Cooperative evolution Multiclass Support Matrix Machines

Support Matrix Machines are one the efficient learning approach for the classification of complex nature data. However, either it can only deal with binary class problem or can deal with multi-class classification problem by breaking the problem into number of binary class problem and solving them individually or through solving larger optimization. Aiming to improve performance of support matrix machines, in this paper, we present Multi-class Support Matrix Machine based on evolutionary optimization (MSMM-CE) by breaking down the original multi-class problem of support matrix into subproblems in cooperative fashion. The proposed objective function is a combination of binary hinge loss function for specific class, Frobenius and nuclear norms as a penalty that promote low rank and sparsity as well as an additional penalty term to penalize the multiclass classification error. The additional penalty term allow us to decompose the problem into sub-problems and solving them in simultaneously in cooperative fashion. The proposed objective function learns for each class and consider the information from other classes, that results in solving the problem in parallel. A comprehensive experimental study on publicly available benchmark EEG dataset is carried out to investigate the proposed approach that confirms the superiority of MSMM-CE for accurate classification of EEG signal associated with motor imagery in BCI applications. MSMM-CE provides a generalized solution to investigate the complex and nonlinear high dimensional data for various real-world applications.