Matrix pattern based minimum within-class scatter support vector machines

Based on minimum within-class scatter support vector machines (MCSVM), a new matrix pattern based MCSSVM (MCSVMmatrix) is presented. Accordingly, it is extended by introducing Mercer's kernels in order to solve the problem of nonlinear decision boundaries, which presents a significant matrix pattern based nonlinear support vector machines: Ker-MCSVMmatrix. The above-mentioned approaches not only keep the merits of MCSVM, but, owing to introducing matrix pattern based within-class scatter matrix into support vector machines, theoretically better solve the singular problem of within-class scatter matrix when small sample size problems are dealt with, reduce the time/place complexity when within-class scatter matrix, its invertible matrix and weight vector ω are calculated. Hence, the classification accuracy is improved to certain extent. Experimental results indicate the above advantages of the proposed methods: both MCSVMmatrixand Ker-MCSVMmatrix.