一种新的最小二乘支持向量机算法

Modified Least Squares Support Vector Machines

基于核方法的学习算法在机器学习领域占有很重要的地位(如支持向量机Support Vector Machines,简称SVM)。但该方法在处理回归问题时的计算复杂度为数据量的立方级。最小二乘支持向量机(Least Squares Support Vector Machines,简称LS-SVM)在计算复杂性方面对传统的支持向量机作了很大改进,但是它的计算量也达到样本点数目的平方级。在处理海量数据回归问题时,求解LS-SVM占用大量的CPU和内存资源。提出了一种带非齐次多项式核的最小二乘支持向量机算法,由于特征向量中含有常数分量,所以去掉了模型中的偏差因子,简化了LS-SVM的回归模型。新方法特别适合于海量数据回归问题。实验显示新方法的求解速度比传统LS-SVM快很多,同时新方法的准确性却丝毫不亚于LS-SVM。

A problem for many kernel-based methods is that the amount of computation required to find the solution scales as O（N^3）,where N is the number of training examples.As an interesting version of SVM,LS-SVM reduces the complexity of standard SVM to O（N^2）.Both SVM and LS-SVM are not suitable for the large scale regression problem.This paper proposes a modified LS-SVM with inhomogeneous polynomial kernel.Besides,the new LS-SVM omits the bias term.This newly proposed LS-SVM has a simpler model than the standard one.Simulations performed on artificial data sets show the modified LS-SVM speeds the training process of standard LS-SVM greatly without significant loss of accuracy.