Multiplicative Sparse Feature Decomposition for Efficient Multi-View Multi-Task Learning.

Multi-view multi-task learning refers to dealing with dual-heterogeneous data, where each sample has multi-view features, and multiple tasks are correlated via common views. Existing methods do not sufficiently address three key challenges: (a) saving task correlation efficiently, (b) building a sparse model and (c) learning view-wise weights. In this paper, we propose a new method to directly handle these challenges based on multiplicative sparse feature decomposition. For (a), the weight matrix is decomposed into two components via low-rank constraint matrix factorization, which saves task correlation by learning a reduced number of model parameters. For (b) and (c), the first component is further decomposed into two subcomponents, to select topic-specific features and learn view-wise importance, respectively. Theoretical analysis reveals its equivalence with a general form of joint regularization, and motivates us to develop a fast optimization algorithm in a linear complexity w.r.t. the data size. Extensive experiments on both simulated and real-world datasets validate its efficiency.