MATHEMATICAL MODELING AND NUMERICAL SIMULATION

On the stochastic gradient descent matrix factorization in application to the supervised classification of microarrays

V. N. Nikulin

Vyatka State University, Faculty of economics and management, department of MME, 36 Moskovskaya st., Kirov, 610000, Russia

Abstract: Microarray datasets are highly dimensional, with a small number of collected samples in comparison to thousands of features. This poses a significant challenge that affects the interpretation, applicability and validation of the analytical results. Matrix factorizations have proven to be a useful method for describing data in terms of a small number of meta-features, which reduces noise, while still capturing the essential features of the data. Three novel and mutually relevant methods are presented in this paper: 1) gradient-based matrix factorization with two adaptive learning rates (in accordance with the number of factor matrices) and their automatic updates; 2) nonparametric criterion for the selection of the number of factors; and 3) nonnegative version of the gradient-based matrix factorization which doesn't require any extra computational costs in difference to the existing methods. We demonstrate effectiveness of the proposed methods to the supervised classification of gene expression data.

Keywords: matrix factorization, unsupervised learning, number of factors, nonnegativity, bioinformatics, leave-one-out, classification.

UDC: 004.9

Received: 18.03.2013
Revised: 05.04.2013

DOI: 10.20537/2076-7633-2013-5-2-131-140