A novel method for classification of matrix data using Twin Multiple Rank SMMs

Graphical abstractDisplay Omitted HighlightsIn order to classify multiple rank matrix data the novel Twin Multiple Rank Support Matrix Machine method is proposed.A new matrix kernel function is introduced.The nonlinear version of the new method is presented.Experiment results show that the presented methods are effective and efficient. It is known that most high-order tensor data are linear inseparable and all of them can be transformed into matrix data through tucker tensor decomposition and the matrices involved are always multiple rank. Hence, how to effectively and efficiently classify matrix data becomes an important research topic. 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 multiple rank matrix data, in this paper, a novel supervised classification method called Linear Twin Multiple Rank Support Matrix Machine (LTMRSMM) is developed, which is also an improvement of TSVM and an extension of MRMLSVM. For linear inseparable matrix data, a nonlinear classification method named Nonlinear Twin Multiple Rank Support Matrix Machine (NTMRSMM) is provided by means of a new matrix kernel function introduced recently by authors of the paper. Experimental results show that the presented methods are effective and competitive classification methods for multiple rank matrix data.