Nonnegative Matrix Factorization (NMF) has acquired a relevant role in the panorama of knowledge extraction, thanks to the peculiarity that non-negativity applies to both bases and weights, which allows meaningful interpretations and is consistent with the natural human part-based learning process. Nevertheless, most NMF algorithms are iterative, so initialization methods affect convergence behaviour, the quality of the final solution, and NMF performance in terms of the residual of the cost function. Studies on the impact of NMF initialization techniques have been conducted for text or image datasets, but very few considerations can be found in the literature when biological datasets are studied, even though NMFs have largely demonstrated their usefulness in better understanding biological mechanisms with omic datasets. This paper aims to present the state-of-the-art on NMF initialization schemes along with some initial considerations on the impact of initialization methods when microarrays (a simple instance of omic data) are evaluated with NMF mechanisms. Using a series of measures to qualitatively examine the biological information extracted by a given NMF scheme, it preliminary appears that some information (e.g., represented by genes) can be extracted regardless of the initialization scheme used.

The rapid development of high-performance technologies has greatly promoted studies of molecular oncology producing large amounts of data. Even if these data are publicly available, they need to be processed and studied to extract information useful to better understand mechanisms of pathogenesis of complex diseases, such as tumors. In this article, we illustrated a procedure for mining biologically meaningful biomarkers from microarray datasets of different tumor histotypes. The proposed methodology allows to automatically identify a subset of potentially informative genes from microarray data matrices, which differs either in the number of rows (genes) and of columns (patients). The methodology integrates nonnegative matrix factorization method, a functional enrichment analysis web tool with a properly designed gene extraction procedure to allow the analysis of omics input data with different row size. The proposed methodology has been used to mine microarray of solid tumors of different embryonic origin to verify the presence of common genes characterizing the heterogeneity of cancer-associated fibroblasts. These automatically extracted biomarkers could be used to suggest appropriate therapies to inactivate the state of active fibroblasts, thus avoiding their action on tumor progression.

Multiple myeloma (MM) is a cancer of terminally differentiated plasma that is part of a spectrum of blood diseases. The role of the micro-environment is crucial for MM clonal evolution. This paper describes the analysis carried out on a limited number of genes automatically extracted by a nonnegative matrix factorization (NMF) based approach from gene expression profiles of bone marrow fibroblasts of patients with monoclonal gammopathy of undetermined significance (MGUS) and MM. Automatic exploration through NMF, combined with a motivated post-processing procedure and a pathways analysis of extracted genes, allowed to infer that a functional switch is required to lead fibroblasts to acquire pro-tumorigenic activity in the progression of the disease from MGUS to MM. The extracted biologically relevant genes may be representative of the considered clinical conditions and may contribute to a deeper understanding of tumor behavior.

One of the main problems in the analysis of real data is often related to the presence of anomalies. Namely, anomalous cases can both spoil the resulting analysis and contain valuable information at the same time. In both cases, the ability to detect these occurrences is very important. In the biomedical field, a correct identification of outliers could allow the development of new biological hypotheses that are not considered when looking at experimental biological data. In this work, we address the problem of detecting outliers in gene expression data, focusing on microarray analysis. We propose an ensemble approach for detecting anomalies in gene expression matrices based on the use of Hierarchical Clustering and Robust Principal Component Analysis, which allows us to derive a novel pseudo-mathematical classification of anomalies.