M. Berry. Large-scale singular value computations. volume 6-1, pages 13--49, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....it again and again in fitting the regression functions with respect to categories. In this sense, this method is quite e#cient when M is very large, as compared to training binary classifiers M times repeatedly and independently. The Lanczos algorithm introduced in [2] and thoroughly analyzed by [1] is particularly e#cient for solving LLSF on very large and sparse matrices, and has a good convergence property. The step wise complexities are given below: Step 1. Compute the truncated SVD X = USV , where U is matrix of right singular vectors, V is the matrix of left singular vectors, S ....

M. Berry. Large-scale singular value computations. volume 6-1, pages 13--49, 1992.

....in the VSM space point in the same (general) direction. 2.2. Latent Semantic Indexing Latent Semantic Indexing (LSI) 7, 8] is a VSM based method for inducing and representing aspects of the meanings of words and passages reflective in their usage. Work applying LSI to natural language text by [5, 14] has shown that that LSI not only captures significant portions of the meaning of individual words but also of whole passages such as sentences, paragraphs, and short essays. The central concept of LSI is that the information about word contexts in which a particular word appears, or does not ....

Berry, M. W., "Large Scale Singular Value Computations", Int. Journal of Supercomputer Applications, 6, 1992, pp. 13-49.

....IR methods (based on statistical and heuristic methods) may not produce as good of results, but they are inexpensive to apply and coupled with the structural information of the program, should produce good quality and low cost results. 2.2. Latent semantic indexing Latent Semantic Indexing (LSI) [6, 24] is a corpusbased statistical method for inducing and representing aspects of the meanings of words and passages (of natural language) reflective in their usage. The method generates a real valued vector description for documents of text. This representation can be used to compare and index ....

....and index documents using a variety of similarity measures. We apply LSI to source code and its associated internal documentation (i.e. comments) and then use the similarity measures to induce the similarity of different source code documents. Work applying LSI to natural language text by [6, 24] has shown that that LSI not only captures significant portions of the meaning of individual words but also of whole passages such as sentences, paragraphs, and short essays. The central concept of LSI is that the information about word contexts in which a particular word appears, or does not ....

Berry, M. W., "Large Scale Singular Value Computations", International Journal of Supercomputer Applications, vol. 6, 1992, pp. 13-49.

....terms (see Section 5) The truncated SVD is usually computed by an iterative technique such as the Lanczos method. The SVDs in this report were computed with the PARPACK software package [13] as well as TRLAN [19] for veri cation) Another popular software package for computing SVDs is SVDPACK[3]. There is some disagreement about using U k , SkU k , or S k U k as the projected terms . In this work we use SkUk primarily because the term term similarity matrix XX can be decomposed as US U if X = USV . Hence the rows of US naturally correspond to the rows of X (see ....

M. W. Berry. Large Scale Singular Value Computations, Int'l J. Supercomputer Applications 6:1, (1992), pp. 13-49. Software online: http://www.netlib.org/svdpack/index.html.

....IR methods (based on statistical and heuristic methods) may not produce as good of results, but they are inexpensive to apply and coupled with the structural information of the program, should produce good quality and low cost results. 2.1. Latent semantic indexing Latent Semantic Indexing (LSI) [5, 25] is a corpusbased statistical method for inducing and representing aspects of the meanings of words and passages (of natural language) reflective in their usage. The method generates a real valued vector description for documents of text. This representation can be used to compare and index ....

....text. This representation can be used to compare and index documents using a variety of similarity measures. By applying LSI to source code and its associated internal documentation (i.e. comments) candidate components can be compared with respect to these similarity measures. Results have shown [5, 25] that LSI captures significant portions of the meaning not only of individual words but also of whole passages such as sentences, paragraphs, and short essays. The central concept of LSI is that the information about word contexts in which a particular word appears or does not appear provides a ....

Berry, M. W., "Large Scale Singular Value Computations", International Journal of Supercomputer Applications, vol. 6, 1992, pp. 13-49.

....one possible avenue of applying the Lanczos bidiagonalization process for finding approximations of A j . Lanczos bidiagonalization process has been used for computing a few dominant singular triplets (singular values and the corresponding left and right singular vectors) of large sparse matrices [3, 5, 8]. We will show that in many cases of interest good approximations can be directly obtained from the Lanczos bidiagonalization process without computing any singular value decomposition. We will also explore relations between the levels of orthogonality of the left Lanczos vectors and the right ....

.... of a general rectangular matrix using orthogonal transformations such as Householder transformations and Givens rotations was first proposed in [7] It was later adapted to solving large sparse least squares problems [18] and to finding a few dominant singular triplets of large sparse matrices [3, 5, 8]. For solving least squares problems the orthogonality of the left and right Lanczos vectors is usually not a concern and therefore no reorthogonalization is incorporated in the proposed algorithm LSQR [18] For computing a few dominant singular triplets, one approach is to completely ignore ....

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M. Berry. Large Scale Singular Value Computations. International Journal of Supercomputer Applications, 6:13-49, 1992.

....these eigenvectors projects a document onto these latent semantic concepts , and the new low dimensional representation consists of the magnitudes of these projections. The eigenanalysis can be computed efficiently by a sparse variant of singular value decomposition of the document term matrix [1]. Although LSI has been proven to be extremely useful in various information retrieval tasks, it is not an optimal representation for classification. LSI PCA are completely unsupervised, that is, they pay no attention to the class labels of the existing training data. LSI aims at optimal ....

....belongs to the class it was trained for. Since there may be several simultaneous such claims, and since the setting is exclusive classification, a simple maximum selector is applied to the SVMs to make the final decision for an exclusive class. The LSI analysis was done using SVDPAKC las2 [1]. Results are depicted in a single chart in Fig. 1. The horizontal axis denotes the dimension of the document representation. Instead of precision recall we are reporting just a single number, the error rate, which is common in pattern recognition literature. This is defined as the number of ....

Michael W. Berry. Large scale singular value computations. International Journal of Supercomputer Applications, 6(1), 1992.

....occurs in a passage. 2) Cell entries (freq ij ) are transformed to: log log freq freq freq freq freq ij ij ij ij ij ( 1 1 1 1 a measure of the first order association of a word and its context. 3) The matrix is then subjected to singular value decomposition (Berry, 1992): ij] ik] kk] jk] in which [ik] and [jk] have orthonormal columns, kk] is a diagonal matrix of singular values, and k = max (i,j) 4) Finally, all but the d largest singular values are set to zero. Pre multiplication of the right hand matrices produces a least squares best ....

Berry, M. W. (1992). Large scale singular value computations. International Journal of Supercomputer Applications, 6, 13-49.

....training corpus. In this way, an n dimensional vector which represents the word s distributional behavior is produced for each vocabulary word. Then the original n dimensional vector space is converted into a condensed, lowerdimensional, real valued matrix using Singular Value Decomposition (SVD) (Berry, 1992). The lower dimensional vector space is called word space. A document vector and a query vector are calculated by summing the vectors corresponding to the vocabulary words in the document or the query, and the proximity between the two vectors is defined as the cosine of the angle between them. ....

Berry, M. W. (1992) Large Scale Singular Value Computations. International Journal of Supercomputer Applications, 6/1, pp. 13-49.

....(LSA) to identify similarities between pieces of source code are being conducted. The objective of this research is to determine how well such a method can be used to support aspects of program understanding, comprehension, and reengineering of software systems. Latent Semantic Analysis (LSA) [1, 12] is a corpus based statistical method for inducing and representing aspects of the meanings of words and passages (of natural language) reflective in their usage. The method generates a real valued vector description for documents of text. This representation can be used to compare and index ....

....By applying LSA to source code and its associated internal documentation (i.e. comments) candidate components can be compared with respect to these similarity measures. A number of metrics are defined based on these similarity measures to help support program understanding. Results have shown [1, 12] that LSA captures significant portions of the meaning not only of individual words but also of whole passages such as sentences, paragraphs, and short essays. Basically, the central concept of LSA is that the information about word contexts in which a particular word appears or does not appear ....

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Berry, M. W., "Large Scale Singular Value Computations," Int. J. of Supercomputer Applications, vol. 6, 1992, pp. 13-49.

....the proposed SVD ANN approach leads to performance gains, it is significantly more computationally expensive than the other approaches discussed here. The SVD implementation used in our experiments is a singlevector Lanczos method which is part of the publicly available software package SVDPACKC (Berry, 1992). Its computational complexity is O(3Dz) where z is the number of non zero elements in the matrix and D is the number of dimensions to be computed. In our experiments we observed training times (SVD network training) ranging from 0.4 seconds for 10 training examples to 2.3 seconds for 50 ....

Berry, M. W. (1992). Large scale singular value computations. International Journal of Supercomputer Applications, 6(1), 13-49.

.... (or noise) is scaled by log(n) and added to one, which assigns high weights to terms with less noise and lower weights to terms that are equally distributed across the collection (i.e. when p ij = 1 n) 3) After creating the weighted matrix A the system performs a singular value decomposition [23] T V S U A = in which U (m x k) and V (n x k) have orthonormal columns, S (k x k) is a diagonal matrix of singular values, k = max(m,n) and m n. Dimensionality reduction is achieved by keeping only the k largest singular values and setting the rest to zero. In my implementation I ....

M. Berry, "Large scale singular value computations," International Journal of Supercomputer Applications, vol. 6, 1992, pp. 13-49.

....method. We want a parallel SVD (Singular Value Decomposition) method for computing pseudo inverses of the G matrix, also yielding information and resolution matrices that will provide statistical information regarding the resolution and quality of the data. We are considering the use of SVD Pack [3]. We are also considering parallelization across our array of SGI Power Challenges (currently we run on a single cabinet) 6. Portability. We would like the environment to be portable for several reasons. First, it is important for the seismologists to share the environment with colleagues, who ....

M. Berry, Large Scale Singular Value Computations, International Journal of Supercomputer Applications, 6 (1992), pp. 13--49. 16 Domain-Specific Environments for Computational Science

....component submatrices, we can compute M s , a rank s approximation to M. In this case, s is considerably smaller than the rank r. Document to document similarity is then computed as M s M s # # D s S s # D s S s and can be derived from the original formula for the rank s approximation to M [6]. Queries can be treated as pseudo documents and can be computed as q # q 0 K s S# s where q 0 is a query vector of the associated term weights [7] The end result of LSI is a reduced space in which to compare two documents at a broader level. The goal is to map similar word usage ....

M.W. Berry. Large Scale Singular Value Computations. International Journal of Supercomputer Applications 6:13-49, 1992. http://loci.cs.utk.edu/ibp/

....5 surveys promising applications of LSI along with parameter estimation problems that arise with its use. 3 2 Background The singular value decomposition is commonly used in the solution of unconstrained linear least squares problems, matrix rank estimation, and canonical correlation analysis [2]. Given an m Theta n matrix A, where without loss of generality m n and rank(A) r, the singular value decomposition of A, denoted by SVD(A) is defined as A=U SigmaV T (1) where U T U=V T V =I n and Sigma=diag(oe 1 ; Delta Delta Delta ; oe n ) oe i 0 for 1 i r; oe j =0 for ....

.... matrix A as an alternative to recomputing the SVD of A in Equation (9) In general, the cost of computing the SVD of a sparse matrix [4] can be generally expressed as I Theta cost (G T Gx) trp Theta cost (Gx) where I is the number of iterations required by a Lanczos type procedure [2] to approximate the eigensystem of G T G and trp is the number of accepted singular triplets (i.e. singular values and corresponding left and right singular vectors) The additional multiplication by G is required to extract the left singular vector given approximate singular values and their ....

M. W. BERRY, Large scale singular value computations, International Journal of Supercomputer Applications, 6 (1992), pp. 13--49.

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M. Berry. Large-scale singular value computations. volume 6-1, pages 13--49, 1992.

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Michael W. Berry. Large scale singular value computations. International Journal of Supercomputer Applications, 6:13--49, 1992.

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M. W. Berry. Large scale singular value computations. International Journal of Supercomputer Applications, 6:13-- 49, 1992.

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M. Berry, "Large Scale Singular Value Computations" , Intl. Journal of Supercomputer Applications , Vol 6, pp. 13-49, 1992

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M. Berry. Large-scale singular value computations. volume 6-1, pages 13-49, 1992.

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Michael W. Berry. Large scale singular value computations. International Journal of Supercomputer Applications, 6(1):13--49, 1992. 104

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M. Berry. Large-scale singular value computations. volume 6-1, pages 13-49, 1992.

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Michael W. Berry. Large scale singular value computations. International Journal of Supercomputer Applications, 6:13--49, 1992.

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M. W. Berry. Large scale singular value computations. International Journal of Supercomputer Applications, 6:13-- 49, 1992.

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Berry, M. W. Large scale singular value computations. International Journal of Supercomputer Applications, 1992, 6(1), 13-49.

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