为了减少最小二乘支持向量机基本剪枝算法的计算量,提出一种快速剪枝算法.在分析剪枝前后两个最小二乘支持向量机对应线性方程组系数矩阵之间关系的基础上,利用置换矩阵的逆等于其转置的性质和分块矩阵求逆公式,导出两个系数矩阵的子阵的逆之间的递推关系,避免剪枝过程中多次进行高阶矩阵求逆,从而减少计算量.在不考虑计算误差时,该算法理论上得出与基本剪枝算法相同结果的稀疏最小二乘支持向量机.仿真结果表明该算法比基本剪枝算法速度快,而且初始训练样本越多,加速比越大.%To reduce the computation amount of basic pruning algorithm(BPA) for least squares support vector machine(LSSVM), a fast pruning algorithm(FPA) is proposed. The connection between two coefficient matrices of linear equations corresponding to LSSVM before pruning and to one after doing is analyzed, and the recursive relation between inversions of sub-matrices of the two coefficient matrices is derived by permutation matrix's property of its inversion equalling to its transpose by the calculation formula of solving inversion of partitioned matrix. Therefore repetation of calculation of inversion of higher order matrices is avoided in pruning process, and computation amount is decreased. FPA produces the same resultant sparse LSSVM as BPA theoretically, when calculating error is neglected. The numerical simulation results show the presented algorithm is quicker than BPA, and the more the training samples are the greater FPA's speedup rate to BPA is.
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