Bicriteria Sparse Nonnegative Matrix Factorization via Two-Timescale Duplex Neurodynamic Optimization

被引:43
作者
Che, Hangjun [1 ]
Wang, Jun [2 ,3 ]
Cichocki, Andrzej [4 ,5 ]
机构
[1] Southwest Univ, Coll Elect & Informat Engn, Chongqing 400715, Peoples R China
[2] City Univ Hong Kong, Dept Comp Sci, Hong Kong, Peoples R China
[3] City Univ Hong Kong, Sch Data Sci, Hong Kong, Peoples R China
[4] Skolkovo Inst Sci & Technol, Moscow 143026, Russia
[5] Polish Acad Sci, Syst Res Inst, PL-01447 Warsaw, Poland
基金
中国国家自然科学基金;
关键词
Optimization; Neurodynamics; Sparse matrices; Matrix converters; Linear programming; Search problems; Recurrent neural networks; Mixed-integer optimization; sparse nonnegative matrix factorization (SNMF); two-timescale duplex neurodynamics; RECURRENT NEURAL-NETWORK; PARTICLE SWARM OPTIMIZATION; ALGORITHMS; INTEGER; SUBJECT;
D O I
10.1109/TNNLS.2021.3125457
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
In this article, sparse nonnegative matrix factorization (SNMF) is formulated as a mixed-integer bicriteria optimization problem for minimizing matrix factorization errors and maximizing factorized matrix sparsity based on an exact binary representation of $l_{0}$ matrix norm. The binary constraints of the problem are then equivalently replaced with bilinear constraints to convert the problem to a biconvex problem. The reformulated biconvex problem is finally solved by using a two-timescale duplex neurodynamic approach consisting of two recurrent neural networks (RNNs) operating collaboratively at two timescales. A Gaussian score (GS) is defined as to integrate the bicriteria of factorization errors and sparsity of resulting matrices. The performance of the proposed neurodynamic approach is substantiated in terms of low factorization errors, high sparsity, and high GS on four benchmark datasets.
引用
收藏
页码:4881 / 4891
页数:11
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