M. W. Berry, S. Dumais And G. O'Brien, The computational complexity of alternative updating approaches for an SVD-encoded indexing scheme, In Proceedings of the Seventh SIAM Conference of Parallel Processing for Sci. Comput., SIAM, Philadelphia, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to be an extremely reliable tool for computing the numerical rank and bases for the null spaces of a matrix. However, the SV D is too expensive when it comes to recursive algorithms or real time applications, since its computation requires O(n 3 ) flops 1 and the SV D is difficult to update [1, 6]. Therefore alternative algorithms that are nearly as accurate as the SV D, cheaper and easier to update are desired. Recently, Stewart [25, 26, 27, 29] proposed two rank revealing factorizations, called ULV and URV factorizations. These two factorizations are 1 Here, a flop is either an ....

M. W. Berry, S. Dumais And G. O'Brien, The computational complexity of alternative updating approaches for an SVD-encoded indexing scheme, In Proceedings of the Seventh SIAM Conference of Parallel Processing for Sci. Comput., SIAM, Philadelphia, 1995.

....Two dimensional plot of the documents returned for the query voice heaven. p A k m Theta n m Theta (n p) U k m Theta k m Theta k Sigma k k Theta k k Theta k p V T k k Theta (n p) k Theta n Figure 1.5: Mathematical representation of folding in p documents. new terms and documents [BDO95] Folding in is based on the existing latent semantic structure (the current A k ) and hence new terms and documents have no effect on the representation of the pre existing terms and documents. Folding in documents is essentially the process described in Section 1.3.4 for pseudo document ....

M. Berry, S. Dumais, and G. O'Brien. The computational complexity of alternative updating approaches for an SVD-encoded indexing scheme. In Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing, Philadelphia, 1995. SIAM.

.... used in the solution of unconstrained linear least squares problems, matrix rank estimation, and canonical correlation analysis [2] Although the SVD provides very accurate subspace information, it is computationally demanding and difficult to update for either dense [5] or sparse matrices [1,19]. This can be a drawback for recursive procedures which require simple matrix updates (e.g. appending or deleting a row or column) Alternatively, rank revealing QR (RRQR) algorithms such as those by Foster [15] Chan [6] and modifications [4] can be used to obtain subspace information from ....

....disease fast generation oestrogen patients pressure rats respect rise study M7 M11 M1 M8 M5 M4 M3 M6 M2 M10 M12 M14 M9 M13 M15 M16 Figure 6. Two dimensional plot of folded in medical topics M15 and M16. can be easily compared to that obtained when the SVD of A is explicitly computed, cf. [1] and [19] 5. ULV Updating The process of ULV updating discussed in Section 2.4. can also be illustrated using titles from Tables 2 and 5. The three steps required to perform a complete ULV update involve adding new documents, adding new terms, and correction for changes in term weightings. The ....

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M. Berry, S. Dumais, and G. O'Brien. The computational complexity of alternative updating approaches for an SVD-encoded indexing scheme. In Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing, Philadelphia, 1995. SIAM.

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