Matrix Factorization Techniques in Machine Learning, Signal Processing, and Statistics

被引:15
作者
Du, Ke-Lin [1 ]
Swamy, M. N. S. [1 ]
Wang, Zhang-Quan [2 ]
Mow, Wai Ho [3 ]
机构
[1] Concordia Univ, Dept Elect & Comp Engn, Montreal, PQ H3G 1M8, Canada
[2] Zhejiang Shuren Univ, Coll Informat Sci & Technol, Hangzhou 310015, Peoples R China
[3] Hong Kong Univ Sci & Technol, Dept Elect & Comp Engn, Hong Kong, Peoples R China
基金
加拿大自然科学与工程研究理事会;
关键词
compressed sensing; dictionary learning; sparse approximation; matrix completion; nonnegative matrix factorization; LOW-RANK MATRIX; ORTHOGONAL MATCHING PURSUIT; RESTRICTED ISOMETRY PROPERTY; PRINCIPAL COMPONENT ANALYSIS; NONNEGATIVE MATRIX; SPARSE SIGNALS; LEAST-SQUARES; VARIABLE SELECTION; DIMENSIONALITY REDUCTION; UNDERDETERMINED SYSTEMS;
D O I
10.3390/math11122674
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Compressed sensing is an alternative to Shannon/Nyquist sampling for acquiring sparse or compressible signals. Sparse coding represents a signal as a sparse linear combination of atoms, which are elementary signals derived from a predefined dictionary. Compressed sensing, sparse approximation, and dictionary learning are topics similar to sparse coding. Matrix completion is the process of recovering a data matrix from a subset of its entries, and it extends the principles of compressed sensing and sparse approximation. The nonnegative matrix factorization is a low-rank matrix factorization technique for nonnegative data. All of these low-rank matrix factorization techniques are unsupervised learning techniques, and can be used for data analysis tasks, such as dimension reduction, feature extraction, blind source separation, data compression, and knowledge discovery. In this paper, we survey a few emerging matrix factorization techniques that are receiving wide attention in machine learning, signal processing, and statistics. The treated topics are compressed sensing, dictionary learning, sparse representation, matrix completion and matrix recovery, nonnegative matrix factorization, the Nystrom method, and CUR matrix decomposition in the machine learning framework. Some related topics, such as matrix factorization using metaheuristics or neurodynamics, are also introduced. A few topics are suggested for future investigation in this article.
引用
收藏
页数:50
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