A Support Third-Order Tensor Machine Model for Tensor Recognition

Recognition of data sets composed fully of tensor modes is one of the challenging problems in the field of machine learning. In this paper, a dual support third-order tensor machine (STTM) optimization model ensuring the accurate recognition of tensor data sets is designed. The main idea is to exploit the unique classification property of a STTM model to avoid the overfitting and dimension disaster caused by the tensor vectorization. Then, by using Lagrangian multiplier method and tensor-Tucker decomposition method, a computable STTM recognizer with Tucker decomposition for tensor recognition problems is developed in the framework of tensor analysis. Based on established results, a learning algorithm is proposed to retain most of the core information of original tensors. Finally, an image recognition example is given to demonstrate the effectiveness of our STTM recognizer.