Multi-Task Nonnegative Matrix Factorization

Multi-task learning is a prominent methodology for learning relationship of multiple related tasks to improve the overall generalization performance. In literature, there are several works of applying nonnegative matrix factorization (NMF) to multi-task clustering (MTC) for its useful behavior as a clustering method. When NMF is applied to a data matrix, the matrix is decomposed into a product of two factor matrices, where one corresponds to basis matrix (cluster centers) and the other is associated with encoding matrix (cluster indicator variables). In this paper, we consider clustering activities of daily living (ADL) as a single task. Given ADL data recorded from different people under the same conditions, our motivation is that related tasks share many common action patterns, while each task also has its own unique action characteristics. Our goal is to learn cross-task basis matrices that capture shared information across multiple related tasks, while try to find within-task basis matrices encoding task-dependent characteristics, which will not appear in any other tasks. To this end, we propose a method for multi-task nonnegative matrix factorization (MTNMF), which enforces cross-task bases to be as close as possible, on the contrary, keeps within-task bases as far as possible. We develop efficient multiplicative update rules to learn MTNMF and numerical experiments on ADL dataset indicate that MTNMF improves clustering performance in multi-task environment.