Fast coordinate descent methods with variable selection for non-negative matrix factorization

This article uses the projected gradient method (PG) for a non-negative matrix factorization problem (NMF), where one or both matrix factors must have orthonormal columns or rows. We penalize the orthonormality constraints and apply the PG method via a block coordinate descent approach. This means that at a certain time one matrix factor is fixed and the other is updated by moving along the steepest descent direction computed from the penalized objective function and projecting onto the space of non-negative matrices. Our method is tested on two sets of synthetic data for various values of penalty parameters. The performance is compared to the well-known multiplicative update (MU) method from Ding (2006), and with a modified global convergent variant of the MU algorithm recently proposed by Mirzal (2014). We provide extensive numerical results coupled with appropriate visualizations, which demonstrate that our method is very competitive and usually outperforms the other two methods.

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Automatic Model Order Selection for Convolutive Non-Negative Matrix Factorization

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences ◽

10.1587/transfun.e99.a.1867 ◽

2016 ◽

Vol E99.A (10) ◽

pp. 1867-1870 ◽

Cited By ~ 1

Author(s):

Yinan LI ◽

Xiongwei ZHANG ◽

Meng SUN ◽

Chong JIA ◽

Xia ZOU

Keyword(s):

Matrix Factorization ◽

Order Selection ◽

Model Order Selection ◽

Model Order ◽

Selection For ◽

Non Negative Matrix Factorization

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Adaptive Test Selection for Factorization-based Surrogate Fitness in Genetic Programming

Foundations of Computing and Decision Sciences ◽

10.1515/fcds-2017-0017 ◽

2017 ◽

Vol 42 (4) ◽

pp. 339-358 ◽

Cited By ~ 1

Author(s):

Krzysztof Krawiec ◽

Paweł Liskowski

Keyword(s):

Genetic Programming ◽

Evolutionary Algorithm ◽

Matrix Factorization ◽

Fitness Function ◽

Interaction Matrix ◽

Simulated Evolution ◽

Adaptive Test ◽

Selection For ◽

Correct Program ◽

Non Negative Matrix Factorization

Abstract Genetic programming (GP) is a variant of evolutionary algorithm where the entities undergoing simulated evolution are computer programs. A fitness function in GP is usually based on a set of tests, each of which defines the desired output a correct program should return for an exemplary input. The outcomes of interactions between programs and tests in GP can be represented as an interaction matrix, with rows corresponding to programs in the current population and columns corresponding to tests. In previous work, we proposed SFIMX, a method that performs only a fraction of interactions and employs non-negative matrix factorization to estimate the outcomes of remaining ones, shortening GP’s runtime. In this paper, we build upon that work and propose three extensions of SFIMX, in which the subset of tests drawn to perform interactions is selected with respect to test difficulty. The conducted experiment indicates that the proposed extensions surpass the original SFIMX on a suite of discrete GP benchmarks.

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