On the gradient-based algorithm for matrix factorization applied to dimensionality reduction

The high dimensionality of microarray data, the expressions of thousands of genes in a much smaller number of samples, presents challenges that affect the applicability of the analytical results. In principle, it would be better to describe the data in terms of a small number of metagenes, derived as a result of matrix factorisation, which could reduce noise while still capturing the essential features of the data. We propose a fast and general method for matrix factorization which is based on decomposition by parts that can reduce the dimension of expression data from thousands of genes to several factors. Unlike classification and regression, matrix decomposition requires no response variable and thus falls into category of unsupervised learning methods. We demonstrate the effectiveness of this approach to the supervised classification of gene expression data