基于核函数的非线性口袋算法

应用满足Mercer条件的核函数设计非线性算法已经成为机器学习领域一项新的非线性技术.核感知器算法利用核思想非线性地推广了线性感知器算法,使其可以处理原始输入空间中的非线性分类问题和高维特征空间中的线性问题.线性口袋算法改进了线性感知器算法,能够直接处理线性不可分问题.为了进一步改进线性口袋算法和核感知器算法,本文提出基于核函数的非线性口袋算法,即核口袋算法,其目标是找到一个使错分样本数最小的非线性判别函数,并证明了其收敛性.核口袋算法的特点是用简单的迭代过程和核函数来实现非线性分类器的设计.基准数据集的实验结果证明核口袋算法的性能优于线性口袋算法和核感知器算法.

Nonlinear Pocket Algorithm with Kernels

Designing nonlinear algorithms with kernel functions satisfying the Mercer condition,has become a novel nonlinear technique in the machine learning. By using kernel idea the kernel perceptron algorithm nonlinearly generalizes the linear perceptron algorithm.It can handle the linearly non-separable classification problems in the original input space and the linearly separable ones in the feature space.The linear pocket algorithm improves the perceptron algorithm and can deal with the linearly non-separable problems directly.In order to improve the linear pocket algorithm and kernel perceptron algorithm,in this paper the nonlinear pocket algorithm based on kernels (i.e.kernel pocket algorithm) is proposed,whose objective is to find a nonlinear discriminant function that can minimize the number of misclassified training samples.Its convergence is also proved.Its advantage is to implement a nonlinear classifier using a simply iterative procedure and kernel functions.The experiment results from some benchmark data sets show that the performance of our kernel technique is prior to that of the linear pocket algorithm and kernel perceptron algorithm.