基于全局代表指标的LSSVM最优稀疏化算法

Global Representative Indicator Based Optimal Sparseness Algorithm for LSSVM

缺少稀疏性是最小二乘支持向量机(least square support vector machine,LSSVM)的主要问题之一,本文针对此问题提出一种LSSVM的最优稀疏化算法.首先,定义了特征空间中样本的密度、离散度并进一步导出样本的全局代表指标(global representative indicator,GRI).然后,以样本剪切率和邻域大小为优化变量,以校验样本集的均方根误差(root-mean-square error,RMSE)为目标函数将LSSVM的稀疏化问题转换为带约束的最优化问题;其中,样本剪切以GRI为指标进行.针对优化问题提出了基于PSO的求解方法.最后,以二维sinc函数模型为对象探讨了GRI指标与样本支持值的关系,验证了本文最优稀疏化算法的正确性和合理性,并呈现了3种稀疏化方法的对比研究结果.

Lack of sparseness is one of the main problems of least square support vector machine(LSSVM).In terms of this issue,an optimal sparseness algorithm for LSSVM is proposed in this paper.Firstly,density and dispersion of a sample are defined in the feature space;then they are further combined to derive a global representative indicator.Secondly,the sparseness of LSSVM is transformed into a constrained optimization problem where the sample removal rate and the neighborhood value in GRI definition are taken as the optimization variables and the root-mean-square error(RMSE)is taken as the objective function for minimization.A PSO based algorithm is proposed to solve the above optimization problem.Finally,a two-dimensional sinc function model is employed to test the optimal sparseness algorithm.The relationship between GRIs and the support values of the training samples are discussed;and the validity of the proposed optimal sparseness algorithm is proven.Furthermore,3 sparseness approaches including ours are tested with this function model;and the convincing comparison results are presented.