关键词: 非正定核, 损失函数, 序列最小最优化算法, 回归型支持向量机模型

Abstract:

Applying the  SVC model algorithm to solving the  SVR model often needs the SVR kernel function is positive and satisfies the Mercer conditions, but in actual applications, while using the  SVR geometric frame to convert the SVC kernel function to the corresponding SVR kernel function, we usually cannot guarantee the converting kernel function is qualitative, which  leads to that the SVR optimization model is not a convex programming model that we cannot solve it. To solve these problems, we propose to use the extended SMO algorithm to solve the SVR problem with a nonpositive kernel and develope its working set selection rule, analyze how to select in the algorithm the current work collection's optimal variable value. Because the algorithm does not require the kernel function is positive, it expands the range of the kernel function’s options. The simulation results show that this algorithm for the nonpositive kernel function SVR model has good generalization performance and regression accuracy, featuring a certain theoretical and practical significance.

Key words: non-positive kernel;loss function;SMO algorithm;SVR model