Berry, M. W., Fierro, R. D., "Low-Rank Orthogonal Decompositions for Information Retrieval Applications", Numerical Linear Algebra with Applications, Vol 3 pp. 301-328, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....matrix [26] or Lanczos decompositions [14] that geometrically reveal semantic relationships. These approximations identify hidden structures in word usage, thus enabling searches that go beyond simple keyword matching (see, for example [14] Rank reduction techniques (SDD [40] SVD [11, 12, 47, 10]) for type clustering are applicable here as they have been shown to be especially appropriate for latent semantic indexing in information retrieval. 9 1 2 1341 16 328 478 482 589 12 592 623 625 739 753 937 950 969 1135 1009 1185 1223 1288 1292 3 8 17 291 1386 1387 314 322 324 329 ....

M.W. Berry and R.D. Fierro. Low-Rank Orthogonal Decompositions for Information Retrieval Applications. Numerical Linear Algebra with Applications, Vol. 3(4):pp. 301--328, 1996.

....data. Such approximations might involve dropping higher order terms in harmonic approximations, adaptive simplification of geometries, or rank reduction in attribute matrices. A very popular technique that has this flavor is called Latent Semantic Indexing [Berry et al. 1999, Berry et al. 1995, Berry and Fierro, 1996, Jiang et al. 1999, Letsche and Berry, 1997] an algorithm that introduces approximations using singular value decompositions of a term document matrix in information retrieval to find hidden structure. This has parallels in Karhunen Loeve expansions in signal representation and principal ....

....in data mining. The more broader task of map analysis using geographical information system (GIS) data is important in identifying clusters of wild life behavior in forests [Berry et al. 1994] modeling population dynamics in ecosystems [Abbott et al. 1997] and socio economic modeling [Berry et al. 1996]. An important application of data mining in geophysics relates to the detection of subsurface mineral deposits, oil reservoirs, and other artifacts. Typical datasets in these applications are collected from excitation and observation stations in borewells. For example, an agent is injected into ....

Berry, M. and Fierro, R. (1996). Low-rank orthogonal decompositions for information retrieval applications. Numerical Linear Algebra with Applications, Vol. 3(4):pp. 301--328.

.... color module, and three texture modules computing the Wold features of periodicity, directionality, and randomness [10] Efforts are underway to expand the system to include face detection and description using eigenfaces [11, 12] and text cue vectors extracted via latent semantic indexing (LSI) [13, 14] on the text surrounding the image in an HTML document. 3.1 Color Color distributions are calculated as follows. Image color histograms are computed in the CIE color space, which has been shown to correspond closely to the human perception of color [15] To transform a point from ....

M. W. Berry and R. D. Fierro. Low-rank orthogonal decompositions for information retrieval applications. Numerical Linear Algebra with Applications, 3(4):301--328, April 1996.

.... color module, and three texture modules computing the Wold features of periodicity, directionality, and randomness [10] Efforts are underway to expand the system to include face detection and description using eigenfaces [11, 12] and text cue vectors extracted via latent semantic indexing (LSI) [13, 14] on the text surrounding the image in an HTML document. 3.1 Color Color distributions are calculated as follows. Image color histograms are computed in the CIE color space, which has been shown to correspond closely to the human perception of color [15] To transform a point from ....

M. W. Berry, S. T. Dumais, and G. W. O'Brien. Lowrank orthogonal decompositions for information retrieval applications. SIAM Review, 37(4):573--595, 1995.

.... presentations for a more general audience are widely available in texts, including [Coleman, Van Loan 1988] Golub, Van Loan 1996] Jennings, McKeown 1979] Press et al. 1982] and [Watkins 1991] Studies of linear algebra techniques and their applications to IR include [Berry et al. 1995b] [Berry, Fierro 1996], and [Letsche, Berry 1997] A comprehensive review and tutorial on using the SVD for IR is [Berry et al. 1995a] and an interesting review paper on the history of the SVD is [Stewart 1992] The LSI algorithm reduces the noise in matrix A by contructing a modi ed matrix A k , from the k largest ....

Berry, M., Fierro, R., \Low-rank orthogonal decompositions for information retrieval applications", Numerical Linear Algebra with Applications, 1, 1, 1996, pp. 1-27.

....V will be referred to as the left and right singular vectors, and is a diagonal matrix with monotonically decreasing diagonal elements i , which are known as the singular values of the matrix A. Studies of linear algebra techniques and their applications to IR include [Berry, et al. 1995b] [Berry, Fierro 1996], and [Letsche, Berry 1997] A comprehensive review and tutorial on using the SVD for IR is [Berry, et al. 1995a] and an interesting review paper on the history of the SVD is [Stewart 1992] The LSI algorithm reduces the noise in matrix A by contructing a modi ed matrix A k , from the k largest ....

Berry, M., Fierro, R., \Low-rank orthogonal decompositions for information retrieval applications", Numerical Linear Algebra with Applications, 1, 1 (1996), 1-27. 39

....in the approximated space. This approach is described in greater detail in Section 3. Singular Value Decomposition (SVD) Press, 1992; Greenacre, 1984, Appx A. is normally used to perform the matrix decomposition, although other orthogonal decomposition approaches, such as the ULV decomposition (Berry Fierro 1996), can be used to replace SVD for this task. Studies have demonstrated that a signi cant reduction in dimensionality can be achieved when used within IR systems; for example from 5000 7000 terms to about 100 dimensions (Deerwester et al. 1990) SVD has also been successfully applied to the problem ....

Berry, M. and Fierro, R. (1996). Low-Rank Orthogonal Decompositions for Information Retrieval Applications. Numerical Linear Algebra with Applications 1 (1), 1-27.

....the sense of minimizing the distance between that matrix and all rank k matrices. LSI has performed well in both large and small tests; see, for example, Dumais [5, 6] LSI is described in Section 3. Thus far, only the singular value decomposition and its relatives, the ULV and URV decompositions [3], have been used in LSI. We propose using a very different decomposition, originally developed for image compression by O Leary and Peleg [10] In this decomposition, which we call the semi discrete decomposition (SDD) the matrix is approximated by summing outer products just as in the SVD, but ....

M.W. Berry and R.D. Fierro. Low-rank orthogonal decompositions for information retrieval applications. Numerical Linear Algebra with Applications, 1:1--27, 1996.

....matrix to the term document matrix in the Frobenius measure [Golub and Van Loan 1989] LSI has performed well on both large and small document collections; see, for example, Dumais [1991, 1995] LSI is described in x3. Thus far, only the SVD and its relatives, the ULV and URV decompositions [Berry and Fierro 1996], have been used in LSI. We propose using a very different decomposition, originally developed for image compression by O Leary and Peleg [1983] In this decomposition, which we call the semi discrete decomposition (SDD) the matrix is approximated by a sum of rank 1 outer products just as in the ....

Berry, M. W. and Fierro, R. D. 1996. Low-rank orthogonal decompositions for information retrieval applications. Numerical Linear Algebra with Applications 1, 1--27.

....matrix is optimal in the sense of minimizing the distance between that matrix and all rank k matrices. LSI has performed well in both large and small tests; see, for example, Dumais [21, 22] Thus far, only the singular value decomposition and its relatives, the ULV and URV decompositions [2], have been used in LSI. We propose using a very different decomposition, the semi discrete decomposition (SDD) described in Chapter 6. This decomposition is constructed via a greedy algorithm and is not an optimal decomposition in the sense that it minimizes with respect to any norm; however, for ....

M. W. Berry and R. D. Fierro. Low-rank orthogonal decompositions for information retrieval applications. Numerical Linear Algebra with Applications, 1:1--27, 1996.

....1] and then normalize homogeneous points according to kxk2 = 1 or kxk1 = 1 (it makes little difference which) is not critical but a good one helps, for example, the first k = 4 columns of a partial, pivoted Gram Schmidt decomposition of M. This is an active research field see, e.g. [2, 3, 6, 10, 4] for details of these and other iterative methods. A good modern C code is M. Berry s SVDPACKC, available from NETLIB (http: www.netlib.org) ....

M. Berry and R. Fierro. Low-rank orthogonal decompositions for information retrieval applications. Technical Report ut-cs-95-284, Computer Science Dept., U. of Tennessee, April 1995. To appear in Numerical Linear Algebra with Applications.

.... color module, and three texture modules computing the Wold features of periodicity, directionality, and randomness [10] Efforts are underway to expand the system to include face detection and description using eigenfaces [11, 12] and text cue vectors extracted via latent semantic indexing (LSI) [13, 14] on the text surrounding the image in an HTML document. 3.1 Color Color distributions are calculated as follows. Image color histograms are computed in the CIE L u v color space, which has been shown to correspond closely to the human perception of color [15] To transform a point from ....

M. W. Berry and R. D. Fierro. Low-rank orthogonal decompositions for information retrieval applications. Numerical Linear Algebra with Applications, 3(4):301--328, April 1996.

.... color module, and three texture modules computing the Wold features of periodicity, directionality, and randomness [10] Efforts are underway to expand the system to include face detection and description using eigenfaces [11, 12] and text cue vectors extracted via latent semantic indexing (LSI) [13, 14] on the text surrounding the image in an HTML document. 3.1 Color Color distributions are calculated as follows. Image color histograms are computed in the CIE L u v color space, which has been shown to correspond closely to the human perception of color [15] To transform a point from ....

M. W. Berry, S. T. Dumais, and G. W. O'Brien. Lowrank orthogonal decompositions for information retrieval applications. SIAM Review, 37(4):573--595, 1995.

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M. W. Berry and R. D. Fierro, Low rank orthogonal decompositions for information retrieval applications, J. Numer. Lin. Alg. and Applic., in press.

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M.W. Berry and R.D. Fierro. Low-rank Orthogonal Decompositions for Information Retrieval Applications. Num. Lin. Alg. with Applics., 3:301-327, 1996.

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Berry, M. W., Fierro, R. D., "Low-Rank Orthogonal Decompositions for Information Retrieval Applications", Numerical Linear Algebra with Applications, Vol 3 pp. 301-328, 1995.

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Michael W. Berry and Ricardo D. Fierro. Low-rank orthogonal decompositions for information retrieval applications. Numerical linear algebra with applications, 3(4):301-- 327, 1996.

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BERRY,M.W.AND FIERRO, R. D. 1996. Low-rank orthogonal decompositions for information retrieval applications. Numer. Lin. Alg. Appl. 1, 1--27.

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