Small sphere and large margin support tensor machines for imbalanced tensor data classification.

The small sphere and large margin approach (SSLM) is a representative learning algorithm for handling imbalanced data classification problems. However, it is only effective for the vector data, and not suitable for the tensor data. How to build a novel model for the imbalanced tensor data is a challenge. In this paper, a small sphere and large margin support tensor machine (SSLMSTM) is proposed by taking full advantage of the structural information of tensor data. Its basic idea is to construct two concentric hyperspheres, whose centers are represented by a rank-1 tensor. The small hypersphere captures as many normal training samples (positive samples) as possible, while most outliers (negative samples) are pushed out of the large hypersphere. It can obtained great performance by increasing the margin of two hyperspheres. Furthermore, we extend SSLMSTM to a higher rank R case, named HR-SSLMSTM. Above two models can be solved by CANDECOMP/PARAFAC decomposition and alternating iteration method. Experiments on multiple datasets are conducted to verify the validity of our proposed SSLMSTM and HR-SSLMSTM.