Coupled Matrix Factorization with Sparse Factors to Identify Potential Biomarkers in Metabolomics

Abstract

Metabolomics focuses on the detection of chemical substances in biological fluids such as urine and blood using a number of analytical techniques including Nuclear Magnetic Resonance (NMR) spectroscopy and Liquid Chromatography-Mass Spectrometry (LC-MS). Among the major challenges in analysis of metabolomics data are (i) joint analysis of data from multiple platforms, and (ii) capturing easily interpretable underlying patterns, which could be further utilized for biomarker discovery. In order to address these challenges, the authors formulate joint analysis of data from multiple platforms as a coupled matrix factorization problem with sparsity penalties on the factor matrices. They developed an all-at-once optimization algorithm, called CMF-SPOPT (Coupled Matrix Factorization with SParse OPTimization), which is a gradient-based optimization approach solving for all factor matrices simultaneously. Using numerical experiments on simulated data, the authors demonstrate that CMF-SPOPT can capture the underlying sparse patterns in data. Furthermore, on a real data set of blood samples collected from a group of rats, the authors use the proposed approach to jointly analyze metabolomics data sets and identify potential biomarkers for apple intake. Advantages and limitations of the proposed approach are also discussed using illustrative examples on metabolomics data sets.