【摘要】 基于最小类内散度支持向量机(MCSVMs)提出一种新的矩阵模式的最小类内散度支持向量机(MCSVMsmatrix).同时为了更好地解决非线性分类问题,将Mercer核函数引入到MCSVMsmatrix方法中,并提出基于矩阵模式的非线性支持向量机:Ker-MCSVMsmatrix.上述两种方法不但继承了MCSVMs的优点,而且由于将矩阵模式的类内散度矩阵引入到支持向量机中,从而在理论上可以较好地解决了MCSVMs方法在处理小样本高维数据集时类内散度矩阵奇异性问题,同时降低了求解类内散度矩阵及其逆矩阵和权重矢量的时间、空间复杂度.因此,在一定程度上提高了分类精度.实验结果也表明MCSVMsmatrix、Ker-MCSVMsmatrix具有上述优势.更多还原

【Abstract】 Based on minimum within-class scatter support vector machines(MCSVMs),a new matrix pattern based MCSVMs(MCSVMsmatrix) 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-MCSVMsmatrix.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 scatter 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 MCSVMsmatrix and Ker-MCSVMsmatrix.更多还原