Rough margin-based ν-twin support tensor machine in pattern recognition

Abstract

In Rough margin-based ν-Twin Support Vector Machine (Rν-TSVM) algorithm, the rough theory is introduced. Rν-TSVM gives different penalties to the corresponding misclassified samples according to their positions, so it avoids the overfitting problem to some extent. While the input data is a tensor, Rν-TSVM cannot handle it directly and may not utilize the data information effectively. Therefore, we propose a novel classifier based on tensor data, termed as Rough margin-based ν-Twin Support Tensor Machine (Rν-TSTM). Similar to Rν-TSVM, Rν-TSTM constructs rough lower margin, rough upper margin and rough boundary in tensor space. Rν-TSTM not only retains the superiority of Rν-TSVM, but also has its unique advantages. Firstly, the data topology is retained more efficiently by the direct use of tensor representation. Secondly, it has better classification performance compared to other classification algorithms. Thirdly, it can avoid overfitting problem to a great extent. Lastly, it is more suitable for high dimensional and small sample size problem. To solve the corresponding optimization problem in Rν-TSTM, we adopt the alternating iteration method in which the parameters corresponding to the hyperplanes are estimated by solving a series of Rν-TSVM optimization problem. The efficiency and superiority of the proposed method are demonstrated by computational experiments.