A nonparametric criterion for the selection of the number of factors and nonnegative extension for gradient-based matrix factorization

The high dimensionality of the data, the expressions of thousands of features in a much smaller number of samples, presents challenges that affect applicability of the analytical results. In principle, it would be better to describe the data in terms of a small number of meta-features, derived as a result of matrix factorization, which could reduce noise while still capturing the essential features of the data. Two novel and mutually relevant methods are presented in this paper: 1) nonparametric criterion for the selection of the number of factors; and 2) nonnegative version of the gradient-based matrix factorization which doesn´t require any extra computational costs in comparison to the existing methods. We demonstrate effectiveness of the proposed methods to the supervised classification of gene expression data.