Efficient matrixized classification learning with separated solution process

The matrix-pattern-oriented Ho–Kashyap classifier (MatMHKS), using two-sided weight vectors to constrain the matrixized samples, can deal with not only the vectorized sample but also the matrixized sample. For vectorized sample, by converting the vectorized mode into matrixized mode, MatMHKS relieves the curse of dimensionality and extends the expressive modes of sample. Although MatMHKS has been demonstrated to be effective in the classification performance, it consumes a lot of time to alternately update two weight vectors in each iteration. Moreover, MatMHKS is not suitable in dealing with imbalanced problems. Finally, there does not exist effective analysis of generalization risk for matrixized classifiers. To this end, this paper proposes an efficient matrixized Ho–Kashyap classifier (EMatMHKS), which separately updates the two-sided weight vectors to avoid repeatedly calculating the inverse matrix in MatMHKS, thus significantly improving the training speed. Moreover, by introducing a weight matrix, both balanced and imbalanced situations can be tackled. Finally, PAC-Bayes bound is used to reflect the error upper bound of matrixized and vectorized classifiers. Both balanced and imbalanced data sets are used to validate the effectiveness and the efficiency of the proposed EMatMHKS in the experiment.