Efficient Tensor Low-Rank Representation with a Closed Form Solution

In recent years, many tensor data processing methods have emerged. Tensor low-rank representation (TLRR) is a recently proposed tensor-based clustering method, and its clustering performance is promising. However, its calculation efficiency is low because its optimization procedure is iterative and needs to calculate tensor product, tensor singular value decomposition (t-SVD) and tensor product (t-product) in each iteration. To address the problem, we propose an efficient TLRR with a closed form solution (ETLRR/CFS). That is, we do not need an iterative procedure for finding the solution to ETLRR/CFS and only need one step to obtain the solution to ETLRR/CFS. Then, the computation efficiency is greatly improved. Specifically, we propose a novel objective function, which integrates tensor nuclear norm (TNN) and Frobenius norm into a unified framework, and give its closed form solution. Experiment results on several datasets shows that ETLRR/CFS not only is much faster than TLRR and its improved methods but can obtain similar clustering performance.