Sparse Non-negative Matrix Factorizations via Alternating Non-negativity-constrained Least Squares

Abstract

Many practical pattern recognition problems require non-negativity constraints. For example, pixels in digital images and chemical concentrations in bioinformatics are non-negative. Non-negative matrix factorization (NMF) is a useful technique in approximating these high dimensional data. Sparse NMFs are also useful when we need to control the degree of sparseness in non-negative basis vectors or non-negative lower-dimensional representations. In this paper, we introduce novel sparse NMFs via alternating non-negativity-constrained least squares. We applied one of the proposed sparse NMFs to cancer class discovery and gene expression data analysis. Our experimental results illustrate that our proposed method achieves better clustering performance than NMF based on multiplicative update rules and sparse NMFs based on the gradient descent method.