Heterogeneous Representation Learning with Structured Sparsity Regularization

Motivated by real applications, heterogeneous learning has emerged as an important research area, which aims to model the co-existence of multiple types of heterogeneity. In this paper, we propose a HEterogeneous REpresentation learning model with structured Sparsity regularization (HERES) to learn from multiple types of heterogeneity. HERES aims to leverage two kinds of information to build a robust learning system. One is the rich correlations among heterogeneous data such as task relatedness, view consistency, and label correlation. The other is the prior knowledge of the data in the form of, e.g., the soft-clustering of the tasks. HERES is a generic framework for heterogeneous learning, which integrates multi-task, multi-view, and multi-label learning into a principled framework based on representation learning. The objective of HERES is to minimize the reconstruction loss of using the factor matrices to recover the input matrix for heterogeneous data, regularized by the structured sparsity constraint. The resulting optimization problem is challenging due to the non-smoothness and non-separability of structured sparsity. We develop an iterative updating method to solve the problem. Furthermore, we prove that the reformulation of structured sparsity is separable, which leads to a family of efficient and scalable algorithms for solving structured sparsity penalized problems. The experimental results in comparison with state-of-the-art methods demonstrate the effectiveness of the proposed approach.