Results 1  10
of
476
Balanced model reduction via the proper orthogonal decomposition
 AIAA Journal
, 2002
"... A new method for performing a balanced reduction of a highorder linear system is presented. The technique combines the proper orthogonal decomposition and concepts from balanced realization theory. The method of snapshots is used to obtain lowrank, reducedrange approximationsto the system control ..."
Abstract

Cited by 134 (6 self)
 Add to MetaCart
A new method for performing a balanced reduction of a highorder linear system is presented. The technique combines the proper orthogonal decomposition and concepts from balanced realization theory. The method of snapshots is used to obtain lowrank, reducedrange approximationsto the system
Clustering Large Graphs via the Singular Value Decomposition
 MACHINE LEARNING
, 2004
"... We consider the problem of partitioning a set of m points in the ndimensional 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 the objective of the ..."
Abstract

Cited by 112 (2 self)
 Add to MetaCart
be solved by computing the Singular Value Decomposition (SVD) of the n matrix A that represents the m points; this solution can be used to get a 2approximation algorithm for the original problem. We then argue that in fact the relaxation provides a generalized clustering which is useful in its own right
ExternalMemory Graph Algorithms
, 1995
"... We present a collection of new techniques for designing and analyzing efficient externalmemory algorithms for graph problems and illustrate how these techniques can be applied to a wide variety of specific problems. Our results include: ffl Proximateneighboring. We present a simple method for der ..."
Abstract

Cited by 186 (22 self)
 Add to MetaCart
for deriving externalmemory lower bounds via reductions from a problem we call the "proximate neighbors" problem. We use this technique to derive nontrivial lower bounds for such problems as list ranking, expression tree evaluation, and connected components. ffl PRAM simulation. We give methods
On the Nyström Method for Approximating a Gram Matrix for Improved KernelBased Learning
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... A problem for many kernelbased methods is that the amount of computation required to find the solution scales as O(n³), where n is the number of training examples. We develop and analyze an algorithm to compute an easilyinterpretable lowrank approximation to an nn Gram matrix G such that compu ..."
Abstract

Cited by 188 (11 self)
 Add to MetaCart
A problem for many kernelbased methods is that the amount of computation required to find the solution scales as O(n³), where n is the number of training examples. We develop and analyze an algorithm to compute an easilyinterpretable lowrank approximation to an nn Gram matrix G
Sparse principal component analysis via regularized low rank matrix approximation
 Journal of Multivariate Analysis
"... Principal component analysis (PCA) is a widely used tool for data analysis and dimension reduction in applications throughout science and engineering. However, the principal components (PCs) can sometimes be difficult to interpret, because they are linear combinations of all the original variables. ..."
Abstract

Cited by 102 (3 self)
 Add to MetaCart
. To facilitate interpretation, sparse PCA produces modified PCs with sparse loadings, i.e. loadings with very few nonzero elements. In this paper, we propose a new sparse PCA method, namely sparse PCA via regularized SVD (sPCArSVD). We use the connection of PCA with singular value decomposition (SVD
THE CLIQUERANK OF 3CHROMATIC PERFECT GRAPHS
"... The cliquerank of a perfect graph G introduced by Fonlupt and Sebö is the linear rank of the incidence matrix of the maximum cliques of G. We study this rank for 3chromatic perfect graphs. We prove that if, in addition, G is diamondfree, G has two distinct colorations. An immediate consequence is ..."
Abstract
 Add to MetaCart
The cliquerank of a perfect graph G introduced by Fonlupt and Sebö is the linear rank of the incidence matrix of the maximum cliques of G. We study this rank for 3chromatic perfect graphs. We prove that if, in addition, G is diamondfree, G has two distinct colorations. An immediate consequence
RELATIVEERROR CUR MATRIX DECOMPOSITIONS
 SIAM J. MATRIX ANAL. APPL
, 2008
"... Many data analysis applications deal with large matrices and involve approximating the matrix using a small number of “components.” Typically, these components are linear combinations of the rows and columns of the matrix, and are thus difficult to interpret in terms of the original features of the ..."
Abstract

Cited by 86 (17 self)
 Add to MetaCart
Many data analysis applications deal with large matrices and involve approximating the matrix using a small number of “components.” Typically, these components are linear combinations of the rows and columns of the matrix, and are thus difficult to interpret in terms of the original features
Network Decomposition and Locality in Distributed Computation (Extended Abstract)
, 1989
"... We introduce a concept of network decomposition, the essence of which is to partition an arbitrary graph into smalldiameter connected components, such that the graph created by contracting each component into a single node has low chromatic number. We present an efficient distributed algorith ..."
Abstract

Cited by 88 (5 self)
 Add to MetaCart
We introduce a concept of network decomposition, the essence of which is to partition an arbitrary graph into smalldiameter connected components, such that the graph created by contracting each component into a single node has low chromatic number. We present an efficient distributed
On the computational complexity of the forcing chromatic number
, 2004
"... We consider vertex colorings of graphs in which adjacent vertices have distinct colors. A graph is schromatic if it is colorable in s colors and any coloring of it uses at least s colors. The forcing chromatic number Fχ(G) of an schromatic graph G is the smallest number of vertices which must be c ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We consider vertex colorings of graphs in which adjacent vertices have distinct colors. A graph is schromatic if it is colorable in s colors and any coloring of it uses at least s colors. The forcing chromatic number Fχ(G) of an schromatic graph G is the smallest number of vertices which must
Biclique Decompositions and Hermitian Rank
 Linear Algebra Appl
, 1999
"... The Hermitian rank, h(A), of a Hermitian matrix A is defined and shown to equal maxfn+ (A); n \Gamma (A)g, the maximum of the numbers of positive and negative eigenvalues of A. Properties of Hermitian rank are developed and used to obtain results on the minimum number, b(G), of complete bipartite su ..."
Abstract

Cited by 16 (4 self)
 Add to MetaCart
The Hermitian rank, h(A), of a Hermitian matrix A is defined and shown to equal maxfn+ (A); n \Gamma (A)g, the maximum of the numbers of positive and negative eigenvalues of A. Properties of Hermitian rank are developed and used to obtain results on the minimum number, b(G), of complete bipartite
Results 1  10
of
476