In this paper, we introduce the concept of sparse bilinear logistic regression for decision problems involving explanatory variables that are two-dimensional matrices. Such problems are common in computer vision, brain-computer interfaces, style/content factorization, and parallel factor analysis. The underlying optimization problem is bi-convex; we study its solution and develop an efficient algorithm based on block coordinate descent. We provide a theoretical guarantee for global convergence and estimate the asymptotical convergence rate using the Kurdyka-{\L}ojasiewicz inequality. A range of experiments with simulated and real data demonstrate that sparse bilinear logistic regression outperforms current techniques in several important applications.
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