Investigating initialization techniques for Nonnegative Matrix Factorization: a survey and a case of study of microarrays

Nonnegative Matrix Factorization (NMF) is a class of low-rank dimensionality reduction methods which approximates a given nonnegative data matrix into the product of two nonnegative matrices of proper dimensions performing the so called additive part-based decomposition of data. Due to the peculiar representation of information through purely additive linear combinations and the preservation of data nonnegativity, NMF has been recognized as one of the most promising method to analyse gene expression data coming from any microarray experiment. This paper brie y reviews some aspects and practical issues related to NMF when this technique is applied to microarray data. In particular, issues such as interpretation of factorization results, mechanisms of information visualization and extraction techniques used in the context of microarray data analysis and their relationship with some concepts usually appearing in information theory are discussed.