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They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well as "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, ... 2 March 2009 Foundations and Trends® in Theoretical Computer Science: Volume 4 Issue 3–4, March 2009 Publisher: Now Publishers Inc. Bibliometrics: Citation Count: 10 Spectral methods refer to the use of eigenvalues, eigenvectors, singular values, and singular vectors. They are widely used in Engineering, Applied Mathematics, and Statistics. More recently, spectral methods have found numerous applications in Computer Science to “discrete” as well as “continuous” problems. This monograph describes modern applications of spectral methods, ... 3 July 2008 SIAM Journal on Computing: Volume 38 Issue 3, June 2008 Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 18 We present an algorithm for learning a mixture of distributions based on spectral projection. We prove a general property of spectral projection for arbitrary mixtures and show that the resulting algorithm is efficient when the components of the mixture are logconcave distributions in $\Re^n$ whose means are separated. The separation ... Keywords: singular value decomposition, principal component analysis, logconcave distributions, mixture models 4 January 2007 SODA '07: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 17 Downloads (6 Weeks): 1,   Downloads (12 Months): 5,   Downloads (Overall): 251 Full text available: PDF We propose and investigate bimatrix games, whose (entry-wise) sum of the pay-off matrices of the two players is of rank k , where k is a constant. We will say the rank of such a game is k . For every fixed k , the class of rank k -games ... 5 January 2007 SODA '07: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 2 Downloads (6 Weeks): 0,   Downloads (12 Months): 5,   Downloads (Overall): 347 Full text available: PDF This paper considers the well-studied problem of clustering a set of objects under a probabilistic model of data in which each object is represented as a vector over the set of features, and there are only k different types of objects. In general, earlier results (mixture models and "planted" problems ... 6 December 2006 ACM Transactions on Database Systems (TODS): Volume 31 Issue 4, December 2006 Publisher: ACM Bibliometrics: Citation Count: 28 Downloads (6 Weeks): 3,   Downloads (12 Months): 25,   Downloads (Overall): 1,487 Full text available: PDF We present a divide-and-merge methodology for clustering a set of objects that combines a top-down “divide” phase with a bottom-up “merge” phase. In contrast, previous algorithms use either top-down or bottom-up methods to construct a hierarchical clustering or produce a flat clustering using local search (e.g., k -means). For the ... Keywords: Clustering, data mining, information retrieval 7 September 2006 ESA'06: Proceedings of the 14th conference on Annual European Symposium - Volume 14 Publisher: Springer-Verlag Bibliometrics: Citation Count: 9 In this paper, we analyze the second eigenvector technique of spectral partitioning on the planted partition random graph model, by constructing a recursive algorithm using the second eigenvectors in order to learn the planted partitions. The correctness of our algorithm is not based on the ratio-cut interpretation of the second ... 8 July 2006 SIAM Journal on Computing: Volume 36 Issue 1, 2006 Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 54 Motivated by applications in which the data may be formulated as a matrix, we consider algorithms for several common linear algebra problems. These algorithms make more efficient use of computational resources, such as the computation time, random access memory (RAM), and the number of passes over the data, than do ... Keywords: massive data sets, matrix multiplication, streaming models, Monte Carlo methods, randomized algorithms 9 July 2006 SIAM Journal on Computing: Volume 36 Issue 1, 2006 Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 88 In many applications, the data consist of (or may be naturally formulated as) an $m \times n$ matrix $A$. It is often of interest to find a low-rank approximation to $A$, i.e., an approximation $D$ to the matrix $A$ of rank not greater than a specified rank $k$, where $k$ ... Keywords: randomized algorithms, massive data sets, Monte Carlo methods, singular value decomposition 10 July 2006 Combinatorics, Probability and Computing: Volume 15 Issue 4, July 2006 Publisher: Cambridge University Press Bibliometrics: Citation Count: 6 The notion of conductance introduced by Jerrum and Sinclair [8] has been widely used to prove rapid mixing of Markov chains. Here we introduce a bound that extends this in two directions. First, instead of measuring the conductance of the worst subset of states, we bound the mixing time by ... 11 July 2006 SIAM Journal on Computing: Volume 36 Issue 1, 2006 Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 62 In many applications, the data consist of (or may be naturally formulated as) an $m \times n$ matrix $A$ which may be stored on disk but which is too large to be read into random access memory (RAM) or to practically perform superlinear polynomial time computations on it. Two algorithms ... Keywords: Monte Carlo methods, CUR matrix decomposition, randomized algorithms, massive data sets 12 January 2006 SODA '06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 9 Downloads (6 Weeks): 2,   Downloads (12 Months): 5,   Downloads (Overall): 274 Full text available: PDF We present multiple pass streaming algorithms for a basic clustering problem for massive data sets. If our algorithm is allotted 2 l passes, it will produce an approximation with error at most ε using Õ ( k 3 /ε 2 / l ) bits of memory, the most critical resource ... 13 June 2005 COLT'05: Proceedings of the 18th annual conference on Learning Theory Publisher: Springer-Verlag Bibliometrics: Citation Count: 28 We present an algorithm for learning a mixture of distributions based on spectral projection. We prove a general property of spectral projection for arbitrary mixtures and show that the resulting algorithm is efficient when the components of the mixture are logconcave distributions in $\Re^{n}$ whose means are separated. The separation ... 14 June 2005 PODS '05: Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems Publisher: ACM Bibliometrics: Citation Count: 24 Downloads (6 Weeks): 0,   Downloads (12 Months): 4,   Downloads (Overall): 422 Full text available: PDF We present a divide-and-merge methodology for clustering a set of objects that combines a top-down "divide" phase with a bottom-up "merge" phase. In contrast, previous algorithms either use top-down or bottom-up methods to construct a hierarchical clustering or produce a flat clustering using local search (e.g., k -means). Our divide ... 15 May 2005 STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing Publisher: ACM Bibliometrics: Citation Count: 13 Downloads (6 Weeks): 1,   Downloads (12 Months): 11,   Downloads (Overall): 322 Full text available: PDF The only general class of MAX-rCSP problems for which Polynomial Time Approximation Schemes (PTAS) are known are the dense problems. In this paper, we give PTAS's for a much larger class of weighted MAX-rCSP problems which includes as special cases the dense problems and, for r = 2, all metric ... Keywords: approximation scheme, tensor decomposition 16 November 2004 Journal of the ACM (JACM): Volume 51 Issue 6, November 2004 Publisher: ACM Bibliometrics: Citation Count: 95 Downloads (6 Weeks): 27,   Downloads (12 Months): 141,   Downloads (Overall): 2,205 Full text available: PDF We consider the problem of approximating a given m × n matrix A by another matrix of specified rank k , which is smaller than m and n . The Singular Value Decomposition (SVD) can be used to find the "best" such approximation. However, it takes time polynomial in m, ... Keywords: sampling, Matrix algorithms, low-rank approximation 17 June 2004 Machine Learning: Volume 56 Issue 1-3 Publisher: Kluwer Academic Publishers Bibliometrics: Citation Count: 88 We consider the problem of partitioning a set of m points in the n -dimensional Euclidean space into k clusters (usually m and n are variable, while k is fixed), so as to minimize the sum of squared distances between each point and its cluster center. This formulation is usually ... Keywords: k-means clustering, randomized algorithms, Singular Value Decomposition 18 May 2004 Journal of the ACM (JACM): Volume 51 Issue 3, May 2004 Publisher: ACM Bibliometrics: Citation Count: 166 Downloads (6 Weeks): 11,   Downloads (12 Months): 146,   Downloads (Overall): 4,125 Full text available: PDF We motivate and develop a natural bicriteria measure for assessing the quality of a clustering that avoids the drawbacks of existing measures. A simple recursive heuristic is shown to have poly-logarithmic worst-case guarantees under the new measure. The main result of the article is the analysis of a popular spectral ... Keywords: Clustering, spectral methods, graph algorithms 19 September 2003 Journal of Computer and System Sciences - STOC 2002: Volume 67 Issue 2, September 2003 Publisher: Academic Press, Inc. Bibliometrics: Citation Count: 25 In a maximum- r -constraint satisfaction problem with variables { x 1 , x 2 , ... , x n }, we are given Boolean functions f 1 , f 2 , ..., f m each involving r of the n variables and are to find the maximum number of ... 20 January 2003 SODA '03: Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms Publisher: Society for Industrial and Applied Mathematics Bibliometrics: Citation Count: 44 Downloads (6 Weeks): 2,   Downloads (12 Months): 15,   Downloads (Overall): 427 Full text available: PDF