On the L1-norm Approximation of a Matrix by Another of Lower Rank

被引：0

作者：

Tsagkarakis, Nicholas ^{[1
]}

Markopoulos, Panos P. ^{[2
]}

Pados, Dimitris A. ^{[1
]}

机构：

[1] SUNY Buffalo, Dept Elect Engn, Buffalo, NY 14260 USA

[2] Rochester Inst Technol, Dept Elect & Microelect Engn, Rochester, NY 14623 USA

来源：

2016 15TH IEEE INTERNATIONAL CONFERENCE ON MACHINE LEARNING AND APPLICATIONS (ICMLA 2016) | 2016年

基金：

美国国家科学基金会;

关键词：

Low rank approximation; L-1-norm; principal component analysis (PCA); erroneous data; faulty measurements; machine learning; outlier resistance; subspace signal processing; uniform feature preservation; FACTORIZATION;

D O I：

10.1109/ICMLA.2016.133

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In the past decade, there has been a growing documented effort to approximate a matrix by another of lower rank minimizing the L(1-)norm of the residual matrix. In this paper, we first show that the problem is NP-hard. Then, we introduce a theorem on the sparsity of the residual matrix. The theorem sets the foundation for a novel algorithm that outperforms all existing counterparts in the L-1-norm error minimization metric and exhibits high outlier resistance in comparison to usual L-2-norm error minimization in machine learning applications.

引用

页码：768 / 773

页数：6

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