Tensor decompositions, alternating least squares and other tales

被引：324
作者：
Comon, P. [1 ]
Luciani, X. [1 ]
de Almeida, A. L. F. [1 ]
机构：
[1] Univ Nice, Lab 13S, UMR6070, F-06903 Sophia Antipolis, France
来源：
JOURNAL OF CHEMOMETRICS | 2009年 / 23卷 / 7-8期
关键词：
tensor rank; PARAFAC; canonical decomposition; three-way array; degeneracy; computational complexity; LOW-RANK APPROXIMATION; TYPICAL RANK; 3-WAY ARRAYS; CANDECOMP/PARAFAC; UNIQUENESS; DEGENERACY; ALGORITHMS; SYSTEMS; ORDER;
D O I：
10.1002/cem.1236
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This work was originally motivated by a classification of tensors proposed by Richard Harshman. In particular, we focus on simple and multiple 'bottlenecks', and on 'swamps'. Existing theoretical results are surveyed, some numerical algorithms are described in details, and their numerical complexity is calculated. In particular, the interest in using the enhanced line search (ELS) enhancement in these algorithms is discussed. Computer simulations feed this discussion. Copyright (C) 2009 John Wiley & Sons, Ltd.
引用
收藏
页码：393 / 405
页数：13
相关论文
共 71 条
[1]  
ABO H, 2006, ARXIVMATH0607191
[2]   HORACE METHOD - APPLICATION TO 4TH-DEGREE INTERPOLATION [J].
ALEXANDER, J ;
HIRSCHOWITZ, A .
INVENTIONES MATHEMATICAE, 1992, 107 (03) :585-602
[3]  
[Anonymous], 1983, Three-Mode Principal Component Analysis: Theory and Applications
[4]   BORDER RANK OF MXNX(MN-Q) TENSORS [J].
BINI, D .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1986, 79 :45-51
[5]  
Bini Dario., 1980, Lecture Notes in Computer Science, P98
[6]   On the Alexander-Hirschowitz theorem [J].
Brambilla, Maria Chiara ;
Ottaviani, Giorgio .
JOURNAL OF PURE AND APPLIED ALGEBRA, 2008, 212 (05) :1229-1251
[7]   PARAFAC. Tutorial and applications [J].
Bro, R .
CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS, 1997, 38 (02) :149-171
[8]   Improving the speed of multiway algorithms part II. Compression [J].
Bro, R ;
Andersson, CA .
CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS, 1998, 42 (1-2) :105-113
[9]  
BURGISSER R, 1997, ALGEBRAIC COMPLEXITY, V315
[10]   ANALYSIS OF INDIVIDUAL DIFFERENCES IN MULTIDIMENSIONAL SCALING VIA AN N-WAY GENERALIZATION OF ECKART-YOUNG DECOMPOSITION [J].
CARROLL, JD ;
CHANG, JJ .
PSYCHOMETRIKA, 1970, 35 (03) :283-&
12345678