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Latent Semantic Indexing via a Semi-discrete Matrix Decomposition

Papers from the same authors with similar topics. Kolda, T.G.

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Latent Semantic Indexing via a Semi-discrete Matrix Decomposition

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    1. Latent Semantic Indexing via a Semi-discrete Matrix Decomposition

    2. Papers from the same authors with similar topics Kolda, T.G. & O'Leary, D.P. A semidiscrete matrix decomposition for latent semantic indexing information retrieval ACM Trans. Inf. Syst., 1998, 16, 322-346 Kolda, T.G. & O’Leary, D.P. George Cybenko, D.P.O. (ed.) Latentsemantic indexing via a semi-discrete matrix decomposition Springer-Verlag, 1999, 107, 73–80 Kolda, T.G. & O'leary, D.P. Algorithm 805: computation and uses of the semidiscrete matrix decomposition ACM Transactions on Mathematical Software, 2000, 26, 415–435

    3. Vector Space Framework Query:

    4. Weight of term in a document

    5. Weight of term in a document

    6. Motivation for using SDD Singular Value Decomposition (SVD) is used for Latent Semantic Indexing (LSI) to estimate the structure of word usage across documents. Use Semi-discrete Decomposition (SDD) instead of SVD for LSI to save storage space and retrieval time.

    7. Why? Claim: SVD has nice theoretical properties but SVD contains a lot of information, probably more than is necessary for this application.

    8. SVD vs SDD SVD: SDD:

    9. SDD is an approximate representation of the matrix. Repackaging, even without removing anything, might not result in the original matrix. Theorems exist that say that as the number of terms k tends to infinity, slowly you will converge to the original matrix. The speed of convergence depends on the original estimate, used to "initialize" the iterative decomposition algorithm.

    10. Result: Storage Space

    11. Medline test case

    12. Results on Medline test case

    13. Method for SDD

    14. Metrics in those papers Kolda, T.G. & O'Leary, D.P. A semidiscrete matrix decomposition for latent semantic indexing information retrieval ACM Trans. Inf. Syst., 1998, 16, 322-346 Kolda, T.G. & O’Leary, D.P. George Cybenko, D.P.O. (ed.) Latentsemantic indexing via a semi-discrete matrix decomposition Springer-Verlag, 1999, 107, 73–80 Kolda, T.G. & O'leary, D.P. Algorithm 805: computation and uses of the semidiscrete matrix decomposition ACM Transactions on Mathematical Software, 2000, 26, 415–435

    15. Greedy Algorithm

    16. Notes on the algorithm Starting vector y: every 100th element is 1 and all the other are 0. Ak ? A as k? 8 Find the minimum F-norm can be simplified to find an optimal x. Improvement threshold may be 0.01. improvement = |new - old| / old

    17. Finding x and d

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