ON THE COMPLEXITY OF NONNEGATIVE MATRIX FACTORIZATION

被引：362
|
作者：
Vavasis, Stephen A. [1 ]
机构：
[1] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada
来源：
SIAM JOURNAL ON OPTIMIZATION | 2009年 / 20卷 / 03期
基金：
加拿大自然科学与工程研究理事会;
关键词：
nonnegative matrix factorization; nonnegative rank; complexity; NP-hard; data mining; feature detection;
D O I：
10.1137/070709967
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Nonnegative matrix factorization (NMF) has become a prominent technique for the analysis of image databases, text databases, and other information retrieval and clustering applications. The problem is most naturally posed as continuous optimization. In this report, we define an exact version of NMF. Then we establish several results about exact NMF: (i) that it is equivalent to a problem in polyhedral combinatorics; (ii) that it is NP-hard; and (iii) that a polynomial-time local search heuristic exists.
引用
收藏
页码：1364 / 1377
页数：14
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