  Nonnegative matrix factorization (NMF) is a powerful tool in data exploratory
analysis by discovering the 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 unified framework is still lacking. In this
paper, we 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. 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.
