Higher order Matching Pursuit for Low Rank Tensor Learning
This work addresses scalability and storage challenges in tensor learning for applications like data completion and multitask learning, representing an incremental improvement over existing matching pursuit methods.
The paper tackles low rank tensor learning problems, such as tensor completion and multilinear multitask learning, by proposing higher order matching pursuit methods that compute rank-one tensors efficiently at each iteration, achieving linear convergence rates and scalability to large-scale problems.
Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex or a nonconvex cost function, which is a generalization of the matching pursuit type methods. At each iteration, the main cost of the proposed methods is only to compute a rank-one tensor, which can be done efficiently, making the proposed methods scalable to large scale problems. Moreover, storing the resulting rank-one tensors is of low storage requirement, which can help to break the curse of dimensionality. The linear convergence rate of the proposed methods is established in various circumstances. Along with the main methods, we also provide a method of low computational complexity for approximately computing the rank-one tensors, with provable approximation ratio, which helps to improve the efficiency of the main methods and to analyze the convergence rate. Experimental results on synthetic as well as real datasets verify the efficiency and effectiveness of the proposed methods.