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CS 430 / INFO 430 Information Retrieval. Lecture 11 Latent Semantic Indexing Extending the Boolean Model. Course Administration. Assignment 1 If you have questions about your grading, send me email.
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CS 430 / INFO 430 Information Retrieval Lecture 11 Latent Semantic Indexing Extending the Boolean Model
Course Administration Assignment 1 If you have questions about your grading, send me email. The following are reasonable requests: the wrong files were graded, points were added up wrongly, comments are unclear, etc. We are not prepared to argue over details of judgment. If you ask for a regrade, the final grade may be lower than the original!
Course Administration Assignment 2 The assignment has been posted. The test data is being checked. Look for changes before Saturday evening.
Course Administration Midterm Examination Wednesday, October 14, 7:30 to 9:00 p.m., Upson B17. Open book. Laptop computers may be used for lecture slides, notes, readings, etc., but no network connections during the examination. A sample examination and discussion of the solution will be posted to the Web site.
CS 430 / INFO 430 Information Retrieval Latent Semantic Indexing
Latent Semantic Indexing Objective Replace indexes that use sets of index terms by indexes that use concepts. Approach Map the term vector space into a lower dimensional space, using singular value decomposition. Each dimension in the new space corresponds to a latent concept in the original data.
Deficiencies with Conventional Automatic Indexing Synonymy: Various words and phrases refer to the same concept (lowers recall). Polysemy: Individual words have more than one meaning (lowers precision) Independence: No significance is given to two terms that frequently appear together
Example Query: "IDF in computer-based information look-up" Index terms for a document:access, document, retrieval, indexing How can we recognize that informationlook-up is related to retrieval and indexing? Conversely, if information has many different contexts in the set of documents, how can we discover that it is an unhelpful term for retrieval?
Technical Memo Example: Titles c1 Human machine interface for Lab ABC computer applications c2 A survey of user opinion of computer system response time c3 The EPS user interface management system c4 System and humansystem engineering testing of EPS c5 Relation of user-perceived responsetime to error measurement m1 The generation of random, binary, unordered trees m2 The intersection graph of paths in trees m3 Graph minors IV: Widths of trees and well-quasi-ordering m4 Graph minors: A survey
Technical Memo Example: Terms and Documents TermsDocuments c1 c2 c3 c4 c5 m1 m2 m3 m4 human 1 0 0 1 0 0 0 0 0 interface 1 0 1 0 0 0 0 0 0 computer 1 1 0 0 0 0 0 0 0 user 0 1 1 0 1 0 0 0 0 system 0 1 1 2 0 0 0 0 0 response 0 1 0 0 1 0 0 0 0 time 0 1 0 0 1 0 0 0 0 EPS 0 0 1 1 0 0 0 0 0 survey 0 1 0 0 0 0 0 0 1 trees 0 0 0 0 0 1 1 1 0 graph 0 0 0 0 0 0 1 1 1 minors 0 0 0 0 0 0 0 1 1
Technical Memo Example: Query Query: Find documents relevant to "human computer interaction" Simple Term Matching: Matches c1, c2, and c4 Misses c3 and c5
The index term vector space t3 The space has as many dimensions as there are terms in the word list. d1 d2 t2 t1
Models of Semantic Similarity Proximity models: Put similar items together in some space or structure • Clustering (hierarchical, partition, overlapping). Documents are considered close to the extent that they contain the same terms. Most then arrange the documents into a hierarchy based on distances between documents. [Covered later in course.] • Factor analysis based on matrix of similarities between documents (single mode). • Two-mode proximity methods. Start with rectangular matrix and construct explicit representations of both row and column objects.
Selection of Two-mode Factor Analysis Additional criterion: Computationally efficient O(N2k3) N is number of terms plus documents k is number of dimensions
Figure 1 • term document query --- cosine > 0.9
Mathematical concepts Singular Value Decomposition Define X as the term-document matrix, with t rows (number of index terms) and d columns (number of documents). There exist matrices T, S and D', such that: X = T0S0D0' T0 and D0 are the matrices of left and right singular vectors T0 and D0 have orthonormal columns S0 is the diagonal matrix of singular values
Dimensions of matrices t x d t x m m x m m x d S0 D0' X = T0 m is the rank of X< min(t, d)
Reduced Rank ~ ~ Diagonal elements of S0 are positive and decreasing in magnitude. Keep the first k and set the others to zero. Delete the zero rows and columns of S0 and the corresponding rows and columns of T0 and D0. This gives: X X = TSD' Interpretation If value of k is selected well, expectation is that X retains the semantic information from X, but eliminates noise from synonymy,and recognizes dependence. ^ ^
Selection of singular values t x d t x k k x k k x d S D' ^ = X T k is the number of singular values chosen to represent the concepts in the set of documents. Usually, k« m.
Comparing Two Terms ^ The dot product of two rows of X reflects the extent to which two terms have a similar pattern of occurrences. ^ ^ XX' = TSD'(TSD')' = TSD'DS'T' =TSS'T Since D is orthonormal = TS(TS)' To calculate thei, jcell, take the dot product between the i and j rows ofTS Since S is diagonal, TS differs from T only by stretching the coordinate system
Comparing Two Documents ^ The dot product of two columns of X reflects the extent to which two columns have a similar pattern of occurrences. ^ ^ X'X = (TSD')'TSD' = DS(DS)' To calculate thei, jcell, take the dot product between the i and j columns ofDS. Since S is diagonal DS differs from D only by stretching the coordinate system
Comparing a Term and a Document Comparison between a term and a document is the value of an individual cell of X. X = TSD' = TS(DS)' where S is a diagonal matrix whose values are the square root of the corresponding elements of S. ^ ^ - - -
Technical Memo Example: Query Terms Query xq human 1 interface 0 computer 0 user 0 system 1 response 0 time 0 EPS 0 survey 0 trees 1 graph 0 minors 0 Query: "humansystem interactions on trees" In term-document space, a query is represented by xq, a t x 1 vector. In concept space, a query is represented by dq, a 1 x k vector.
Comparing a Query and a Document A query can be expressed as a vector in the term-document vector space xq. xqi= 1 if term i is in the query and 0 otherwise. Let pqj be the inner product of the queryxqwith document dj in the term-document vector space. pqj is the jth element in the product of xq'X. ^
Comparing a Query and a Document ^ X [pq1... pqj ... pqt] = [xq1 xq2 ... xqt] document dj is column j of X ^ inner product of query q with document dj query ^ pq' = xq'X = xq'TSD' = xq'T(DS)' similarity(q, dj) = cosine of angle is inner product divided by lengths of vectors pqj |xq| |dj| Revised October 6, 2004
Comparing a Query and a Document In the reading, the authors treat the query as a pseudo-document in the concept space dq: dq = xq'TS-1 To compare a query against document j, they extend the method used to compare document i with document j. Take the jth element of the product of: dqS and(DS)' This is the jth element of product of: xq'T (DS)' which is the same expression as before. Note that dq is a row vector. Revised October 6, 2004
Experimental Results Deerwester, et al. tried latent semantic indexing on two test collections, MED and CISI, where queries and relevant judgments available. Documents were full text of title and abstract. Stop list of 439 words (SMART); no stemming, etc. Comparison with: (a) simple term matching, (b) SMART, (c) Voorhees method.
CS 430 / INFO 430 Information Retrieval Extending the Boolean Model
Boolean Diagram not (A or B) A and B A B A or B
Problems with the Boolean model Counter-intuitive results: Query q = A and B and C and D and E Document d has terms A, B, C and D, but not E Intuitively, d is quite a good match for q, but it is rejected by the Boolean model. Query q = A or B or C or D or E Document d1 has terms A, B, C,D and E Document d2 has term A, but not B, C,D or E Intuitively, d1 is a much better match than d2, but the Boolean model ranks them as equal.
Problems with the Boolean model (continued) Boolean is all or nothing • Boolean model has no way to rank documents. • Boolean model allows for no uncertainty in assigning index terms to documents. • The Boolean model has no provision for adjusting the importance of query terms.
Boolean model as sets d is either in the set A or not in A. d A
Extending the Boolean model Term weighting • Give weights to terms in documents and/or queries. • Combine standard Boolean retrieval with vector ranking of results Fuzzy sets • Relax the boundaries of the sets used in Boolean retrieval
Ranking methods in Boolean systems SIRE (Syracuse Information Retrieval Experiment) Term weights • Add term weights to documents Weights calculated by the standard method of term frequency * inverse document frequency. Ranking • Calculate results set by standard Boolean methods • Rank results by vector distances
Relevance feedback in SIRE SIRE (Syracuse Information Retrieval Experiment) Relevance feedback is particularly important with Boolean retrieval because it allow the results set to be expanded • Results set is created by standard Boolean retrieval • User selects one document from results set • Other documents in collection are ranked by vector distance from this document
Boolean model as fuzzy sets d is more or less in A. d A
Basic concept • A document has a term weight associated with each index term. The term weight measures the degree to which that term characterizes the document. • Term weights are in the range [0, 1]. (In the standard Boolean model all weights are either 0 or 1.) • For a given query, calculate the similarity between the query and each document in the collection. • This calculation is needed for every document that has a non-zero weight for any of the terms in the query.
MMM: Mixed Min and Max model Fuzzy set theory dAis the degree of membership of an element to set A intersection (and) dAB = min(dA, dB) union (or) dAB = max(dA, dB)
MMM: Mixed Min and Max model Fuzzy set theory example standard fuzzy set theory set theory dA1 1 0 0 0.5 0.5 0 0 dB 1 0 1 0 0.7 0 0.7 0 and dAB1 0 0 0 0.5 0 0 0 or dAB 1 1 1 0 0.7 0.5 0.7 0
MMM: Mixed Min and Max model Terms: A1, A2, . . . , An DocumentD, with index-term weights: dA1, dA2, . . . , dAn Qor = (A1or A2or . . . or An) Query-document similarity: S(Qor, D) = Cor1 * max(dA1, dA2,.. , dAn) + Cor2 * min(dA1, dA2,.. , dAn) where Cor1 + Cor2 = 1
MMM: Mixed Min and Max model Terms: A1, A2, . . . , An DocumentD, with index-term weights: dA1, dA2, . . . , dAn Qand = (A1and A2and . . . and An) Query-document similarity: S(Qand, D) = Cand1 * min(dA1,.. , dAn) + Cand2 * max(dA1,.. , dAn) where Cand1 + Cand2 = 1
MMM: Mixed Min and Max model Experimental values: Cand1 in range [0.5, 0.8] Cor1 > 0.2 Computational cost is low. Retrieval performance much improved.
Other Models Paice model The MMM model considers only the maximum and minimum document weights. The Paice model takes into account all of the document weights. Computational cost is higher than MMM. P-norm model DocumentD, with term weights: dA1, dA2, . . . , dAn Query terms are given weights, a1, a2, . . . ,an Operators have coefficients that indicate degree of strictness Query-document similarity is calculated by considering each document and query as a point in n space.
Test data CISI CACM INSPEC P-norm 79 106 210 Paice 77 104 206 MMM 68 109 195 Percentage improvement over standard Boolean model (average best precision) Lee and Fox, 1988
Reading E. Fox, S. Betrabet, M. Koushik, W. Lee, Extended Boolean Models, Frake, Chapter 15 Methods based on fuzzy set concepts