Chapter 2 Modeling

Hsin-Hsi Chen 1

Chapter 2 Modeling

Hsin-Hsi Chen

Department of Computer Science and Information Engineering

National Taiwan University

Hsin-Hsi Chen 2

Indexing

Hsin-Hsi Chen 3

Indexing

• indexing: assign identifiers to text items.• assign: manual vs. automatic indexing• identifiers:

– objective vs. nonobjective text identifiers cataloging rules define, e.g., author names, publisher names, dates of publications, …

– controlled vs. uncontrolled vocabulariesinstruction manuals, terminological schedules, …

– single-term vs. term phrase

Hsin-Hsi Chen 4

Two Issues

• Issue 1: indexing exhaustivity– exhaustive: assign a large number of terms– nonexhaustive

• Issue 2: term specificity– broad terms (generic)

cannot distinguish relevant from nonrelevant items

– narrow terms (specific)retrieve relatively fewer items, but most of them are relevant

Hsin-Hsi Chen 5

Parameters of retrieval effectiveness

• Recall

• Precision

• Goalhigh recall and high precision

P Number of relevant items retrieved

Total number of items retrieved

R Number of relevant items retrieved

Total number of relevant items in collection

Hsin-Hsi Chen 6

NonrelevantItems

RelevantItems

RetrievedPartab

c d

Precisiona

a + bRecall

a

a + d

Hsin-Hsi Chen 7

A Joint Measure

• F-score

is a parameter that encode the importance of recall and procedure.

=1: equal weight >1: precision is more important <1: recall is more important

FP R

P R

( )

2

2

1

Hsin-Hsi Chen 8

Choices of Recall and Precision

• Both recall and precision vary from 0 to 1.

• In principle, the average user wants to achieve both high recall and high precision.

• In practice, a compromise must be reached because simultaneously optimizing recall and precision is not normally achievable.

Hsin-Hsi Chen 9

Choices of Recall and Precision (Continued)

• Particular choices of indexing and search policies have produced variations in performance ranging from 0.8 precision and 0.2 recall to 0.1 precision and 0.8 recall.

• In many circumstance, both the recall and the precision varying between 0.5 and 0.6 are more satisfactory for the average users.

Hsin-Hsi Chen 10

Term-Frequency Consideration

• Function words– for example, "and", "or", "of", "but", …– the frequencies of these words are high in all

texts• Content words

– words that actually relate to document content – varying frequencies in the different texts of a

collect– indicate term importance for content

Hsin-Hsi Chen 11

A Frequency-Based Indexing Method

• Eliminate common function words from the document texts by consulting a special dictionary, or stop list, containing a list of high frequency function words.

• Compute the term frequency tfij for all remaining terms Tj in each document Di, specifying the number of occurrences of Tj in Di.

• Choose a threshold frequency T, and assign to each document Di all term Tj for which tfij > T.

Hsin-Hsi Chen 12

Discussions

• high-frequency termsfavor recall

• high precisionthe ability to distinguish individual documents from each other

• high-frequency termsgood for precision when its term frequency is not equally high in all documents.

Hsin-Hsi Chen 13

Inverse Document Frequency

• Inverse Document Frequency (IDF) for term Tj

where dfj (document frequency of term Tj) is number of documents in which Tj occurs.

– fulfil both the recall and the precision– occur frequently in individual documents but ra

rely in the remainder of the collection

idfN

dfj

j

log

Hsin-Hsi Chen 14

New Term Importance Indicator

• weight wij of a term Tj in a document ti

• Eliminating common function words

• Computing the value of wij for each term Tj in each document Di

• Assigning to the documents of a collection all terms with sufficiently high (tf x idf) factors

w tfN

dfij ij

j

log

Hsin-Hsi Chen 15

Term-discrimination Value

• Useful index termsdistinguish the documents of a collection from each other

• Document Space– two documents are assigned very similar term sets,

when the corresponding points in document configuration appear close together

– when a high-frequency term without discrimination is assigned, it will increase the document space density

Hsin-Hsi Chen 16

Original State After Assignment of good discriminator

After Assignment of poor discriminator

A Virtual Document Space

Hsin-Hsi Chen 17

Good Term Assignment

• When a term is assigned to the documents of a collection, the few items to which the term is assigned will be distinguished from the rest of the collection.

• This should increase the average distance between the items in the collection and hence produce a document space less dense than before.

Hsin-Hsi Chen 18

Poor Term Assignment

• A high frequency term is assigned that does not discriminate between the items of a collection.

• Its assignment will render the document more similar.

• This is reflected in an increase in document space density.

Hsin-Hsi Chen 19

Term Discrimination Value

• definitiondvj = Q - Qj

where Q and Qj are space densities before and after the assignments of term Tj.

• dvj>0, Tj is a good term; dvj<0, Tj is a poor term.

QN N

sim D Di kki k

N

i

N

1

1 11( )( , )

Hsin-Hsi Chen 20

DocumentFrequency

Low frequency

dvj=0Medium frequency

dvj>0

High frequency

dvj<0

N

Thesaurustransformation

Phrasetransformation

Variations of Term-Discrimination Valuewith Document Frequency

Hsin-Hsi Chen 21

Another Term Weighting

• wij = tfij x dvj

• compared with

– : decrease steadily with increasing documentfrequency

– dvj: increase from zero to positive as the document frequency of the term increase,

decrease shapely as the document frequency becomes still larger.

w tfN

dfij ij

j

log

N

df j

Hsin-Hsi Chen 22

Term Relationships in Indexing

• Single-term indexing– Single terms are often ambiguous.– Many single terms are either too specific or too

broad to be useful.

• Complex text identifiers– subject experts and trained indexers– linguistic analysis algorithms, e.g., NP chunker– term-grouping or term clustering methods

Hsin-Hsi Chen 23

Term Classification (Clustering)

T T T T

D

D

D

d d d

d d d

d d d

t

n

t

t

n n nt

1 2 3

1

2

11 12 1

21 22 2

1 2

Hsin-Hsi Chen 24

Term Classification (Clustering)

• Column partGroup terms whose corresponding column representation reveal similar assignments to the documents of the collection.

• Row partGroup documents that exhibit sufficiently similar term assignment.

Hsin-Hsi Chen 25

Linguistic Methodologies

• Indexing phrases:nominal constructions including adjectives and nouns– Assign syntactic class indicators (i.e., part of speech) to

the words occurring in document texts.

– Construct word phrases from sequences of words exhibiting certain allowed syntactic markers (noun-noun and adjective-noun sequences).

Hsin-Hsi Chen 26

Term-Phrase Formation

• Term Phrasea sequence of related text words carry a more specific meaning than the single termse.g., “computer science” vs. computer;

DocumentFrequency

Low frequency


dvj>0

High frequency

dvj<0

N



Hsin-Hsi Chen 27

Simple Phrase-Formation Process

• the principal phrase component (phrase head)a term with a document frequency exceeding a stated threshold, or exhibiting a negative discriminator value

• the other components of the phrasemedium- or low- frequency terms with stated co-occurrence relationships with the phrase head

• common function wordsnot used in the phrase-formation process

Hsin-Hsi Chen 28

An Example

• Effective retrieval systems are essential for people in need of information.– “are”, “for”, “in” and “of”:

common function words– “system”, “people”, and “information”:

phrase heads

Hsin-Hsi Chen 29

The Formatted Term-Phrases

Phrase Heads and ComponentsMust Be Adjacent

Phrase Heads and ComponentsCo-occur in Sentence

1. retrieval system* 6. effective systems

2. systems essential 7. systems need

3. essential people 8. effective people

4. people need 9. retrieval people

5. need information* 10. effective information*

11. retrieval information*

12. essential information*

effective retrieval systems essential people need information

*: phrases assumed to be useful for content identification2/5 5/12

Hsin-Hsi Chen 30

The Problems

• A phrase-formation process controlled only by word co-occurrences and the document frequencies of certain words in not likely to generate a large number of high-quality phrases.

• Additional syntactic criteria for phrase heads and phrase components may provide further control in phrase formation.

Hsin-Hsi Chen 31

Additional Term-Phrase Formation Steps

• Syntactic class indicator are assigned to the terms, and phrase formation is limited to sequences of specified syntactic markers, such as adjective-noun and noun-noun sequences.

Adverb-adjective adverb-noun • The phrase elements are all chosen from within

the same syntactic unit, such as subject phrase, object phrase, and verb phrase.

Hsin-Hsi Chen 32

Consider Syntactic Unit

• effective retrieval systems are essential for people in the need of information

• subject phrase– effective retrieval systems

• verb phrase– are essential

• object phrase– people in need of information

Hsin-Hsi Chen 33

Phrases within Syntactic Components

• Adjacent phrase heads and components within syntactic components– retrieval systems*– people need– need information*

• Phrase heads and components co-occur within syntactic components– effective systems

[subj effective retrieval systems] [vp are essential ]for [obj people need information]

2/3

Hsin-Hsi Chen 34

Problems

• More stringent phrase formation criteria produce fewer phrases, both good and bad, than less stringent methodologies.

• Prepositional phrase attachment, e.g.,The man saw the girl with the telescope.

• Anaphora resolutionHe dropped the plate on his foot and broke it.

Hsin-Hsi Chen 35

Problems (Continued)

• Any phrase matching system must be able to deal with the problems of– synonym recognition

– differing word orders

– intervening extraneous word

• Example– retrieval of information vs. information retrieval

Hsin-Hsi Chen 36

Equivalent Phrase Formulation

• Base form: text analysis system• Variants:

– system analyzes the text– text is analyzed by the system– system carries out text analysis– text is subjected to system analysis

• Related term substitution– text: documents, information items– analysis: processing, transformation, manipulation– system: program, process

Hsin-Hsi Chen 37

Thesaurus-Group Generation

• Thesaurus transformation– broadens index terms whose scope is too narrow to be

useful in retrieval

– a thesaurus must assemble groups of related specific terms under more general, higher-level class indicators

DocumentFrequency

Low frequency


dvj>0

High frequency

dvj<0

N



Hsin-Hsi Chen 38

Sample Classes of Roget’s Thesaurus

Class Indicator Entry Class Indicator Entrypermission offerleave presentation

760 sanction tenderallowance 763 overture

tolerance advanceauthorization submissionprohibition proposalveto proposition

761 disallowance invitationinjunction refusalban declining

taboo 764 noncompliance

consent rejection

acquiescence denial

762 compliance

agreement

acceptance

Hsin-Hsi Chen 39

The Indexing Prescription (1)

• Identify the individual words in the document collection.

• Use a stop list to delete from the texts the function words.

• Use an suffix-stripping routine to reduce each remaining word to word-stem form.

• For each remaining word stem Tj in document Di, compute wij.

• Represent each document Di byDi=(T1, wi1; T2, wi2; …, Tt, wit)

Hsin-Hsi Chen 40

Word Stemming

• effectiveness --> effective --> effect

• picnicking --> picnic

• king -\-> k

Hsin-Hsi Chen 41

Some Morphological Rules

• Restore a silent e after suffix removal from certain words to produce “hope” from “hoping” rather than “hop”

• Delete certain doubled consonants after suffix removal, so as to generate “hop” from “hopping” rather than “hopp”.

• Use a final y for an I in forms such as “easier”, so as to generate “easy” instead of “easi”.

Hsin-Hsi Chen 42

The Indexing Prescription (2)• Identify individual text words.• Use stop list to delete common function words.• Use automatic suffix stripping to produce word stems.• Compute term-discrimination value for all word stems.• Use thesaurus class replacement for all low-frequency

terms with discrimination values near zero.• Use phrase-formation process for all high-frequency terms

with negative discrimination values.• Compute weighting factors for complex indexing units.• Assign to each document single term weights, term

phrases, and thesaurus classes with weights.

Hsin-Hsi Chen 43

Query vs. Document

• Differences– Query texts are short.

– Fewer terms are assigned to queries.

– The occurrence of query terms rarely exceeds 1.

Q=(wq1, wq2, …, wqt) where wqj: inverse document frequencyDi=(di1, di2, …, dit) where dij: term frequency*inverse document frequency

sim Q D w dqj ij

j

t

( , ) ‧

1

Hsin-Hsi Chen 44

Query vs. Document• When non-normalized documents are used, the longer

documents with more assigned terms have a greater chance of matching particular query terms than do the shorter document vectors.

sim Q Diw d

d w

qj ij

j

t

ij qjj

t

j

t( , )

( ) ( )

‧

‧

1

2 2

11

sim Q Diw d

d

qj ij

j

t

ijj

t( , )

( )

‧1

2

1

or

Hsin-Hsi Chen 45

Relevance Feedback

• Terms present in previously retrieved documents that have been identified as relevant to the user’s query are added to the original formulations.

• The weights of the original query terms are altered by replacing the inverse document frequency portion of the weights with term-relevance weights obtained by using the occurrence characteristics of the terms in the previous retrieved relevant and nonrelevant documents of the collection.

Hsin-Hsi Chen 46

Relevance Feedback• Q = (wq1, wq2, ..., wqt)• Di = (di1, di2, ..., dit)• New query may be the following form

Q’ = {wq1, wq2, ..., wqt}+{w’qt+1, w’qt+2, ..., w’qt+m}

• The weights of the newly added terms Tt+1 to Tt+m may consist of a combined term-frequency and term-relevance weight.

Hsin-Hsi Chen 47

Final Indexing

• Identify individual text words.• Use a stop list to delete common words.• Use suffix stripping to produce word stems.• Replace low-frequency terms with thesaurus classes.• Replace high-frequency terms with phrases.• Compute term weights for all single terms, phrases, and th

esaurus classes.• Compare query statements with document vectors.• Identify some retrieved documents as relevant and some as

nonrelevant to the query.

Hsin-Hsi Chen 48

Final Indexing

• Compute term-relevance factors based on available relevance assessments.

• Construct new queries with added terms from relevant documents and term weights based on combined frequency and term-relevance weight.

• Return to step (7).Compare query statements with document vectors ……..

Hsin-Hsi Chen 49

Summary of expected effectiveness of automatic indexing

• Basic single-term automatic indexing -• Use of thesaurus to group related terms in the given topic area

+10% to +20%• Use of automatically derived term associations obtained from

joint term assignments found in sample document collections0% to -10%

• Use of automatically derived term phrases obtained by using co-occurring terms found in the texts of sample collections

+5% to +10%• Use of one iteration of relevant feedback to add new query

terms extracted from previously retrieved relevant documents+30% to +60%

Hsin-Hsi Chen 50

Models

Hsin-Hsi Chen 51

Ranking

• central problem of IR– Predict which documents are relevant and which are

not

• Ranking– Establish an ordering of the documents retrieved

• IR models– Different model provides distinct sets of premises to

deal with document relevance

Hsin-Hsi Chen 52

Information Retrieval Models• Classic Models

– Boolean model• set theoretic• documents and queries are represented as sets of index terms• compare Boolean query statements with the term sets used to identify

document content.

– Vector model• algebraic model• documents and queries are represented as vectors in a t-dimensional space• compute global similarities between queries and documents.

– Probabilistic model• probabilistic• documents and queries are represented on the basis of probabilistic theory• compute the relevance probabilities for the documents of a collection.

Hsin-Hsi Chen 53

Information Retrieval Models(Continued)

• Structured Models– reference to the structure present in written text– non-overlapping list model– proximal nodes model

• Browsing– flat– structured guided– hypertext

Hsin-Hsi Chen 54

Taxonomy of Information Retrieval Models

USER

TASK

Retrieval:Adhoc

Filtering

Browsing

Classic Modelsbooleanvector

probabilistic

Structured Modelsbooleanvector

probabilistic

BrowsingFlat

Structured GuidedHypertext

Set Theoretic

FuzzyExtended Boolean

Algebraic

Generalized VectorLat. Semantic Index

Neural Network

Probabilistic

Inference NetworkBrief Network

Hsin-Hsi Chen 55

Issues of a retrieval system

• Models– boolean– vector– probabilistic

• Logical views of documents– full text– set of index terms

• User task– retrieval– browsing

Hsin-Hsi Chen 56

Combinations of these issues

Index Terms Full TextFull Text+Structure

Retrieval

ClassicSet Theoretic

AlgebraicProbabilistic

Structured

Browsing FlatHypertext

Flat

ClassicSet Theoretic

AlgebraicProbabilistic

Structure GuidedHypertext

USER

TASK

LOGICAL VIEW OF DOCUMENTS

Hsin-Hsi Chen 57

Retrieval: Ad hoc and Filtering

• Ad hoc retrieval– Documents remain relatively static while new queries are

submitted

• Filtering– Queries remain relatively static while new documents come into

the system• e.g., news wiring services in the stock market

– User profile describes the user’s preferences• Filtering task indicates to the user which document might be interested to

him• Which ones are really relevant is fully reserved to the user

– Routing: a variation of filtering• Ranking filtered documents and show this ranking to users

Hsin-Hsi Chen 58

User profile

• Simplistic approach– The profile is described through a set of keywor

ds– The user provides the necessary keywords

• Elaborate approach– Collect information from the user– initial profile + relevance feedback (relevant inf

ormation and nonrelevant information)

Hsin-Hsi Chen 59

Formal Definition of IR Models

• /D, Q, F, R(qi, dj)/– D: a set composed of logical views (or representations)

for the documents in collection

– Q: a set composed of logical views (or representations) for the user information needs

– F: a framework for modeling documents representations, queries, and their relationships

– R(qi, dj): a ranking function which associations a real number with qiQ and dj D

query

Hsin-Hsi Chen 60

Formal Definition of IR Models(continued)

• classic Boolean model– set of documents– standard operations on sets

• classic vector model– t-dimensional vector space– standard linear algebra operations on vector

• classic probabilistic model– sets– standard probabilistic operations, and Bayes’ theorem

Hsin-Hsi Chen 61

Basic Concepts of Classic IR

• index terms (usually nouns): index and summarize• weight of index terms• Definition

– K={k1, …, kt}: a set of all index terms– wi,j: a weight of an index term ki of a document dj

– dj=(w1,j, w2,j, …, wt,j): an index term vector for the document dj

– gi(dj)= wi,j

• assumption– index term weights are mutually independent

wi,j associated with (ki,dj) tells us nothingabout wi+1,j associated with (ki+1,dj)

The terms computer and network in the area of computer networks

Hsin-Hsi Chen 62

Boolean Model

• The index term weight variables are all binary, i.e., wi,j{0,1}

• A query q is a Boolean expression (and, or, not)

• qdnf: the disjunctive normal form for q• qcc: conjunctive components of qdnf

• sim(dj,q): similarity of dj to q– 1: if qcc | (qcc qdnf(ki, gi(dj)=gi(qcc))– 0: otherwise

dj is relevant to q

Hsin-Hsi Chen 63

Boolean Model (Continued)

• Example– q=ka (kb kc)

– qdnf=(1,1,1) (1,1,0) (1,0,0)

(ka kb) (ka kc)= (ka kb kc) (ka kb kc)(ka kb kc) (ka kb kc)= (ka kb kc) (ka kb kc) (ka kb kc)

ka kb

kc

(1,0,0)(1,1,0)

(1,1,1)

Hsin-Hsi Chen 64

Boolean Model (Continued)

• advantage: simple

• disadvantage– binary decision (relevant or non-relevant) witho

ut grading scale– exact match (no partial match)

• e.g., dj=(0,1,0) is non-relevant to q=(ka (kb kc)

– retrieve too few or too many documents

Hsin-Hsi Chen 65

Basic Vector Space Model

• Term vector representation of documents Di=(ai1, ai2, …, ait)queries Qj=(qj1, qj2, …, qjt)

• t distinct terms are used to characterize content.

• Each term is identified with a term vector T.

• t vectors are linearly independent.

• Any vector is represented as a linear combination of the t term vectors.

• The rth document Dr can be represented as a document vector, written as

D a Tr r i

i

t

i

1

Hsin-Hsi Chen 66

Document representation in vector spacea document vector in a two-dimensional vector space

Hsin-Hsi Chen 67

Similarity Measure

• measure by product of two vectorsx • y = |x| |y| cos

• document-query similarity

• how to determine the vector components and term correlations?

D Q a q T Tr s r s i

i j

t

ji j‧ ‧

, 1

D a Tr r i

i

t

i

1

Q q

j

t

s sj jT

1

term vector:document vector:

Hsin-Hsi Chen 68

Similarity Measure (Continued)

• vector components

T T T T

A

D

D

D

a a a

a a a

a a a

t

n

t

t

n n nt

1 2 3

1

2

11 12 1

21 22 2

1 2

Hsin-Hsi Chen 69

Similarity Measure (Continued)

• term correlations Ti • Tj are not availableassumption: term vectors are orthogonal

Ti • Tj =0 (ij) Ti • Tj =1 (i=j)

• Assume that terms are uncorrelated.

• Similarity measurement between documents

sim D Q a qr s r s

i j

t

i j( ),

,

1

sim D D a ar s r s

i j

t

i j( ),

,

1

Hsin-Hsi Chen 70

Sample query-documentsimilarity computation

• D1=2T1+3T2+5T3 D2=3T1+7T2+1T3

Q=0T1+0T2+2T3

• similarity computations for uncorrelated termssim(D1,Q)=2•0+3 •0+5 •2=10sim(D2,Q)=3•0+7 •0+1 •2=2

• D1 is preferred

Hsin-Hsi Chen 71

Sample query-documentsimilarity computation (Continued)

• T1 T2 T3

T1 1 0.5 0T2 0.5 1 -0.2T3 0 -0.2 1

• similarity computations for correlated termssim(D1,Q)=(2T1+3T2+5T3) • (0T1+0T2+2T3 )

=4T1•T3+6T2 •T3 +10T3 •T3 =-6*0.2+10*1=8.8

sim(D2,Q)=(3T1+7T2+1T3) • (0T1+0T2+2T3 )=6T1•T3+14T2 •T3 +2T3 •T3 =-14*0.2+2*1=-0.8

• D1 is preferred

Hsin-Hsi Chen 72

Vector Model

• wi,j: a positive, non-binary weight for (ki,dj)

• wi,q: a positive, non-binary weight for (ki,q)

• q=(w1,q, w2,q, …, wt,q): a query vector, where t is the total number of index terms in the system

• dj= (w1,j, w2,j, …, wt,j): a document vector

Hsin-Hsi Chen 73

Similarity of document dj w.r.t. query q

• The correlation between vectors dj and q

• | q | does not affect the ranking

• | dj | provides a normalization

tj qi

ti ji

ti qiji

j

jj

ww

ww

qd

qdqdsim

12,1

2,

1 ,,

||||),(

Q

dj

cos(dj,q)

Hsin-Hsi Chen 74

document ranking

• Similarity (i.e., sim(q, dj)) varies from 0 to 1.

• Retrieve the documents with a degree of similarity above a predefined threshold(allow partial matching)

Hsin-Hsi Chen 75

term weighting techniques

• IR problem: one of clustering– user query: a specification of a set A of objects– clustering problem: determine which documents are in the set A (r

elevant), which ones are not (non-relevant)– intra-cluster similarity

• the features better describe the objects in the set A• tf factor in vector model

the raw frequency of a term ki inside a document dj

– inter-cluster similarity• the features better distinguish the the objects in the set A from the remaining

objects in the collection C• idf factor (inverse document frequency) in vector model

the inverse of the frequency of a term ki among the documents in the collection

Hsin-Hsi Chen 76

Definition of tf

• N: total number of documents in the system

• ni: the number of documents in which the index term ki appears

• freqi,j: the raw frequency of term ki in the document dj

• fi,j: the normalized frequency of term ki in document dj jll

jiji freq

freqf

,

,, max

Term tl has maximum frequencyin the document dj

(0~1)

Hsin-Hsi Chen 77

Definition of idf and tf-idf scheme

• idfi: inverse document frequency for ki

• wi,j: term-weighting by tf-idf scheme

• query term weight (Salton and Buckley)

ii n

Nidf log

ijiji n

Nfw log,,

iqil

qiqi n

N

freq

freqw log)

max

5.05.0(

,

,,

freqi,q: the raw frequency of the term ki in q

Hsin-Hsi Chen 78

Analysis of vector model

• advantages– its term-weighting scheme improves retrieval

performance– its partial matching strategy allows retrieval of

documents that approximate the query conditions– its cosine ranking formula sorts the documents

according to their degree of similarity to the query

• disadvantages– indexed terms are assumed to be mutually

independently

Hsin-Hsi Chen 79

Probabilistic Model

• Given a query, there is an ideal answer set– a set of documents which contains exactly the

relevant documents and no other

• query process– a process of specifying the properties of an

ideal answer set

• problem: what are the properties?

Hsin-Hsi Chen 80

Probabilistic Model (Continued)

• Generate a preliminary probabilistic description of the ideal answer set

• Initiate an interaction with the user– User looks at the retrieved documents and

decide which ones are relevant and which ones are not

– System uses this information to refine the description of the ideal answer set

– Repeat the process many times.

Hsin-Hsi Chen 81

Probabilistic Principle

• Given a user query q and a document dj in the collection, the probabilistic model estimates the probability that user will find dj relevant

• assumptions– The probability of relevance depends on query and docum

ent representations only– There is a subset of all documents which the user prefers a

s the answer set for the query q

• Given a query, the probabilistic model assigns to each document dj a measure of its similarity to the query

)(

)(

qtotnonrelevandP

qtorelevantdP

j

j

Hsin-Hsi Chen 82

Probabilistic Principle

• wi,j{0,1}, wi,q{0,1}: the index term weight variables are all binary non-relevant

• q: a query which is a subset of index terms• R: the set of documents known to be relevant• R (complement of R): the set of documents

• P(R|dj): the probability that the document dj is relevant to the query q

• P(R|dj): the probability that dj is non-relevant to q

Hsin-Hsi Chen 83

similarity• sim(dj,q): the similarity of the document dj t

o the query q

)|(

)|(),(

j

jj dRP

dRPqdsim (by definition)

)()|(

)()|(),(

RPRdP

RPRdPqdsim

j

jj

(Bayes’ rule)

)|(

)|(),(

RdP

RdPqdsim

j

jj (P(R) and P(R) are the

same for all documents)

)|( RdP j : the probability of randomly selecting the documentdj from the set of R of relevant documents

P(R): the probability that a document randomly selected fromthe entire collection is relevant

Hsin-Hsi Chen 84

t

i i

i

ii

iij

t

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i i

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ii

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RdPqdsim

11

11

1)(

)(

1)(1)(

)(1)(

1

)(1)(

1

)(1)(

)|(

)|(

))|(1()|(

))|(1()|(log)(

)|(

)|(

)|()|(

)|()|(log)(

))|(())|()|((

))|(())|()|((log

))|(())|((

))|(())|((log

))|(())|((

))|(())|((

log

)|(

)|(),(

P(ki|R): the probability that the indexterm ki is present in a document randomly selected from the set R.

P(ki|R): the probability that the indexterm ki is not present in a document randomly selected from the set R.

independence assumption of index terms

Hsin-Hsi Chen 85

))|(

))|(1(log)

))|(1(

)|((log)(

)|(

)|()

)|(

))|(1(log)

))|(1(

)|((log)(

)|(

)|(

))|(1()|(

))|(1()|(log)(

)|(

)|(),(

1

11

11

RkP

RkP

RkP

RkPdg

RkP

RkP

RkP

RkP

RkP

RkPdg

RkP

RkP

RkPRkP

RkPRkPdg

RdP

RdPqdsim

i

i

i

ij

t

ii

t

i i

i

i

i

i

ij

t

ii

t

i i

i

ii

iij

t

ii

j

jj

Problem: where is the set R?

Hsin-Hsi Chen 86

Initial guess

• P(ki|R) is constant for all index terms ki.

• The distribution of index terms among the non-relevant documents can be approximated by the distribution of index terms among all the documents in the collection.

5.0)|( Rkp i

N

nRkP i

i )|(

( 假設 N>>|R|,N|R|)

Hsin-Hsi Chen 87

Initial ranking

• V: a subset of the documents initially retrieved and ranked by the probabilistic model (top r documents)

• Vi: subset of V composed of documents which contain the index term ki

• Approximate P(ki|R) by the distribution of the index term ki among the documents retrieved so far.

• Approximate P(ki|R) by considering that all the non-retrieved documents are not relevant.

V

VRkP i

i )|(

VN

VnRkP ii

i

)|(

Hsin-Hsi Chen 88

Small values of V and Vi

• alternative 1

• alternative 2

1

5.0)|(

1

5.0)|(

VN

VnRkP

V

VRkP

iii

ii

1)|(

1)|(

VNNn

VnRkP

VNn

VRkP

iii

i

ii

i

V

VRkP i

i )|(

VN

VnRkP ii

i

)|(

a problem when V=1 and Vi=0

Hsin-Hsi Chen 89

Analysis of Probabilistic Model

• advantage– documents are ranked in decreasing order of

their probability of being relevant

• disadvantages– the need to guess the initial separation of

documents into relevant and non-relevant sets– do not consider the frequency with which an

index terms occurs inside a document– the independence assumption for index terms

Hsin-Hsi Chen 90

Comparison of classic models

• Boolean model: the weakest classic model

• Vector model is expected to outperform the probabilistic model with general collections (Salton and Buckley)

Hsin-Hsi Chen 91

Alternative Set Theoretic Models-Fuzzy Set Model

• Model– a query term: a fuzzy set– a document: degree of membership in this set– membership function

• Associate membership function with the elements of the class

• 0: no membership in the set• 1: full membership • 0~1: marginal elements of the set

documents

Hsin-Hsi Chen 92

Fuzzy Set Theory

• A fuzzy subset A of a universe of discourse U is characterized by a membership function µA: U[0,1] which associates with each element u of U a number µA(u) in the interval [0,1]– complement:– union:– intersection:

)(1)( uu AA

))(),(max()( uuu BABA

))(),(min()( uuu BABA

a class

a document

Hsin-Hsi Chen 93

Examples

• Assume U={d1, d2, d3, d4, d5, d6}

• Let A and B be {d1, d2, d3} and {d2, d3, d4}, respectively.

• Assume A={d1:0.8, d2:0.7, d3:0.6, d4:0, d5:0, d6:0} and B={d1:0, d2:0.6, d3:0.8, d4:0.9, d5:0, d6:0}

• ={d1:0.2, d2:0.3, d3:0.4, d4:1, d5:1, d6:1}

• ={d1:0.8, d2:0.7, d3:0.8, d4:9, d5:0, d6:0}

• ={d1:0.2, d2:0.6, d3:0.6, d4:0, d5:0, d6:0}

)(1)( uu AA

))(),(max()( uuu BABA

))(),(min()( uuu BABA

Hsin-Hsi Chen 94

Fuzzy Information Retrieval

• basic idea– Expand the set of index terms in the query with

related terms (from the thesaurus) such that additional relevant documents can be retrieved

– A thesaurus can be constructed by defining a term-term correlation matrix c whose rows and columns are associated to the index terms in the document collection

keyword connection matrix

Hsin-Hsi Chen 95

Fuzzy Information Retrieval(Continued)

• normalized correlation factor ci,l between two terms ki and kl (0~1)

• In the fuzzy set associated to each index term ki, a document dj has a degree of membership µi,j

lili

lili nnn

nc

,

,,

)1(1 ,,

jdlk

liji c

where ni is # of documents containing term ki

nl is # of documents containing term kl

ni,l is # of documents containing ki and kl

Hsin-Hsi Chen 96

Fuzzy Information Retrieval(Continued)

• physical meaning– A document dj belongs to the fuzzy set associated to the

term ki if its own terms are related to ki, i.e., i,j=1.

– If there is at least one index term kl of dj which is strongly related to the index ki, then i,j1.

ki is a good fuzzy index

– When all index terms of dj are only loosely related to ki, i,j0.

ki is not a good fuzzy index

Hsin-Hsi Chen 97

Example

• q=(ka (kb kc)=(ka kb kc) (ka kb kc) (ka kb kc)=cc1+cc2+cc3

Da

Db

Dc

cc3cc2

cc1

Da: the fuzzy set of documents associated to the index ka

djDa has a degree of membership a,j > a predefined threshold K

Da: the fuzzy set of documents associated to the index ka

(the negation of index term ka)

Hsin-Hsi Chen 98

Example

))1)(1(1())1(1()1(1

)1(1

,,,,,,,,,

3

1,

,321,

jcjbjajcjbjajcjbja

ijicc

jccccccjq

Query q=ka (kb kc)

disjunctive normal form qdnf=(1,1,1) (1,1,0) (1,0,0)

(1) the degree of membership in a disjunctive fuzzy set is computedusing an algebraic sum (instead of max function) more smoothly(2) the degree of membership in a conjunctive fuzzy set is computedusing an algebraic product (instead of min function)

Recall )(1)( uu AA

Hsin-Hsi Chen 99

Alternative Algebraic Model:Generalized Vector Space Model• independence of index terms

– ki: a vector associated with the index term ki

– the set of vectors {k1, k2, …, kt} is linearly independent• orthogonal:

– The index term vectors are assumed linearly independent but are not pairwise orthogonal in generalized vector space model

– The index term vectors, which are not seen as the basis of the space, are composed of smaller components derived from the particular collection.

0 jkk i for ij

Hsin-Hsi Chen 100

Generalized Vector Space Model• {k1, k2, …, kt}: index terms in a collection• wi,j: binary weights associated with the term-document pair {ki, dj}• The patterns of term co-occurrence (inside documents) can be repre

sented by a set of 2t minterms

• gi(mj): return the weight {0,1} of the index term ki in the minterm mj (1 i t)

m1=(0, 0, …, 0): point to documents containing none of index termsm2=(1, 0, …, 0): point to documents containing the index term k1 onlym3=(0,1,…,0): point to documents containing the index term k2 onlym4=(1,1,…,0): point to documents containing the index terms k1 and k2

…

m2t=(1, 1, …, 1): point to documents containing all the index terms

Hsin-Hsi Chen 101

Generalized Vector Space Model(Continued)

• mi (2t-tuple vector) is associated with minterm mi (t-tuple vector)

• e.g., m4 is associated with m4 containing k1 and k2, and no others

• co-occurrence of index terms inside documents: dependencies among index terms

)1,0,...,0,0(

0...

)0,0,...,1,0(

)0,0,...,0,1(

2

2

1

t

im

jiformm

m

m

j

(the set of mi are pairwise orthogonal)

Hsin-Hsi Chen 102

28,1

27,1

26,1

25,1

88,177,16,155,11

6

cccc

mcmcmcmck

minterm mr mr vectorm1=(0,0,0) m1=(1,0,0,0,0,0,0,0)m2=(0,0,1) m2=(0,1,0,0,0,0,0,0)m3=(0,1,0) m3=(0,0,1,0,0,0,0,0)m4=(0,1,1) m4=(0,0,0,1,0,0,0,0)m5=(1,0,0) m5=(0,0,0,0,1,0,0,0)m6=(1,0,1) m6=(0,0,0,0,0,1,0,0)m7=(1,1,0) m7=(0,0,0,0,0,0,1,0)m8=(1,1,1) m8=(0,0,0,0,0,0,0,1)

t=3

d1 (t1) d11 (t1 t2)d2 (t3) d12 (t1 t3)d3 (t3) d13 (t1 t2)d4 (t1) d14 (t1 t2)d5 (t2) d15 (t1 t2 t3)d6 (t2) d16 (t1 t2)d7 (t2 t3) d17 (t1 t2)d8 (t2 t3) d18 (t1 t2)d9 (t2) d19 (t1 t2 t3)d10 (t2 t3) d20 (t1 t2)

19,115,18,1

20,118,117,116,114,113,111,17,1

12,16,14,11,15,1

wwc

wwwwwwwc

wcwwc

Hsin-Hsi Chen 103

28,2

27,2

24,2

23,2

88,277,24,233,22

4

cccc

mcmcmcmck


t=3


19,215,28,2

20,218,217,216,214,213,211,27,2

10,28,27,24,29,26,25,23,2

wwc

wwwwwwwc

wwwcwwwc

Hsin-Hsi Chen 104


t=3

12,36,310,38,37,34,33,32,32,3

28,3

26,3

24,3

22,3

88,366,34,322,33

4

wcwwwcwwc

cccc

mcmcmcmck

19,315,38,3 wwc


Hsin-Hsi Chen 105


• Determine the index vector ki associated with the index term ki

1)(,2

1)(, ,

,ri ri

ri

mgr

mgrrri

ic

mck

lallformgdgd

jiri

rljlj

wc)()(|

,,

Collect all the vectors mr in which the index term ki is in state 1.

Sum up wi,j associated withthe index term ki and documentdj whose term occurrence pattern coincides with minterm mr

Hsin-Hsi Chen 106


• kikj quantifies a degree of correlation between ki and kj

• standard cosine similarity is adopted

1)(1)(|

,,

rri mgjmgr

rjriji cckk

ii qii

i jij kwqkwd ,,

1)(,2

1)(, ,

,ri ri

ri

mgr

mgrrri

ic

mck

Hsin-Hsi Chen 107

28,3

26,3

24,3

22,3

88,366,34,322,33

4

cccc

mcmcmcmck

8,38,24,34,232

8,38,16,36,131

8,28,17,27,121

cccckk

cccckk

cccckk

28,1

27,1

26,1

25,1

88,177,16,155,11

6

cccc

mcmcmcmck

28,2

27,2

24,2

23,2

88,277,24,233,22

4

cccc

mcmcmcmck

Hsin-Hsi Chen 108

Comparison with Standard Vector Space Model

d1 (t1): (w1,1,0,0) d11 (t1 t2)

d2 (t3): (0,0,w3,2) d12 (t1 t3)

d3 (t3): (0,0,w3,3) d13 (t1 t2)

d4 (t1): (w1,4,0,0) d14 (t1 t2)

d5 (t2): (0,w2,5,0) d15 (t1 t2 t3)

d6 (t2): (0,w2,6,0) d16 (t1 t2)

d7 (t2 t3): (0,w2,7,w3,7) d17 (t1 t2)

d8 (t2 t3): (0,w2,8,w3,8) d18 (t1 t2)

d9 (t2): (0,w2,9,0) d19 (t1 t2 t3)

d10 (t2 t3): (0,w2,10,w3,10) d20 (t1 t2)

Hsin-Hsi Chen 109

Latent Semantic Indexing Model

• representation of documents and queries by index terms– problem 1: many unrelated documents might be

included in the answer set– problem 2: relevant documents which are not

indexed by any of the query keywords are not retrieved

• possible solution: concept matching instead of index term matching– application in cross-language information retrieval

Hsin-Hsi Chen 110

basic idea

• Map each document and query vector into a lower dimensional space which is associated with concepts

• Retrieval in the reduced space may be superior to retrieval in the space of index terms

Hsin-Hsi Chen 111

Definition

• t: the number of index terms in the collection

• N: the total number of documents

• M=(Mij): a term-document association matrix with t rows and N columns

• Mij: a weight wi,j associated with the term-document pair [ki, dj] (e.g., using tf-idf)

Hsin-Hsi Chen 112

Singular Value Decomposition

})()({

:sin

}{

)1(

AQDQQDQQDQAQDQA

iondecompositvaluegular

IQQIQQstRQ

AA

RA

TTTTTTTTT

TTnn

T

nn

where D =

1

2

n

.

.

.0

0diagonal matrix

orthogonal

1 2 … n 0

Hsin-Hsi Chen 113

TTTTTTT

T

TTnn

T

nn

UUDVDUUDVUDVUDVAA

UDVA

iondecompositvaluegular

IVVIUUstRVU

AA

RA

2))(())((

:sin

,,

)2(

where D =

1

2

n

.

.

.0

0diagonal matrix

orthogonal

(AB)T= BT AT

1 2 … n 0

Hsin-Hsi Chen 114

vectorcolumnaqqqqQwhere

QDQQDQAQ

QDQA

in

T

T

:],[ 21

][][ 2121 nn qqqqqqA

1

2

n

.

.

.

0

nnn

nnn

qAqqAqqAq

qqqAqAqAq

222111

221121 ][][

1, 2, …, n 為 A 之 eigenvalues ， qk 為 A 相對於 k 之 eigenvector

Hsin-Hsi Chen 115

Singular Value Decomposition

matrixtermtotermttaMM

matrixdocumenttodocumentNNaMM

DSKM

columnsNandrowstwithmatrixdocumenttermaM

t

t

t

:

:

:

According to

t

t

t

Nt

DSKM

MMfromderivedrseigenvectoofmatrixtheD

MMfromderivedrseigenvectoofmatrixtheK

RM

:

:

IDD

IKKt

t

Hsin-Hsi Chen 116

t

ttt

ttt

t

DSD

DSKKSD

DSKDSK

matrixdocumenttodocumentMM

2

))((

)()(

:

t

ttt

ttt

t

KSK

KSDDSK

DSKDSK

matrixtermtotermMM

2

))((

))((

:

對照 A=QDQT

Q is matrix of eigenvectors of AD is diagonal matrix of singular values

tMMfromderived

rseigenvectoofmatrixtheK :

MMfromderived

rseigenvectoofmatrixtheDt

:得到

),min(,

sin:

Ntrwherevalues

gularofmatrixdiagonalrrS

s < r (Concept space is reduced)

Hsin-Hsi Chen 117

Consider only the s largest singular values of S

1

2

n

.

.

.0

0

1 2 … n 0

The resultant Ms matrix is the matrix of rank s which is closestto the original matrix M in the least square sense.

t

ssss DSKM (s<<t, s<<N)

Hsin-Hsi Chen 118

Ranking in LSI

• query: a pseudo-document in the original M term-document– query is modeled as the document with number

0

– MstMs: the ranks of all documents w.r.t this que

ry

Hsin-Hsi Chen 119

Structured Text Retrieval Models

• Definition– Combine information on text content with information on the document

structure– e.g., same-page(near(‘atomic holocaust’, Figure(label(‘earth’))))

• Expressive power vs. evaluation efficiency – a model based on non-overlapping lists– a model based on proximal nodes

• Terminology– match point: position in the text of a sequence of words that matches the user

query– region: a contiguous portion of the text– node: a structural component of the document (chap, sec, …)

Hsin-Hsi Chen 120

Non-Overlapping Lists

• divide the whole text of each document in non-overlapping text regions (lists)

• example

• Text regions from distinct lists might overlap

L0 Chapter

L1 Sections

L2 Subsections

L3 Subsubsections

indexinglists

a list of all chapters in the document

a list of all sections in the document

a list of all subsections in the document

a list all subsubsections in the document

1 5000

1 3000

Chapter 1

3001 50001.1 1.2

1 1000 1001 3000 3001 50001.1.1 1.1.2 1.2.1

1 500 5011000 1001

Hsin-Hsi Chen 121

Non-Overlapping Lists(Continued)

• Data structure– a single inverted file – each structural component stands as an entry– for each entry, there is a list of text regions as a list

occurrences

• Operations– Select a region which contains a given word– Select a region A which does not contain any other region B

(where B belongs to a list distinct from the list for A)– Select a region not contained within any other region– …

Recall that there is another invertedfile for the words in the text

Hsin-Hsi Chen 122

Inverted Files

• File is represented as an array of indexed records.

Term 1 Term 2 Term 3 Term 4

Record 1 1 1 0 1

Record 2 0 1 1 1

Record 3 1 0 1 1

Record 4 0 0 1 1

Hsin-Hsi Chen 123

Inverted-file process

• The record-term array is inverted (transposed).

Record 1 Record 2 Record 3 Record 4

Term 1 1 0 1 0

Term 2 1 1 0 0

Term 3 0 1 1 1

Term 4 1 1 1 1

Hsin-Hsi Chen 124

Inverted-file process (Continued)

• Take two or more rows of an inverted term-record array, and produce a single combined list of record identifiers.

Query (term2 and term3)1 1 0 00 1 1 1

---------------------------------1 <-- R2

Hsin-Hsi Chen 125

Extensions of Inverted Index Operations(Distance Constraints)

• Distance Constraints– (A within sentence B)

terms A and B must co-occur in a common sentence

– (A adjacent B)terms A and B must occur adjacently in the text

Hsin-Hsi Chen 126


• Implementation– include term-location in the inverted indexes

information: {R345, R348, R350, …}retrieval: {R123, R128, R345, …}

– include sentence-location in the indexes information:

{R345, 25; R345, 37; R348, 10; R350, 8; …}retrieval:

{R123, 5; R128, 25; R345, 37; R345, 40; …}

Hsin-Hsi Chen 127


– include paragraph numbers in the indexessentence numbers within paragraphsword numbers within sentencesinformation: {R345, 2, 3, 5; …}retrieval: {R345, 2, 3, 6; …}

– query examples(information adjacent retrieval)(information within five words retrieval)

– cost: the size of indexes

Hsin-Hsi Chen 128

Model Based on Proximal Nodes

• hierarchical vs. flat indexing structures

Chapter

Sections

Subsections

Subsubsections

…holocaust 10 256 48,324…

paragraphs, pages, lines

…

an inverted list for holocaust

hierarchicalindex

flat index

entries: positions in the text

nodes: position in the text

Hsin-Hsi Chen 129

Model Based on Proximal Nodes(Continued)

• query language– Specification of regular expressions– Reference to structural components by name– Combination– Example

• Search for sections, subsections, or subsubsections which contain the word ‘holocaust’

• [(*section) with (‘holocaust’)]

Hsin-Hsi Chen 130

Model Based on Proximal Nodes(Continued)

• Basic algorithm– Traverse the inverted list for the term ‘holocaust’– For each entry in the list (i.e., an occurrence), search the

hierarchical index looking for sections, subsections, and sub-subsections

• Revised algorithm– For the first entry, search as before– Let the last matching structural component be the innermost

matching component– Verify the innermost matching component also matches the

second entry.• If it does, the larger structural components above it also do.

nearby nodes

Hsin-Hsi Chen 131

Models for Browsing

• Browsing vs. searching– The goal of a searching task is clearer in the

mind of the user than the goal of a browsing task

• Models– Flat browsing– Structure guided browsing– The hypertext model

Hsin-Hsi Chen 132

Models for Browsing

• Flat organization– Documents are represented as dots in a 2-D plan

– Documents are represented as elements in a 1-D list, e.g., the results of search engine

• Structure guided browsing– Documents are organized in a directory, which group

documents covering related topics

• Hypertext model– Navigating the hypertext: a traversal of a directed graph

Hsin-Hsi Chen 133

Trends and Research Issues• Library systems

– Cognitive and behavioral issues oriented particularly at a better understanding of which criteria the users adopt to judge relevance

• Specialized retrieval systems– e.g., legal and business documents– how to retrieve all relevant documents without retrieving a large

number of unrelated documents

• The Web– User does not know what he wants or has great difficulty in

formulating his request– How the paradigm adopted for the user interface affects the ranking– The indexes maintained by various Web search engine are almost

disjoint