Based on minimum within-class scatter support vector machines (MCSVMs)

a new matrix pattern based MCSVMs (MCSVMs

matrix

) 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- MCSVMs

matrix

.The above-mentioned approaches not only keep the merits of MCSVMs

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 s

catter matrix

its invertible matrix and coefficient vector omega are calculated.Hence

the classification accuracy is improved to certain extent.Experimental results indicate the above advantages of the proposed methods:both MCSVMs

matrix

and Ker- MCSVMs

matrix

.