In the fields of machine learning, image processing, and pattern recognition, the existing least squares support tensor machine for tensor classification involves a non-convex optimization problem and needs to be solved by the iterative technique. Obviously, it is very time-consuming and may suffer from local minima. In order to overcome these two shortcomings, in this paper, we present a tensor factorization based least squares support tensor machine (TFLS-STM) for tensor classification. In TFLS-STM, we combine the merits of least squares support vector machine (LS-SVM) and tensor rank-one decomposition. Theoretically, TFLS-STM is an extension of the linear LS-SVM to tensor patterns. When the input patterns are vectors, TFLS-STM degenerates into the standard linear LS-SVM. A set of experiments is conducted on six secondorder face recognition datasets to illustrate the performance of TFLS-STM. The experimental results show that compared with the alternating projection LSSTM (APLS-STM) and LS-SVM, the training speed of TFLS-STM is faster than those of APLS-STM and LS-SVM. In term of testing accuracy, TFLSSTM is comparable with LS-SVM and is superiors to APLS-STM.
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