Abstract: As a traditional classification method, support vector machine (SVM) has limitations for high order tensorial data, since direct vectorization will lead to the loss of intrinsic spatial structures in tensors, and the small sample size problem as well. As a higher-order extension of SVM, support tensor machine (STM), which targets at tensorial data classification, has attracted more and more attention of many scholars, with wide applications in remote sensing imaging, video processing, finance, fault diagnosis, etc. Analogous to SVM, the involved loss functions in most of the existing STM models are surrogates of the L_0/1 function. In this paper, the original L_0/1 loss is employed, based on which, a low rank STM model is proposed for the binary classification problem, with consideration of the intrinsic low-rankness of tensorial data. The resulting nonconvex discontinuous tensor optimization problem is solved by an alternating direction method of multipliers. Numerical experiments are conducted on synthetic data and real data sets to demonstrate the effectiveness of the proposed approach.

Key words: support tensor machine, L_0/1 soft-margin loss, alternating direction method of multipliers, Tucker rank