and M. Kamber. Data Mining – Concepts and Techniques. 2001. Morgan Kaufmann.

• D. Hand, H. Mannila, P. Smyth. Principals of Data Mining. 2001. MIT.

• T. G. Dietterich. Ensemble Methods in Machine Learning. I. J. Kittler and F. Roli (eds.) 1st Intl Workshop on Multiple Classifier Systems, pp 1-15, Springer-Verlag, 2000.