A v -Twin Support Tensor Machine

Abstract

The traditional vector-based algorithms, such as Support Vector Machine (SVM) and Twin Support Vector Machine (TSVM), have many limitations especially when tensor is considered as input matrix. In this paper, we proposed a novel algorithm with a tensor-based classification paradigm to utilize the structural information. The new proposed algorithm is called  -Twin Support Tensor Machine (  -TSTM), which is an extension of  -Twin Support Vector Machine (  -TSVM). Similarly,  -TSTM solves a pair of smaller-sized Quadratic Programming Problems (QPPs). It reduces the computational complexity substantially. Besides, we formulate  -TSTM, which separates samples in the tensor space with two non-parallel hyperplanes, and the pair of parameters ( ) have theoretical interpretation which are used to control the bounds of the fractions of support tensors and the error margins. What's more, the structure information of data is retained by the direct use of tensor representation. The proposed  -TSTM can preferably overcome overfitting problem and deal with big data while most vector-based algorithms could hardly compare. In addition, it has better performances on high dimensional and small-sample-size (S3) problem. The efficiency and superiority of the proposed method are demonstrated by experiments on various datasets.