Group Nonnegative Matrix Factorization with Sparse Regularization in Multi-set Data

Constrained joint analysis of data from multiple sources has received widespread attention for that it allows us to explore potential connections and extract meaningful hidden components. In this paper, we formulate a flexible joint source separation model termed as group nonnegative matrix factorization with sparse regularization (GNMF-SR), which aims to jointly analyze the partially coupled multi-set data. In the GNMF-SR model, common and individual patterns of particular underlying factors can be extracted simultaneously with imposing nonnegative constraint and sparse penalty. Alternating optimization and alternating direction method of multipliers (ADMM) are combined to solve the GNMF-SR model. Using the experiment of simulated fMRI-like data, we demonstrate the ADMM-based GNMF-SR algorithm can achieve the better performance.