1. IR Models: Latent Semantic Analysis

2. IR Model Taxonomy Non-Overlapping Lists Proximal Nodes Structured Models U s e r T a s k Set Theoretic Fuzzy Extended Boolean Probabilistic Inference Network Belief Network Algebraic Generalized Vector Lat. Semantic Index Neural Networks Browsing Flat Structure Guided Hypertext Classic Models boolean vector probabilistic Retrieval: Adhoc Filtering Browsing

3. Vocabulary Problem The “vocabulary problem” causes classic IR to potentially experience poor retrieval: –Polysemy - same term means many things so unrelated documents might be included in the answer set Leads to poor precision –Synonymy - different terms mean the same thing so relevant documents that do not contain any index term are not retrieved. Leads to poor recall

4. Latent Semantic Indexing Retrieval based on index terms is vague and noisy The user information need is more related to concepts and ideas than to index terms A document that shares concepts with another document known to be relevant might be of interest

5. Latent Semantic Indexing The key idea –Map documents and queries into a lower dimensional space –Lower dimensional space represents higher level concepts which are fewer in number than the index terms Retrieval in this reduced concept space might be superior to retrieval in the space of index terms

6. Latent Semantic Indexing Definitions –Let t be the total number of index terms –Let N be the number of documents –Let (M ij ) be a term-document matrix with t rows and N columns –Each element of this matrix is assigned a weight w ij associated with the pair [k i,d j ] –The weight w ij can be based on a tf-idf weighting scheme

7. Singular Value Decomposition The matrix (M ij ) can be decomposed into 3 matrices: –(M ij ) = (K) (S) (D) t –(K) is the matrix of eigenvectors derived from (M)(M) t –(D) t is the matrix of eigenvectors derived from (M) t (M) –(S) is an r x r diagonal matrix of singular values where r = min(t,N) that is, the rank of (M ij )

8. Latent Semantic Indexing In the matrix (S), select only the s largest singular values Keep the corresponding columns in (K) and (D) t The resultant matrix is called (M) s and is given by –(M) s = (K) s (S) s (D) t –where s, s < r, is the dimensionality of the concept space The parameter s should be –large enough to allow fitting the characteristics of the data –small enough to filter out the non-relevant details

9. LSI Ranking The user query can be modelled as a pseudo- document in the original (M) matrix Assume the query is modelled as the document numbered 0 in the (M) matrix The matrix (M) t (M) s quantifies the relantionship between any two documents in the reduced concept space The first row of this matrix provides the rank of all the documents with regard to the user query (represented as the document numbered 0)

10. Latent Semantic Analysis as Model of Human Language Learning Psycho-linguistic model: –Acts like children who acquire word meanings not through explicit definitions but by observing how they are used. –LSA is a pale reflection of how humans learn language, but it is a reflection. –LSA offers an explanation of how people can agree enough to share meaning.

11. LSA Applications In addition for typical query systems, LSA has been used for: –Cross-language search –Reviewer assignment at conferences –Finding experts in an organization –Identifying reading level of documents

12. Concept-based IR Beyond LSA LSA/LSI uses principle component analysis Principle components are not necessarily good for discrimination in classification. Linear Discriminant Analysis (LDA) identifies linear transformations –maximizing between-class variance while –minimizing within class variance LDA requires training data

13. Linear Discriminant Analysis Projecting a 2D space to 1 PC B. 2.0 1.5 1.0 0.5 0.5 1.0 1.5 2.0............. A w. (from slides by Shaoqun Wu)

14. Linear Discriminant Analysis B. 2.0 1.5 1.0 0.5 0.5 1.0 1.5 2.0............. A w. B. 2.0 1.5 1.0 0.5 0.5 1.0 1.5 2.0............. A w. PCA LDA: discovers a discriminating projection

15. LDA results LDA reduces number of dimensions (concepts) required for classification tasks

16. Conclusions Latent semantic indexing provides an intermediate representation of concept to aid IR, minimizing the vocabulary problem. It generates a representation of the document collection which might be explored by the user. Alternative methods for identifying clusters (e.g. LDA) may improve results.