Results 311 to 320 of about 3,570,033 (364)

Householder's tridiagonalization of a symmetric matrix

Numerische Mathematik, 1968
In an early paper in this series [4] Householder’s algorithm for the tridiagonalization of a real symmetric matrix was discussed. In the light of experience gained since its publication and in view of its importance it seems worthwhile to issue improved versions of the procedure given there.
R. Martin, C. Reinsch, J. H. Wilkinson
semanticscholar   +4 more sources

Symmetric Nonnegative Matrix Factorization-Based Community Detection Models and Their Convergence Analysis

IEEE Transactions on Neural Networks and Learning Systems, 2021
Community detection is a popular yet thorny issue in social network analysis. A symmetric and nonnegative matrix factorization (SNMF) model based on a nonnegative multiplicative update (NMU) scheme is frequently adopted to address it.
Xin Luo, Zhigang Liu, Long Jin, Yue Zhou, Mengchu Zhou   +4 more
semanticscholar   +1 more source

Semisupervised Adaptive Symmetric Non-Negative Matrix Factorization

IEEE Transactions on Cybernetics, 2020
As a variant of non-negative matrix factorization (NMF), symmetric NMF (SymNMF) can generate the clustering result without additional post-processing, by decomposing a similarity matrix into the product of a clustering indicator matrix and its transpose.
Yuheng Jia, Hui Liu, Junhui Hou, S. Kwong   +3 more
semanticscholar   +1 more source

Approximating a Symmetric Matrix [PDF]

Psychometrika, 1990
We examine the least squares approximation C to a symmetric matrix B, when all diagonal elements get weight w relative to all nondiagonal elements. When B has positivity p and C is constrained to be positive semi-definite, our main result states that, when w ≥1/2, then the rank of C is never greater than p, and when w ≤1/2 then the rank of C is at ...
R. A. Bailey, John C. Gower
openaire   +1 more source

Fundamental limits of symmetric low-rank matrix estimation

Probability theory and related fields, 2016
We consider the high-dimensional inference problem where the signal is a low-rank symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension setting ...
M. Lelarge, Léo Miolane
semanticscholar   +1 more source

Pairwise Constraint Propagation-Induced Symmetric Nonnegative Matrix Factorization

IEEE Transactions on Neural Networks and Learning Systems, 2018
As a variant of nonnegative matrix factorization (NMF), symmetric NMF (SNMF) has shown to be effective for capturing the cluster structure embedded in the graph representation.
Wenhui Wu, Yuheng Jia, S. Kwong, Junhui Hou   +3 more
semanticscholar   +1 more source

Matrix Symmetrization

Journal of Guidance, Control, and Dynamics, 1998
Summary: In this note we point out that the symmetrized real matrix is also the symmetric matrix that is the closest, in the Euclidean norm, to the matrix being symmetrized. This implies that, when symmetrizing the solutions to Riccati and Lyapunov equations, one actually replaces the solution by its closest symmetric matrix.
openaire   +2 more sources

Determinant of the Sum of a Symmetric and a Skew-Symmetric Matrix

SIAM Journal on Matrix Analysis and Applications, 1997
Assume \(\alpha=(\alpha_1\geq\ldots\geq\alpha_n)\), and \(\beta=(\beta_1=\beta_2\geq\beta_3=\beta_4\geq\ldots\geq\beta_n)\), where \(\beta_n=0\) if \(n\) is odd. Using standard notation, write \(\widetilde A=\text{diag}(\alpha_n,\ldots,\alpha_1)\), \(\widetilde B=\sum_{k\leq n/2}\beta_{2k}(E_{2k-1,2k}-E_{2k,2k-1})\).
Bebiano, Natália, Li, Chi-Kwong, da Providência, João   +2 more
openaire   +3 more sources

An algorithm for matrix symmetrization

Journal of the Franklin Institute, 1981
Abstract In this paper we characterize a symmetrizability property using the theory of output sets. Employing the basic properties of symmetric matrices and an efficient algorithm for systematic generation of output sets, an algorithm for testing the symmetrizability of a matrix is presented and illustrated.
openaire   +2 more sources

Multi-document summarization via sentence-level semantic analysis and symmetric matrix factorization

Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, 2008
Multi-document summarization aims to create a compressed summary while retaining the main characteristics of the original set of documents. Many approaches use statistics and machine learning techniques to extract sentences from documents. In this paper,
Dingding Wang, Tao Li, Shenghuo Zhu, C. Ding   +3 more
semanticscholar   +1 more source