Latent Semantic Analysis

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1 Latent Semantic Analysis Adapted from: (from Melanie Martin) and (from Thomas Hoffman)

2 What is it? statistical method for automatic indexing and retrieval that attempts to solve the major problems of the current technology Intended to uncover latent semantic structure in the data that is hidden Creates a semantic space wherein terms and documents that are associated are placed near one another

3 Searching & Finding " What is by far the most popular portal to information? Site Search Web for Organizations Search News search Search in Portals

4 Ad Hoc Retrieval Magic: Identify relevant documents based on short, ambiguous, and incomplete query

5 The Problem (historical context) Information Retrieval in the 1980s Given a collection of documents: retrieve documents that are relevant to a given query Match terms in documents to terms in query Vector space method

6 Document-Term Matrix D = Document collection W = Lexicon/Vocabulary intelligence w j Texas Instruments said it has developed the first 32-bit computer chip designed specifically for artificial intelligence applications [...] d i d i = X term weighting t Document-Term Matrix D d 1... d i... d I W w 1... w j... w J

7 A 100 Million ths of a Typical Document-Term Matrix Typical: Number of documents 1Million Vocabulary 100,000 Sparseness < 0.1 % Fraction depicted 1e

8 The Problem Example: Vector Space Model (from Lillian Lee) auto engine bonnet tyres lorry boot car emissions hood make model trunk make hidden Markov model emissions normalize Synonymy Polysemy Will have small cosine but are related Will have large cosine but not truly related

9 The Problem Two problems that arose using the vector space model: synonymy: many ways to refer to the same object, e.g. car and automobile leads to poor recall polysemy: most words have more than one distinct meaning, e.g.model, python, chip leads to poor precision

10 Query= IDF in computer-based information look-up

11 Robust Information Retrieval Beyond Keyword-based Search Vocabulary Mismatch Problem different people using different vocabulary to describe the same concept matching queries and documents based on keywords is insufficient query labour immigrants Germany match query German job market for immigrants? query foreign workers in Germany? query German green card G. W. Furnas, T. K. Landauer, L. M. Gomez, S. T. Dumais, The Vocabulary Problem in Human-System Communication: an Analysis and a Solution, Bell Communications Research, 1987?

12 Challenges Compactness: few search terms Variability: Synonyms and semantically Average number of search terms per query = 2.5 related terms, expressions, writing styles, etc. Ambiguity: Terms with multiple senses (Source: Spink et al.: From E-sex to E-commerce: (polysems), Web search z.b. changes, Java, IEEE jaguar, Computer, bank, March 2002 head )

13 Latent Structure Given a matrix that encodes data, e.g. co-occurrence counts Is there a simpler way to explain entries? There might be a latent structure underlying the data. How can we reveal or discover this structure?

14 Matrix Decomposition Common approach: approximately factorize matrix approximation left factor right factor Factors are typically constrained to be thin reduction factors = latent structure

15 Latent Semantic Analysis Perform a low-rank approximation of document-term matrix (typical rank ) General idea Map documents (and terms) to a low-dimensional representation. Design a mapping such that the low-dimensional space reflects semantic associations (latent semantic space). Compute document similarity based on the inner product in the latent semantic space Goals Similar terms map to similar location in low dimensional space Noise reduction by dimension reduction M. Berry, S. Dumais, and G. O'Brien. Using linear algebra for intelligent information retrieval. SIAM Review, 37(4): , 1995.

16 Some History Latent Semantic Indexing was developed at Bellcore (now Telcordia) in the late 1980s (1988). It was patented in 1989.

17 Some History The first papers about LSI: Dumais, S. T., Furnas, G. W., Landauer, T. K. and Deerwester, S. (1988), "Using latent semantic analysis to improve information retrieval." In Proceedings of CHI'88: Conference on Human Factors in Computing, New York: ACM, Deerwester, S., Dumais, S. T., Landauer, T. K., Furnas, G. W. and Harshman, R.A. (1990) "Indexing by latent semantic analysis." Journal of the Society for Information Science, 41(6), Foltz, P. W. (1990) "Using Latent Semantic Indexing for Information Filtering". In R. B. Allen (Ed.) Proceedings of the Conference on Office Information Systems, Cambridge, MA,

18 LSA But first: What is the difference between LSI and LSA??? LSI refers to using it for indexing or information retrieval. LSA refers to everything else.

19 LSA Idea (Deerwester et al): We would like a representation in which a set of terms, which by itself is incomplete and unreliable evidence of the relevance of a given document, is replaced by some other set of entities which are more reliable indicants. We take advantage of the implicit higher-order (or latent) structure in the association of terms and documents to reveal such relationships.

20 Singular Value Decomposition For an arbitrary matrix A there exists a factorization (Singular Value Decomposition = SVD) as follows: Where (i) (ii) orthonormal columns (iii) (iv) singular values (ordered)

21 Low-rank Approximation SVD can be used to compute optimal lowrank approximations. Approximation problem: Frobenius norm Solution via SVD set small singular values to zero column notation: sum of rank 1 matrices C. Eckart, G. Young, The approximation of a matrix by another of lower rank. Psychometrika, 1, , 1936.

22 LSA Decomposition The LSA decomposition via SVD can be summarized as follows: documents... =... LSA term vectors terms LSA document vectors Document similarity <, > Folding-in queries

23 Latent Semantic Analysis Latent semantic space: illustrating example courtesy of Susan Dumais Bellcore

24 LSA - Implementation: four basic steps term by document matrix tend to be sparse convert matrix entries to weights Rank-reduced Singular Value Decomposition (SVD) performed on matrix all but the k highest singular values are set to 0 produces k-dimensional approximation of the original matrix this is the semantic space Compute similarities between entities in semantic space (usually with cosine)

25 A Small Example Technical Memo Titles c1: Human machine interface for ABC computer applications c2: A survey of user opinion of computer system response time c3: The EPS user interface management system c4: System and human system engineering testing of EPS c5: Relation of user perceived response time to error measurement m1: The generation of random, binary, ordered 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

26 A Small Example 2 c1 c2 c3 c4 c5 m1 m2 m3 m4 human interface computer user system response time EPS survey trees graph minors r (human.user) = -.38 r (human.minors) = -.29

27 A Small Example 3 Singular Value Decomposition {A}={U}{S}{V} T

28 A Small Example 4 {U} =

29 A Small Example 5 {S} =

30 A Small Example 6 {V} =

31 A Small Example 7 c1 c2 c3 c4 c5 m1 m2 m3 m4 human interface computer user system response time EPS survey trees graph minors r(human.user) =.94 r(human.minors) = -.83

32 A Small Example 2 reprise c1 c2 c3 c4 c5 m1 m2 m3 m4 human interface computer user system response time EPS survey trees graph minors

33 LSA Titles example: Correlations between titles in raw data c1 c2 c3 c4 c5 m1 m2 m3 c c c c m m m m Correlations in first-two dimension space c c c c m m m m

34

35 Summary of LSA Some Issues SVD Algorithm complexity O(n^2k^3) n = number of terms k = number of dimensions in semantic space (typically small ~50 to 350) for stable document collection, only have to run once dynamic document collections: might need to rerun SVD, but can also fold in new documents

36 Search as Statistical Inference Document in bag-of-words representation China US trade relations relations Disney economic Beijing intellectual property negotiations Given the context, how probable is it that terms like China or trade might occur? free US human rights imports China? Document expansion: Additional index terms can be added automatically via statistical inference

37 Naive Approach Documents Terms number of occurrences of term w in document d Zero frequency problem: terms not occurring in a document get zero probability Maximum Likelihood Estimation Learning from Dyadic Data 37

38 Estimation Problem (i.i.d) sample document estimation other documents learning from other documents in a collection? Crucial question: In which way can the document collection be utilized to improve probability estimates?

39 Probabilistic Latent Semantic Analysis Documents Terms economic Concept expression probabilities are estimated based on all documents that are dealing with a concept. imports TRADE Latent Concepts trade Conclusion: No prior knowledge about concepts required, context and term co-occurrences are exploited Learning from Dyadic Data 39

40 plsa Latent Variable Model Structural modeling assumption (mixture model) Document language model Document-specific mixture proportions Latent concepts or topics Concept expression probabilities Model fitting T. Hofmann, Probabilistic Latent Semantic Analysis, UAI 1999.

41 plsa: Graphical Model shared by all words in a document single document P(z d) in collection shared by all documents in collection P(w z) document collection collection z word occurrences in a document w n(d) N Learning from Dyadic Data 41

42 plsa via Likelihood Maximization Log-Likelihood argmax Observed word frequencies Predictive probability of plsa mixture model Goal: Find model parameters that maximize the loglikelihood, i.e. maximize the average predictive probability for observed word occurrences (nonconvex optimization problem)

43 E and M steps Expectation: Given the current model, figure out the expected probabilities of the documents belonging to each cluster p(x θ c ) Maximization: Given the probabilistic assignment of all the documents, estimate a new model, θ c Each iteration increases the likelihood of the data and it is guaranteed to converge!

44 Expectation Maximization E step: posterior probability of latent variables ( concepts ) Probability that the occurence of term w in document d can be explained by concept z M step: parameter estimation based on completed statistics how often is term w associated with concept z? how often is document d associated with concept z? A.P. Dempster, N.M. Laird, and D.B. Rubin, Maximum Likelihood from Incomplete Data via the EM Algorithm, Journal of Royal Statistical Society B, vol. 39, no. 1, pp. 1-38, 1977

45 Example (1) Concepts (3 of 100) extracted from AP news Concept 1 securities firm drexel investment bonds sec bond junk milken firms investors lynch insider shearson boesky lambert merrill brokerage corporate burnham Concept 2 ship coast guard sea boat fishing vessel tanker spill exxon boats waters valdez alaska ships port hazelwood vessels ferry fishermen Concept 3 india singh militants gandhi sikh indian peru hindu lima kashmir tamilnadu killed india's punjab delhi temple shining menem hindus violence

46 Example (2) Concepts (10 of 128) extracted from Science Magazine articles (12K) P(w z) P(w z)

47 Experimental Evaluation Average Precision VSM LSA PLSA Summary of quantitative evaluation Consistent improvements of retrieval accuracy Relative Gain in Average Prec % 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% -5% Medline CRAN CACM CISI TREC Medline CRAN CACM CISI TREC VSM LSA PLSA Relative improvements of average precision 15-45% On TREC3: 18% improvement compared to SMART retrieval metric

48 Live Implementation

49 Concept-based Text Categorization Text categorization algorithms: Perceptron, naive Bayes, k-nearest neighbor, SVM, AdaBoost, etc. Term-based document representation: vulnerable to linguistic variations Explore the use of concept-based document representation in text categorization Concepts are extracted automatically using plsa (potentially using unlabeled documents) Learning algorithms: AdaBoost.MH and.mr R. E. Schapire and Y. Singer. Boostexter: A boosting-based system for text categorization. Machine Learning, 39(2/3): , 2000.

50 Terms & Concepts as Features Two types of weak hypotheses Indicator function for term features Standard features used in TextBooster (or SVMs) Indicator function for concept features Features automatically extracted by plsa L. Cai and T. Hofmann, Text Categorization by Boosting Automatically Extracted Concepts, ACM SIGIR 2003.

51 Improvements on Reuters Reuters 1987 newswire: 21,578 documents & 37,926 word types Train plsa model with all data, use ModApte split for categorization: 9,603 training documents, 3,299 test documents, 8,676 unused

52 Improvements on OHSUMED87 OHSUMED87 collection consists of Medline documents from the year 1987: 54,708 instances and 67,096 words of which 19,066 word types remain after pruning Train plsa model with all the remaining data. Randomly split the collection into 10 folds. 9 of them are used for training and the remaining one for testing. Evaluation on top 50 categories

53 Probabilistic HITS Probabilistic model of link structure Probabilistic graph model, i.e., predictive model for additional links/nodes based on existing ones Centered around the notion of Web communities Probabilistic version of HITS Enables to predict the existence of hyperlinks: estimate the entropy of the Web graph Combining with content Text at every node...

54 Finding Latent Web Communities Web Community: densely connected bipartite subgraph Probabilistic model phits (cf. plsa model) Source nodes s t Target nodes probability that a random out-link from s is part of the community z probability that a random in-link from t is part of the community z identical

55 Decomposing the Web Graph Web subgraph Community 1 Links (probabilistically) belong to exactly one community. Nodes may belong to multiple communities. Community 2 Community 3

56 Linking Hyperlinks and Content plsa and phits (probabilistic HITS) can be combined into one joint decomposition model P(z s) P(w z) z P(t z) w t concept/topic Web community D. Cohn and T. Hofmann. The missing link - a probabilistic model of document content and hypertext connectivity. In Advances in Neural Information Processing Systems (NIPS), volume 13, 2001.

57 Example: Ulysses Decomposition of a base set generated from Altavista with query Ulysses (combined decomposition based on links and text) ulysses space page home nasa science solar esa mission ulysses.jpl.nasa.gov/ helio.estec.esa.nl/ulysses Ulysses grant s ulysses online war school poetry president civil /usgrant/ /WH/glimpse /presidents /ug18.html saints.css.edu/mkelsey /gppg.html page ulysses new web site joyce net teachers information /Joyce/Ulysses.htm /Fiction/joyce/ulysses /index.html /chatroom/

58 Predictions & Recommendations Goal: Predict future user behavior, ratings or preferences based on past behavior... your typical user user profile?

59 Collaborative Filtering: Data Items, e.g. Multimedia Documents Database with User Profiles Users UserI D ItemI D Rating Ratings

60 plsa for Collaborative Filtering Application of plsa for collaborative filtering: rating variable needs to be added Community variant u Categorized variant y z z y v u v

61

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