INFORMATION SEARCH

Presenter: Pham Kim Son

Saint Petersburg State University

Overview Introduction Overview of IR system and basic terminologies Classical models of Information Retrieval

Boolean Model Vector Model

Modern models of Information Retrieval Latent Semantic Indexing Correlation Method

Conclusion

Introduction People need information to solve problem

Very simple thing Complex thing

“Perfect search machine” defined by Larry Page is something that understand exactly what you mean and return exactly what you want.

Challenges to IR Introduction of www

www is large Heterogeneous

Gives challenges to IR

Overview of IR and basic terminologies

IR can be divided in to 3 components Input Processor Output

Processor

Query

Documents

Output

Input

Input The main task: Obtain a good

representation of each document and query for computer to use A document representative: a list of extracted

keywords Idea: Let the computer process the natural

language in the document

Input

Input (cont) Obstacles

Theory of human language has not been sufficiently developed for every language

Not clear how to use it to enhance information retrieval

Input (cont) Representing documents by keywords

Step1:Removing common words Step2: Stemming

Step1: Removing common words Very high frequency words very common

words They should removed comparing with stop-list So

Non-significant words not interfere IR process Reduce the size document between 30->50 per

cent (C.J. van Rijsbergen)

willof the

be

are

By

Step2:Stemming Def: Stemming : The process of chopping

the ending of a term, e.g. removing “ed”, ”ing”

Algorithm Porter

Processor

This part of the IR system are concerned with the retrieval process Structuring the documents in an appropriate

way Performing actual retrieval function, using a

predefined model

Input ProcessorInput

Output The output will be a set of documents,

assumed to be relevant to users. Purpose of IR:

Retrieved all relevant documents Retrieved irrelevant documents as few as

possible

Input Processor output

Definition

documents relevant of number Total

retrieved documents relevant of Number recall

retrieved documents of number Total

retrieved documents relevant of Number precision

Relevant docs retrieved

relevant docs

Relevant docs retrieved

All docs retrieved

Returns relevant documents butmisses many useful ones too

Returns most relevantdocuments but includes lots of junk

The ideal

0

Pre

cisi

on

Recall

1

1

Information Retrieval Models Classical models

Boolean model Vector model

Novel models Latent semantic indexing model Correlation method

Boolean model Earliest and simplest method, widely used

in IR systems today Based on set theories and Boolean algebra. Queries are Boolean expressions of

keywords, connected by operators AND, OR, ANDNOT

Ex: (Saint Petersburg AND Russia) | (beautiful city AND Russia)

Inverted files are widely used Ex:

Term1 : doc 2 , doc 5, doc6 ; Term2 : doc 2, doc4, doc5; Query : q = (term1 AND term2) Result: doc2, doc5

Term-document matrix can be used

Thinking about Boolean model Advantages:

Very simple model based on sets theory Easy to understand and implement Supports exact query

Disadvantages: Retrieval based on binary decision criteria , without notion of

partial matching Sets are easy, but complex Boolean expressions are not The Boolean queries formulated by users are most often so

simplistic Retrieves so many or so few documents Gives unranked results

Vector Model Why Vector Model ?

Boolean model just takes into account the existence or

nonexistence of terms in a document Has no sense about their different contributions to

documents

Overview theory of vector model Documents and queries are displayed as vectors

in index-term space Space dimension is equal to the vocabulary size Components of these vectors: the weights of the

corresponding index term, which reflects its significant in terms of representative and discrimination power

Retrieval is based on whether the “query vector” and “document vector” are closed enough.

Set of document:

A finite set of terms :

Every document can be displayed as vector:

the same to the query:

1 2{ , ,..., }mD D D D

1 2{ , ,..., }nT t t t

1 2( , ,..., )j j j njd w w w

1 2( , ,..., )q q nqq w w w

Similarity of query q and document d:

Given a threshold , all documents with similarity > threshold are retrieved

i

j

dj

q

( , )( , ) cos( )

(|| || * || ||)

d qsimilarity q d

d q

Compute a good weight A variety of weighting schemes are available They are based on three proven principles:

Terms that occur in only a few documents are more valuable than ones that appear in many

The more often a term occur in a document, the more likely it is to be important to that document

A term that appears the same number of times in a short document and in a long one is likely to be more available for the former

tf-idf-dl (tf-idf) scheme The term frequency of a term ti in document dj:

The length of document dj: DLj = total number of terms occurrences in document dj Inverted document frequency: collection of N documents,

inverted document frequency of a term ti that appears in n document is :

Weight:

ij i jTF Number of occurences of term t in document d

logi

NIDF

n

*ij iij

j

TF IDFw

DL

Think about Vector model Advantages:

Term weighting improves the quality of the answer Partial matching allows to retrieve the documents

that approximate the query conditions Cosine ranking formula sorts the answer

Disadvantages Assumes the independences of terms Polysemy and synonymy problem are unsolved

Modern models of IR Why ?

Problems with polysemy: Bass (fish or music ?)

Problems with synonymy: Car or automobile ?

These failures can be traced to : The way index terms are identified is incomplete Lack of efficient methods to deal with polysemy

Idea to solve this problem: take the advance of implicit higher order structure(latent) in the association terms with documents .

Latent Semantic Indexing (LSI) LSI overview

Representing documents roughly by terms is unreliability, ambiguity and redundancy

Should find a method , which can : Documents and terms are displayed as vectors in

a k-dim concepts space. Its weights indicating the strength of association with each of these concepts

That method should be flexible enough to remove the weak concepts, considered as noises

Document-term matrix A[mxn] are built

Matrix A is factored in to 3 matrices, using Singular value decomposition SVD

U,V are orthogonal matrices

d1 d2 …. dm

t1 w11 w12 … w1m

t2 w21 w22 … w2m

: : : : : : : :tn wn1 wn2 … wnm

TA U V T T

nU U V V I

1 2( , ,..., )ndiag

1 2 1Let ( ) ... ... 0r r nrank A r

These special matrices show a break down of the original relationship (doc-term) to a linearly independent components (factors)

Many of these components are very small: ( considered as noises) and should be ignored

1 0 ... 0

0 ... 0 ...

... ... ...

0 0 ... 0

T

r

A U V

Criteria to choose k: Ignore noises Important information are

not lost

Documents and terms are displayed as vectors in k-dim space

Theory Eckart & Young ensures us about not losing important information

2 2 2 21

( )min || || || || ...F k F k r

rank B kA B A A

Tk k kA U V

Query Should find a method to display a query to

k-dim space Query q can be seen as a document. From equation: We have

Tk k kA U V

1Tk k kq q U

Similarity between objects

Term-Term: Dot product between two rows vector of matrix Ak

reflects the similarity between two terms Term-term similarity matrix :

Can consider the rows of matrix as coordinate of terms.

The relation between taking rows of as coordinate and rows of as coordinates is simple

( )( )T T T Tk k k k k k k k k k k kT A A U V V U U U

k kU

kU

k kU

Document-document Dot product between two columns vectors of matrix Ak

reflect the similarity between two documents.

Can consider the row of matrix as coordinates of documents.

Term-document This value can be obtained by looking at the element of

matrix Ak

Drawback: between and within comparisons can not be done simultaneously without resizing the coordinate.

( )( )T T T Tk k k k k k k k k k k kD A A V U U V V V

k kV

1/ 2 1/ 2Tk k k k k k k kA U V U V

Example q1: human machine interface for Lab ABC computer applications q2: a survey of user opinion of computer system response time. q3: the EPS user interface management system q4: System and human system engineering testing of EPS q5:Relation of user-perceived response time to error measurement

q6: The generation of random, binary, unordered tree q7: The intersection graph of paths in trees q8: Graph minors IV: Widths of trees and well-quasi-ordering q9: Graph minors: A survey

Numerical results1 2 3 4 5 6 7 8 9

1 0 0 1 0 0 0 0 0

1 0 1 0 0 0 0 0 0

1 1 0 0 0 0 0 0 0

0 1 1 0 1 0 0 0 0

0 1 1 2 0 0 0 0 0

0 1 0 0 1 0 0 0 0

0 1 0 0 1 0 0 0 0

0 0 1 1 0 0 0 0 0

0 1 0 0 0 0 0 0 1

0 0 0 0 0 1 1 1 0

0 0 0 0 0 0 1 1 1

0 0 0 0 0 0 0 1 1

q q q q q q q q q

human

interface

computer

user

system

A response

time

EPS

survey

trees

graph

minors

0.22 0.11

0.20 0.07

0.24 0.04

0.40 0.06

0.64 0.17

0.27 0.11 3.34 0 0.20 0.61 0.46 0.54 0.28 0.00 0.02 0.02 0.08

0.27 0.11 0 2.54 0.06 0.

0.30 0.14

0.21 0.27

0.01 0.49

0.04 0.62

0.03 0.45

kA

17 0.13 0.23 0.11 0.19 0.44 0.62 0.53

T Tk k k kA U V A U V

Query: human computerinteraction

Updating

Folding in New document New terms and docs has no effect on the

presentation of pre-existing docs and terms Re-computing SVD

Re-compute SVD Requires times and memory

Choosing one of these two methods

1k Tnew new k kd d U

Think about LSI Advantages:

Synonymy problem is solved Displaying documents in a more reliable

space: Concepts space Disadvantages:

Polysemy problem is still unsolved A special algorithms for handling with large

size matrices should be implemented

Correlation Method Idea: If a keyword is present in the document,

correlated keywords should be taken into account as well. So, the concepts containing in the document aren’t obscured by the choices of a specific vocabulary.

In vector space model: similarity vector :

Depend on the user query q, we now build the best query, taking the correlated keyword into account as well.

Tr A q

The correlation matrix is built based on the term-document matrix Let: A is the term-document matrix D : number of document, is the mean vector.

Clearly that : Covariance matrix is computed:

Correlation Matrix S :

d

1

1 D

jj

d dD

1

1( )( )

1

D

j jj

C d d d dD

ijij

ii jj

cs

c c

,ij m m

S s

Better query: We now use SVD to reduce noises in the

correlation of keywords: We choose the first k largest factors to obtain

the k dimensional of S

Generate our best query: Vector of similarity :

Define a projection, defined by :

betterq Sq

Tk k k kS X X

best kq S q

1/ 2 1/ 2T T T T Tk k k k k k k kr A S q A X X q A X X q

1/ 2 Tk kP X

Strength of correlation method In real world, correlation between words are static. Number of terms has a higher stability level when

comparing with number of documents Number of documents are many times larger than

number of keywords. This method is able to handle database with a

very large number of documents and doesn’t have to update the correlation matrix every time adding new documents.

Its importance in the electronic networks.

Conclusion IR overview Classical IR models :

Boolean model Vector model

Modern IR models : LSI Correlation methods

Any questions ?

References Gheorghe Muresan: Using document Clustering and

language modeling in mediated IR. Georges Dupret: Latent Concepts and the Number

Orthogonal Factors in Latent Semantic Indexing C.J. van RIJSBERGEN: Information Retrieval Ricardo Baeza-Yates: Modern Information Retrieval Sandor Dominich: Mathematical foundation of

information retrieval. IR lectures note from : www.cs.utexas.edu Scott Deerwester, Susan T.Dumais: Indexing by Latent

Semantic Analysis

Desktop Search Design the desktop search that satisfies

Not affects computer’s performance Privacy is protected Ability to search as many types of files as

possible( consider music file) Multi languages search User-friendly Support semantic search if possible