Nonnegative Matrix Factorization models for knowledge extraction from biomedical and other real world data

Inspect data for searching valuable information hidden in represents a key aspect in several fields. Fortunately, most of the available data presents an embedded mathematical structure which can be profitably exploited to better investigate latent patterns hidden in them. Dimensionality Reduction (DR) approaches represent one of the most suitable instrument to untangle latent information. These techniques aim to represent data under analysis onto a low-dimensional space allowing to consider most of all of intrinsic knowledge as ideal sources (namely basis) of the process under consideration. In this work we consider Nonnegative Matrix Factorizations (NMFs), which prove to be the most effective among DR approaches in analyzing real-life nonnegative data. NMF simulates the human part-based learning process which states that parts are combined additively to form a whole. Some variants of NMF will be also presented as minimization tasks to which regularization terms can be added in accordance to some additional characteristics (such as sparsity or orthogonality). We investigate significant computational and interpretative aspects related to NMF according to different application domains, with a specific attention to the analysis of biological data. Moreover we present a new NMF model designed for microarray data analysis that incorporates specific biological proprieties as different constraints. Since NMF and its variants are daily used in several application domains, we conclude stressing how NMF and its constrained variants work in some real life applications, showing some original works related to the analysis of data from engineering field.