- Referenced in 33 articles
- approximates a nonnegative matrix by the product of two low-rank nonnegative matrix factors ... optimally at rate in optimizing each matrix factor, it is superior ... terms of efficiency as well as approximation accuracy. Compared to PNLS and AS that suffer...
- Referenced in 15 articles
- rank approximation of a similarity matrix for graph clustering. Nonnegative matrix factorization (NMF) provides ... lower rank approximation of a matrix by a product of two nonnegative factors ... data matrix as an input, SymNMF takes a nonnegative similarity matrix as an input ... symmetric nonnegative lower rank approximation is computed. We show that SymNMF is related to spectral...
- Referenced in 50 articles
- matrix is then re-ordered according to the independent set ordering and an approximate block ... factorization is performed with a reduced system of smaller size. The multi-level structure...
- Referenced in 71 articles
- define your own (coupled) matrix and tensor factorizations with structured factors and support for dense ... term decompositions (BTD) and low multilinear rank approximation (LMLRA), complex optimization: quasi-Newton and nonlinear...
- Referenced in 42 articles
- solve approximately the Newton equations. The preconditioner M is factored in PCG using ... sparse modified Cholesky factorization based on the Yale Sparse Matrix Package. In this paper...
- Referenced in 26 articles
- matrix level. Since these factorizations are nonlocal, we introduce a second order local approximation...
- Referenced in 7 articles
- Matrix Factorization. Matrix factorizations—where a given data matrix is approximated by a product ... powerful data mining tools. Among other tasks, matrix factorizations are often used to separate global...
- Referenced in 11 articles
- scalable, kernel-independent method for approximately evaluating kernel matrix-vector products. ASKIT is based ... efficiently factoring off-diagonal blocks of the kernel matrix using approximate nearest neighbor information...
- Referenced in 3 articles
- rank matrix approximation via the nonnegative matrix factorization (NMF). NMF is a constrained low rank ... where a matrix is approximated by a product of two nonnegative factors. The role...
- Referenced in 12 articles
- full rank matrix. Numerically it is more robust than an incomplete Cholesky factorization preconditioner ... Cholesky factorization of the normal equations. Theoretical results show that the CIMGS factorization has better ... factor as the set of dropped positions gets smaller. CIMGS lies between complete Cholesky factorization ... factorization in its approximation properties. These theoretical properties usually hold numerically, even when the matrix...
- Referenced in 35 articles
- problem of approximating, in the Frobenius-norm sense, a positive, semidefinite symmetric matrix ... rank-one matrix, with an upper bound on the cardinality of its eigenvector. The problem ... decomposition of a covariance matrix into sparse factors, and has wide applications ranging from biology...
- Referenced in 41 articles
- sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK ... eliminates singletons by permuting the input matrix A into the form ... pattern of ATA. Approximate rank-detection is performed within each frontal matrix using Heath ... sufficiently large problems, the resulting sparse QR factorization obtains a substantial fraction of the theoretical...
- Referenced in 32 articles
- discussed, COLAMD and SYMAMD, that compute approximate minimum degree orderings for sparse matrices ... ordering prior to numerical factorization, and (2) sparse Cholesky factorization, which requires a symmetric permutation ... both the rows and columns of the matrix being factorized. These orderings are computed...
- Referenced in 29 articles
- Frobenius norm) minimization to compute a sparse approximate inverse. The sparsity pattern used ... pattern of a power of a sparsified matrix. ParaSails also uses a post-filtering technique ... symmetric positive definite (SPD) problems using a factorized SPD preconditioner. ParaSails can also solve general...
- Referenced in 5 articles
- Generic Approximate Sparse Inverse (GenASPI) matrix algorithm based on ILU(0) factorization. The proposed scheme ... Generic Approximate Banded Inverse (GenAbI), which is a banded approximate inverse used in conjunction with ... large sparse linear systems. The proposed GenASPI matrix algorithm, is based on Approximate Inverse Sparsity...
- Referenced in 27 articles
- Variational inference is a scalable technique for approximate Bayesian inference. Deriving variational inference algorithms requires ... across hierarchical generalized linear models, nonconjugate matrix factorization, and a mixture model. We train...
- Referenced in 32 articles
- factors a matrix completely, but it can drop small elements from the factorization ... Factorization. Solves huge systems by storing the Cholesky factors in files. Can work with factors ... symmetric orderings. Matrix Operations. Matrix-vector multiplication, triangular solvers, matrix reordering. Matrix Input/Output. Routines ... dropping nonzeros from the coefficient matrix and them factoring the preconditioner directly. Recursive Vaidya...
- Referenced in 5 articles
- variational approximation, with a parsimonious but flexible factor parameterization of the covariance matrix. We implement...
- Referenced in 22 articles
- efficient block algorithm for approximating an RRQR factorization, employing a windowed version of the commonly ... Ipsen} [SIAM J. Matrix Anal. Appl...
- Referenced in 9 articles
- propose an algorithm to compute an approximate singular value decomposition (SVD) of least-squares operators ... with multiple events. Such factorizations can be used to accelerate matrix-vector multiplications ... background medium and, by invoking the Born approximation, we obtain a linear least-squares problem ... describe in this paper constructs an approximate SVD of the Born operator (the operator...