Computing symmetric nonnegative rank factorizations

被引：11
|
作者：
Kalofolias, V. [1 ]
Gallopoulos, E. [1 ]
机构：
[1] Univ Patras, Dept Comp Engn & Informat, GR-26110 Patras, Greece
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2012年 / 436卷 / 02期
关键词：
Nonnegative rank factorization; Nonnegative matrix factorization; Symmetric; Rotation; Isometry; Principal submatrix; Pivoted Cholesky factorization; Symmetric positive semidefinite; Arrowhead matrix; Extreme ray; Maximum independent set; Rank reduction; MATRIX FACTORIZATION; MODEL;
D O I：
10.1016/j.laa.2011.03.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An algorithm is described for the nonnegative rank factorization (NRF) of some completely positive (CP) matrices whose rank is equal to their CP-rank. The algorithm can compute the symmetric NRF of any nonnegative symmetric rank-r matrix that contains a diagonal principal submatrix of that rank and size with leading cost O(rm(2)) operations in the dense case. The algorithm is based on geometric considerations and is easy to implement. The implications for matrix graphs are also discussed. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：421 / 435
页数：15
相关论文
共 50 条
  • [1] COMPUTING NONNEGATIVE RANK FACTORIZATIONS
    CAMPBELL, SL
    POOLE, GD
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1981, 35 (FEB) : 175 - 182
  • [2] THE NONNEGATIVE RANK FACTORIZATIONS OF NONNEGATIVE MATRICES
    CHEN, JC
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1984, 62 (NOV) : 207 - 217
  • [3] A NOTE ON NONNEGATIVE RANK FACTORIZATIONS
    JETER, MW
    PYE, WC
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1981, 38 (JUN) : 171 - 173
  • [4] FACTORIZATIONS OF NONNEGATIVE SYMMETRIC OPERATORS
    Arlinskii, Yury
    Kovalev, Yury
    METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 2013, 19 (03): : 211 - 226
  • [5] On Mixed Memberships and Symmetric Nonnegative Matrix Factorizations
    Mao, Xueyu
    Sarkar, Purnamrita
    Chakrabarti, Deepayan
    INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 70, 2017, 70
  • [6] On reduced rank nonnegative matrix factorization for symmetric nonnegative matrices
    Catral, M
    Han, LX
    Neumann, M
    Plemmons, RJ
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 393 : 107 - 126
  • [7] Multiplicative Algorithms for Symmetric Nonnegative Tensor Factorizations and Its Applications
    Che, Maolin
    Wei, Yimin
    JOURNAL OF SCIENTIFIC COMPUTING, 2020, 83 (03)
  • [8] Multiplicative Algorithms for Symmetric Nonnegative Tensor Factorizations and Its Applications
    Maolin Che
    Yimin Wei
    Journal of Scientific Computing, 2020, 83
  • [9] Computing symmetric rank for symmetric tensors
    Bernardi, Alessandra
    Gimigliano, Alessandro
    Ida, Monica
    JOURNAL OF SYMBOLIC COMPUTATION, 2011, 46 (01) : 34 - 53
  • [10] MINIMUM-VOLUME RANK-DEFICIENT NONNEGATIVE MATRIX FACTORIZATIONS
    Leplat, Valentin
    Ang, Andersen M. S.
    Gillis, Nicolas
    2019 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), 2019, : 3402 - 3406
12345