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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 Spectroscopy (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, we formulate joint analysis of data from multiple platforms as a coupled matrix factorization problem with sparsity constraints on the factor matrices. We develop 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, we 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, we use the proposed approach to jointly analyze metabolomic data sets and identify potential biomarkers for apple intake.