SVRRP_(MCC):一种支持向量回归机的正则化路径近似算法

SVRRP_(MCC):A Regularization Path Approximation Algorithm of Support Vector Regression

正则化路径算法是数值求解支持向量回归机(Support Vector Regression,SVR)的有效方法。根据SVR正则化路径的分段线性性质,该类算法可在相当于一次SVR求解的时间复杂度内求得正则化参数的所有可能取值及对应SVR的解。由于在解路径建立过程中需要求解线性方程组,已有的精确计算方法难以处理大规模的样本数据,因此研究了正则化路径近似算法,并提出了SVR正则化路径近似算法SVRRP_(MCC)。首先,应用Monte Carlo方法实现线性方程组系数矩阵的随机采样,求得近似系数矩阵;然后,应用Cholesky分解方法实现快速求解系数逆矩阵;进一步,分析了SVRRP_(MCC)算法的近似误差和计算复杂性;最后,在标准数据集上的实验验证了SVRRP_(MCC)算法的合理性和较高的计算效率。

The regularization path algorithm is an efficient method for numerical solution to the support vector regression(SVR)problem,which can obtain all possible values of regularization parameters and the solutions of SVR in the time complexity equivalent to a SVR solution.Existing SVR regularization path algorithms include solving a system of iteration equations.The existing accurate approaches are difficult to apply to large-scale problems.Recently,there has been many interests about the approximation approach.And a new approxirnation algorithm for SVR regularization path named SVRRPMCC was proposed in this paper.Firstly,SVRRPMCC applied Monte Carlo method to randomly sample the coefficient rnatrix of the system of iteration equations.Then it used the Cholesky factorization method to obtain the coefficientinverse matrix.Further,the error bound and the computational complexity about the algorithm SVRRPMCC were analyzed.Experimental results on benchmark datasets it used show the validity and efficiency of the SVRRPMCC.