从近似超平面到SVR的算法研究

本文证明了SVM存在近似超平面；根据SV分布于SVM超平面附近，也必然分布于其近似超平面附近的特点，提出了从近似超平面出发，通过向量距近似超平面的距离的大小逐步搜索SV，建立SVR的算法思想；列举了基于该算法思想的一个算法实例——从多元回归平面构建LS-SVM;分析了其时空复杂度，并与LS-SVM的线性方程组解法和直接分解算法进行比较，其结果是该算法能够收敛到l个训练样本直接建立的SVR，并降低了计算时间复杂度和显著降低了计算空间复杂度。

Research on Algorithms of Constructing SVR Based on its Approximate Hyperplane

This paper contributes a class of algorithms of constructing SVR based on its different approximate hyperplanes. It proves that SVM has its approximate hyperplanes. According as there are Support Vectors near the SVM and the Support Vectors are consequentially near the approximate hyperplane of the SVM too, to bring forward the idea of constructing SVR starting from its approximate hyperplane to search the Support Vectors step by step. It represents an algorithm instance starting from the Multiple Linear Regression Model to constructing LS-SVM, based on the idea, and analyzes its complexity. Comparing between it, the method of solving LS-SVM with system of linear equations and the decomposition algorithm, the result is the algorithm can converge to LS-SVM and decrease the time complexity and reduce evidently the space complexity.