A General Joint Matrix Factorization Framework for Data Integration and Its Systematic Algorithmic Exploration

Nonnegative matrix factorization (NMF) is a powerful tool in data exploratory analysis by discovering hidden features and part-based patterns from high-dimensional data. NMF and its variants have been successfully applied into diverse fields such as pattern recognition, signal processing, data mining, bioinformatics, and so on. Recently, NMF has been extended to analyze multiple matrices simultaneously. However, a general framework and its systematic algorithmic exploration are still lacking. In this paper, we first introduce a sparse multiple relationship data regularized joint matrix factorization (JMF) framework and two adapted prediction models for pattern recognition and data integration. Next, we present four update algorithms to solve this framework in a very comprehensive manner. The merits and demerits of these algorithms are systematically explored. Furthermore, extensive computational experiments using both synthetic data and real data demonstrate the effectiveness of JMF framework and related algorithms on pattern recognition and data mining.