Chapter 5' Query Operations

1
Chapter 5. Query Operations

• Wang Jimin
• Oct. 24

2

• Formulating ones information need is difficult.
• Good way initial query formulation, and then
  query reformulation.
• Query Expansion Expanding the original query
  with new terms
• Term Reweighting Reweighting the term in the
  expanded query

3
Outline

• User Relevance Feedback
• Automatic Local Analysis
• Automatic Global Analysis

4
5.2 User Relevance Feedback

• Query Expansion and Term Reweighting for the
  Vector Model
• Term Reweighting for the Probabilistic Model
• A Variant of Probabilistic Term Reweighting
• Evaluation of Relevance Feedback Strategies

5
5.2.1 Query Expansion and Term Reweighting for
the Vector Model

• Basic idea Reformulate the query such that it
  gets closer to the term-weight vector space of
  the relevant documents
• Some symbols for a given query, retrieved
  documents DrDn. Let Cr set of relevant
  documents in the collection D.
• Their relations can be represented as follow.

6
Relationship
Dr
D
Cr
Dn
7
Formula

• If Cr is known in advance, then the best query
  will be represented P119 (5.1).
• According to the user feedback, we get the
  modified query q_m which can be written in three
  ways, i.e. P119 middle.

8

• Three techniques above yield similar results.
• Use a positive feedback strategy only r0
• Advantage simplicity and good results
• Disadvantage no optimality criterion

9
5.2.2 Term Reweighting for the Probabilistic
Model

• sim(dj,q) ? wiq wij (log
  P(ki R) log P(ki ?R) ) P(?ki
  R) P(?ki ?R)
• Probabilities P(ki R) and P(ki ?R) ?
• Estimates based on assumptions
• P(ki R) 0.5
• P(ki ?R) ni N where
  ni is the number of docs that contain ki
• Use this initial guess to retrieve an initial
  ranking
• Improve upon this initial ranking

10

• Let
• Dr set of relevent docs judged by the users
• Dr,i subset of Dr contained ki
• Reevaluate estimates
• P(ki R) Dr,i Dr
• P(ki ?R) ni - Dr,i N - Dr

11

• Some small adjustment factor could be used in
  the computing formula. 0.5, ni/N
• Advantage term rewighting is optimal under
  probabilistic model
• Disadvantage no query expansion.

12
5.2.3 A Variant of Probabilistic Term Reweighting

• In 1983, Croft extended this weighting Scheme
  the initial query and the feedback query use
  distinct formulations.
• The probabilistic formula includes
  within-document frequency weights.
• some modified formula list on P122.

13
5.2.4 Evaluation of Relevance Feedback Strategies

• Simple approach compare the two recall-precision
  figures for the query q and the modified query
  q_m. But the evaluation is unrealistic since the
  user has pointed them as relevant documents.
• Another approach evaluate the performance by
  considering only the residual collection. But the
  search results may be worse because of the high
  ranked documents moving from the collection.

14
5.3 Automatic Local Analysis

• 5.3.1 Query Expansion Through Local Clustering
• done by Attar and Fraenkel in 1977 
• 5.3.2 Query Expansion Through Local Context
  Analysis
• combine techniques from local and global
  analysis, done by Xu and Croft in 1996

15
5.3.1 Query Expansion Through Local Clustering

• Basic idea build a association matrix to
  quantify the term correlations
• Some symbols
• V(s) grammatical variants of a stem s
• D_l retrieved documents for a given query
  q
• V_l set of distinct words in D_l
• S_l set of distinct stems in V_l

16
Association Clusters

• Based on the co-occurrence of stems inside
  documents
• Definition an association matrix m(m_ij) with
  S_l rows and D_l columns, m_ijf_ij, the
  frequency of a stem s_i in a doc d_j, then
  smmt is a local stem-stem association matrix.
  s_ij can be expressed by c_u,v Sum_(d_j \in D_l)
  f_s_u,j f_s_v,j

17

• S_u,v can be normalized, i.e. P125 (5.7)
• Definition Consider the u-th row in matrix s,
  take n largest values s_u,v and get S_u(n) ,
  called it a local association cluster around the
  stems S_u.
• Instead of stem, using keywords is similar.

18
Metric Clusters

• Consider the distance r(ki, kj) between the term
  ki and kj
• Metric correlation c_u,v of stem s_u and stem
  s_v can be expressed as
• c_u,vsum_ki\inV(s_u) sum_kj\inV(s_v)
  1/r(ki,kj)
• Let s_u,vc_u,v, get a stem-stem metric
  correlation metrix

19
Scalar Clusters

• Basic idea two stems with similar neighborhoods
  have some synonymity relationship
• Use a scalar measure to compare two stems
  vectors s_u(n) and s_v(n)

20
Interactive Search Formulation

• Neighbor stems have a synonymity relationship,
  they are not necessarily synonyms in the
  grammatical sense
• Query expansion neighbor stems by using
  normalized, unnormalized clusters or merging the
  two clusters.

21
5.3.2 Query Expansion Through Local Context
Analysis

• Global analysis Terms as concepts, thesaurus
  as a concept relation structure.
• Use thesaurus to do Query expansion, and
  thesaurus can be used as a browsing tool.
• Instead of simple keywords, concepts (noun
  groups) are introduced. Query is a concept, not
  individual terms

22
Local Context Analysis procedure

• Step1. Retrieve the top n ranked passages using
  the original query,
• Step 2. Compute sim(c,q), (a detail formula, see
  P130 )
• Step 3. Add the top m ranked concepts to the
  query q

23
Automatic Global Analysis

• Motivation
• Methods of local analysis extract information
  from local set of documents retrieved to expand
  the query
• An alternative is to expand the query using
  information from the whole set of documents
• Until the beginning of the 1990s this techniques
  failed to yield consistent improvements in
  retrieval performance
• Now, with moderns variants, some times based in
  thesaurus, this perception has changed

24
Automatic global Analysis

• There are two modern variants based on a
  thesaurus-like structure built using all
  documents in collection
• Query Expansion based on a Similarity Thesaurus
• Query Expansion based on a Statistical Thesaurus

25
Similarity Thesaurus

• The similarity thesaurus is based on term to term
  relationships rather than on a matrix of
  co-occurrence.
• This relationship are not derived directly from
  co-occurrence of terms inside documents.
• They are obtained by considering that the terms
  are concepts in a concept space.
• In this concept space, each term is indexed by
  the documents in which it appears.
• Terms assume the original role of documents while
  documents are interpreted as indexing elements

26
Similarity Thesaurus

• The following definitions establish the proper
  framework
• t number of terms in the collection
• N number of documents in the collection
• fi,j frequency of occurrence of the term ki in
  the document dj
• tj vocabulary of document dj
• itfj inverse term frequency for document dj

27
Similarity Thesaurus

• Inverse term frequency for document dj
• To ki is associated a vector

28
Similarity Thesaurus

• where wi,j is a weight associated to
  index-document pairki,dj. These weights are
  computed as follows

29
Similarity Thesaurus

• The relationship between two terms ku and kv is
  computed as a correlation factor cu,v given by
• The global similarity thesaurus is built through
  the computation of correlation factor Cu,v for
  each pair of indexing terms ku,kv in the
  collection

30
Similarity Thesaurus

• This computation is expensive
• Global similarity thesaurus has to be computed
  only once and can be updated incrementally

31
Query Expansion based on a Similarity Thesaurus

• Query expansion is done in three steps as
  follows
• Represent the query in the concept space used for
  representation of the index terms
• Based on the global similarity thesaurus, compute
  a similarity sim(q,kv) between each term kv
  correlated to the query terms and the whole query
  q.
• Expand the query with the top r ranked terms
  according to sim(q,kv)

32
Query Expansion - step one

• To the query q is associated a vector q in the
  term-concept space given by
• where wi,q is a weight associated to the
  index-query pairki,q

33
Query Expansion - step two

• Compute a similarity sim(q,kv) between each term
  kv and the user query q
• where cu,v is the correlation factor

34
Query Expansion - step three

• Add the top r ranked terms according to sim(q,kv)
  to the original query q to form the expanded
  query q
• To each expansion term kv in the query q is
  assigned a weight wv,q given by
• The expanded query q is then used to retrieve
  new documents to the user

35
Query Expansion Sample

• Doc1 D, D, A, B, C, A, B, C
• Doc2 E, C, E, A, A, D
• Doc3 D, C, B, B, D, A, B, C, A
• Doc4 A
• c(A,A) 10.991
• c(A,C) 10.781
• c(A,D) 10.781
• ...
• c(D,E) 10.398
• c(B,E) 10.396
• c(E,E) 10.224

36
Query Expansion Sample

• Query q A E E
• sim(q,A) 24.298
• sim(q,C) 23.833
• sim(q,D) 23.833
• sim(q,B) 23.830
• sim(q,E) 23.435
• New query q A C D E E
• w(A,q') 6.88
• w(C,q') 6.75
• w(D,q') 6.75
• w(E,q') 6.64

37
Query Expansion Based on a Global Statistical
Thesaurus

• Global thesaurus is composed of classes which
  group correlated terms in the context of the
  whole collection
• Such correlated terms can then be used to expand
  the original user query
• This terms must be low frequency terms
• However, it is difficult to cluster low frequency
  terms
• To circumvent this problem, we cluster documents
  into classes instead and use the low frequency
  terms in these documents to define our thesaurus
  classes.
• This algorithm must produce small and tight
  clusters.

38
Complete link algorithm

• This is document clustering algorithm with
  produces small and tight clusters
• Place each document in a distinct cluster.
• Compute the similarity between all pairs of
  clusters.
• Determine the pair of clusters Cu,Cv with the
  highest inter-cluster similarity.
• Merge the clusters Cu and Cv
• Verify a stop criterion. If this criterion is not
  met then go back to step 2.
• Return a hierarchy of clusters.
• Similarity between two clusters is defined as the
  minimum of similarities between all pair of
  inter-cluster documents

39
Selecting the terms that compose each class

• Given the document cluster hierarchy for the
  whole collection, the terms that compose each
  class of the global thesaurus are selected as
  follows
• Obtain from the user three parameters
• TC Threshold class
• NDC Number of documents in class
• MIDF Minimum inverse document frequency

40
Selecting the terms that compose each class

• Use the parameter TC as threshold value for
  determining the document clusters that will be
  used to generate thesaurus classes
• This threshold has to be surpassed by sim(Cu,Cv)
  if the documents in the clusters Cu and Cv are to
  be selected as sources of terms for a thesaurus
  class

41
Selecting the terms that compose each class

• Use the parameter NDC as a limit on the size of
  clusters (number of documents) to be considered.
• A low value of NDC might restrict the selection
  to the smaller cluster Cuv

42
Selecting the terms that compose each class

• Consider the set of document in each document
  cluster pre-selected above.
• Only the lower frequency documents are used as
  sources of terms for the thesaurus classes
• The parameter MIDF defines the minimum value of
  inverse document frequency for any term which is
  selected to participate in a thesaurus class

43
Query Expansion based on a Statistical Thesaurus

• Use the thesaurus class to query expansion.
• Compute an average term weight wtc for each
  thesaurus class C

44
Query Expansion based on a Statistical Thesaurus

• wtc can be used to compute a thesaurus class
  weight wc as

45
Query Expansion Sample
Doc1 D, D, A, B, C, A, B, C Doc2 E, C, E, A,
A, D Doc3 D, C, B, B, D, A, B, C, A Doc4 A
q A E E
sim(1,3) 0.99 sim(1,2) 0.40 sim(1,2)
0.40 sim(2,3) 0.29 sim(4,1) 0.00 sim(4,2)
0.00 sim(4,3) 0.00
idf A 0.0 idf B 0.3 idf C 0.12 idf D
0.12 idf E 0.60

• TC 0.90 NDC 2.00 MIDF 0.2

q'A B E E
46
Query Expansion based on a Statistical Thesaurus

• Problems with this approach
• initialization of parameters TC,NDC and MIDF
• TC depends on the collection
• Inspection of the cluster hierarchy is almost
  always necessary for assisting with the setting
  of TC.
• A high value of TC might yield classes with too
  few terms

47
5.4 Conclusion

• Thesaurus is a efficient method to expand queries
• The computation is expensive but it is executed
  only once
• Query expansion based on similarity thesaurus may
  use high term frequency to expand the query
• Query expansion based on statistical thesaurus
  need well defined parameters

48
5.5 Trends and research Issues

• Graphical interfaces display the docs as points a
  2D or 3D
• Build a thesaurus to get a hierarchy of concepts,
  like Yahoo!
• Combination of several techniques is also current
  and important research problem for MIR

49
Chapter 5. Query Operations

• User Relevance Feedback
• Automatic Local Analysis
• Automatic Global Analysis

50

• Thank you !