In this paper, a new classification method named as improved least squares twin support matrix machines (ILS-TSMM) is presented, which is an improvement of linear support tensor machines (STM) and linear least squares twin support vector machines (LS-TSVM). We know that nonlinear classifiers for vector data are a lot of but for matrix data are few. In order to study the nonlinear version of ILS-TSMM (NILS-TSMM), a new matrix kernel function is introduced and based on which, we provide a

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... theoretical derivation for NILS-TSMM. The advantage of our methods is that the structural risk minimization problem is considered by introducing the regularization term and that the utility of twin skill and least squares technology aims to reduce the computation time (training time and testing time). The experiment results show that the proposed methods are effective and efficient.