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.

本文提出了一种高阶匹配追踪的低秩张量学习方法，适用于凸或非凸损失函数，可以高效地计算出秩为一的张量，且具有较小的存储需求和较好的收敛速率，实验证明该方法在合成和实际数据集上都具有高效性和有效性。

低秩张量学习的高阶匹配追踪