22 International Journal of Knowledge Discovery in Bioinformatics, 3(3), 22-43, July-September 2012 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. ABSTRACT Metabolomics focuses on the detection of chemical substances in biological luids 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 optimiza- tion 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. Coupled Matrix Factorization with Sparse Factors to Identify Potential Biomarkers in Metabolomics Evrim Acar, Department of Food Science, Faculty of Science, University of Copenhagen, Copenhagen, Denmark Gozde Gurdeniz, Department of Human Nutrition, Faculty of Science, University of Copenhagen, Copenhagen, Denmark Morten A. Rasmussen, Department of Food Science, Faculty of Science, University of Copenhagen, Copenhagen, Denmark Daniela Rago, Department of Human Nutrition, Faculty of Science, University of Copenhagen, Copenhagen, Denmark Lars O. Dragsted, Department of Human Nutrition, Faculty of Science, University of Copenhagen, Copenhagen, Denmark Rasmus Bro, Department of Food Science, Faculty of Science, University of Copenhagen, Copenhagen, Denmark Keywords: Coupled Matrix Factorization, Gradient-Based Optimization, Metabolomics, Missing Data, Sparsity DOI: 10.4018/jkdb.2012070102