Multiple rank multi-linear kernel support vector machine for matrix data classification

High-order tensors especially matrices are one of the common forms of data in real world. How to classify tensor data is an important research topic. We know that all high-order tensor data can be transformed into matrix data through tucker tensor decomposition and most of them are linear inseparable and the matrices involved are multiple rank. However, up to now most known classifiers for matrix data are linear and a few nonlinear classifiers are only for rank-one matrices. In order to classify linear inseparable multiple rank matrix data, in this paper, a novel nonlinear classifier named as multiple rank multi-linear kernel SVM (MRMLKSVM) is proposed, which is also an extension of MRMLSVM and an improvement of NLS-TSTM. For verifying the effectiveness of the proposed method, a series of comparative experiments are performed on four data sets taken from different databases. Experiment results indicate that MRMLKSVM is an effective and efficient nonlinear classifier.