Chapter 5: Query Operations Baeza-Yates, 1999 Modern Information Retrieval.

Chapter 5: Query Operations

Baeza-Yates, 1999Modern Information Retrieval

Query Modification

Improving initial query formulation Relevance feedback

• approaches based on feedback information from users Local analysis

• approaches based on information derived from the set of documents initially retrieved (called the local set of documents)

Global analysis• approaches based on global information derived from the

document collection

Relevance Feedback Relevance feedback process

it shields the user from the details of the query reformulation process

it breaks down the whole searching task into a sequence of small steps which are easier to grasp

it provides a controlled process designed to emphasize some terms and de-emphasize others

Two basic techniques Query expansion

• addition of new terms from relevant documents Term reweighting

• modification of term weights based on the user relevance judgement

Vector Space Model Definition

wi,j: the ith term in the vector for document dj

wi,k: the ith term in the vector for query qk

t: the number of unique terms in the data set

t

i

kijikj wwqdsimilarity1

,,),(),,,( ,,2,1 jtjjj wwwd ),,,( ,,2,1 ktkkk wwwq

t

k ktf

tf

itf

tf

ji

idf

idfw

jkk

jk

jkk

ji

1

22}{max

}{max

,

)5.05.0(

)5.05.0(

,

,

,

,

Query Expansion and and Term Reweighting for the Vector Model

Ideal situation CR: set of relevant documents among all documents in the collectio

n

Rocchio (1965, 1971) R: set of relevant documents, as identified by the user among

the retrieved documents S: set of non-relevant documents among the retrieved docu

ments

RjRj Cdj

RCd

j

Ropt d

CNd

Cq

||

1

||

1

Sdj

Rdjm jj

dS

dR

qq||||

Rocchio’s Algorithm Ide_Regular (1971)

Ide_Dec_Hi

Parameters = = =1 >

}|{ SddMaxdqq jjRd

jm j

Sdj

Rdjm jj

ddqq

Probabilistic Model Definition

pi: the probability of observing term ti in the set of relevant documents

qi: the probability of observing term ti in the set of nonrelevant documents

Initial search assumption pi is constant for all terms ti (typically 0.5) qi can be approximated by the distribution of ti in the who

le collection

t

i ii

iiqijij pq

qpwwqdsim

1,, )1(

)1(log),(

iii

i

ii

iii idf

df

N

df

dfN

pq

qpwt

log)(

log)1(

)1(log

Term Reweighting for the Probabilistic Model

Robertson and Sparck Jones (1976) With relevance feedback from user

N: the number of documents in the collectionR: the number of relevant documents for query qni: the number of documents having term ti

ri: the number of relevant documents having term ti

Document Relevance

DocumentIndexing

+

-

+

ri

R-ri

R

N-ni-R+ri

-

ni-ri

N-R

ni

N-ni

N

Initial search assumptionpi is constant for all terms ti (typically 0.5)qi can be approximated by the distribution of ti in the whole collection

With relevance feedback from userspi and qi can be approximated by

hence the term weight is updated by

)(R

rp i

i )(RN

rnq ii

i

t

i i

iqijij n

nNwwqdsim

1,, log),(

t

i iii

iiiqijij rnrR

rRnNrwwqdsim

1,, ))((

)(log),(

Term Reweighting for the Probabilistic Model (cont.)

However, the last formula poses problems for certain small values of R and ri (R=1, ri=0)

Instead of 0.5, alternative adjustments have been propsed

)1

5.0(

R

rp i

i )1

5.0(

RN

rnq ii

i

)1

(

R

rp N

ni

i

i

)1

(

RN

rnq N

nii

i

i

Term Reweighting for the Probabilistic Model (Cont.)

Characteristics Advantage

• the term reweighting is optimal under the asumptions of • term independence • binary document indexing (wi,q {0,1} and wi,j {0,1})

Disadvantage• no query expansion is used• weights of terms in the previous query formulations are also dis

regarded• document term weights are not taken into account during the f

eedback loop

Term Reweighting for the Probabilistic Model (Cont.)

Evaluation of relevance feedback

Standard evaluation method is not suitable (i.e., recall-precision) because the relevant documents used to r

eweight the query terms are moved to higher ranks. The residual collection method

the set of all documents minus the set of feedback documents provided by the user

because highly ranked documents are removed from the collection, the recall-precision figures for tend to be lower than the figures for the original query

as a basic rule of thumb, any experimentation involving relevance feedback strategies should always evaluate recall-precision figures relative to the residual collection

mq

q

Automatic Local Analysis

Definition local document set Dl : the set of documents retrieved by a q

uery local vocabulary Vl : the set of all distinct words in Dl

stemed vocabulary Sl : the set of all distinct stems derived from Vl

Building local clusters association clusters metric clusters scalar clusters

Association Clusters

Idea co-occurrence of stems (or terms) inside documents

• fu,j: the frequency of a stem ku in a document dj

local association cluster for a stem ku

• the set of k largest values c(ku, kv) given a query q, find clusters for the |q| query terms normalized form

||

1,,),(

D

jjvjuvu ffkkc

),(),(),(

),(),(

vuvvuu

vuvu kkckkckkc

kkckks

Metric Clusters

Idea consider the distance between two terms in the same cluste

r Definition

V(ku): the set of keywords which have the same stem form as ku

distance r(ki, kj)=the number of words between term ku and kv

normalized form

)( )( ),(

1),(

u vkVi kVj jivu kkr

kkc

|)(||)(|

),(),(

vu

vuvu kVkV

kkckks

Scalar Clusters

Idea two stems with similar neighborhoods have some synony

mity relationships Definition

cu,v=c(ku, kv) vectors of correlation values for stem ku and kv

scalar association matrix

scalar clusters• the set of k largest values of scalar association

),,,( ,2,1, tuuuu cccs ),,,( ,2,1, tvvvv cccs

||||,

vu

vuvu

ss

ssS

Automatic Global Analysis

A thesaurus-like structure Short history

Until the beginning of the 1990s, global analysis was considered to be a technique which failed to yield consistent improvements in retrieval performance with general collections

This perception has changed with the appearance of modern procedures for global analysis

Query Expansion based on a Similarity Thesaurus

Idea by Qiu and Frei [1993] Similarity thesaurus is based on term to term relationships rath

er than on a matrix of co-occurrence Terms for expansion are selected based on their similarity to the

whole query rather than on their similarities to individual query terms

Definition N: total number of documents in the collection t: total number of terms in the collection tfi,j: occurrence frequency of term ki in the document dj

tj: the number of distinct index terms in the document dj

itfj : the inverse term frequency for document dj

jj t

titf log

Similarity Thesaurus Each term is associated with a vector

where wi,j is a weight associated to the index-document pair

The relationship between two terms ku and kv is

Note that this is a variation of the correlation measure used for computing scalar association matrices

),,,( ,2,1, Niii wwwki

N

k ktf

tf

jtf

tf

ji

itf

itfw

kik

ki

kik

ji

1

22}{max

}{max

,

)5.05.0(

)5.05.0(

,

,

,

,

N

jjvjuvuvu wwkkc

1,,,

Term weighting vs. Term concept space

tfij

Term ki

Doc dj tfijTerm ki

Doc dj

t

k ktf

tf

itf

tf

ji

idf

idfw

jkk

jk

jkk

ji

1

22}{max

}{max

,

)5.05.0(

)5.05.0(

,

,

,

,

N

k ktf

tf

jtf

tf

ji

itf

itfw

kik

ki

kik

ji

1

22}{max

}{max

,

)5.05.0(

)5.05.0(

,

,

,

,

Query Expansion Procedure with Similarity Thesaurus

1. Represent the query in the concept space by using the representation of the index terms

2. Compute the similarity sim(q,kv) between each term kv and the whole query

3. Expand the query with the top r ranked terms according to sim(q,kv)

uqk

kwqu

qu

,

vuQk

quvqk

uquvv cwkkwkqkqsimuu

,,,),(

qk qu

vqv

uw

kqsimw

,',

),(

Example of Similarity Thesaurus

The distance of a given term kv to the query centroid QC might be quite distinct from the distances of kv to the individual query terms

ka kb

ki

kj

kv

QC

QC={ka ,kb}

Query Expansion based on a Similarity Thesaurus

A document dj is represented term-concept space by

If the original query q is expanded to include all the t index terms, then the similarity sim(q, dj) between the document dj and the query q can be computed as

• which is similar to the generalized vector space model

jv u

jvu

dkvu

qkqujvj

dkvjv

qkuquj

cwwdqsim

kwkwdqsim

,,,

,,

),(

),(

jv dk

vjvj kwd ,

Query Expansion based on a Statistical Thesaurus

Idea by Crouch and Yang (1992) Use complete link algorithm to produce small and

tight clusters Use term discrimination value to select terms for

entry into a particular thesaurus class Term discrimination value

A measure of the change in space separation which occurs when a given term is assigned to the document collection

Term Discrimination Value Terms

good discriminators: (terms with positive discrimination values)• index terms

indifferent discriminators: (near-zero discrimination values)• thesaurus class

poor discriminators: (negative discrimination values)• term phrases

Document frequency dfk dfk >n/10: high frequency term (poor discriminators) dfk <n/100: low frequency term (indifferent discriminators) n/100 dfk n/10: good discriminator

Statistical Thesaurus

Term discrimination value theory the terms which make up a thesaurus class must be

indifferent discriminators The proposed approach

cluster the document collection into small, tight clusters A thesaurus class is defined as the intersection of all

the low frequency terms in that cluster documents are indexed by the thesaurus classes the thesaurus classes are weighted by

||

||

1 ,

C

wwt

C

i CiC

Discussion

Query expansion useful little explored technique

Trends and research issues The combination of local analysis, global analysis,

visual displays, and interactive interfaces is also a current and important research problem