摘要
为了提高经典 Rosenblatt感知器算法的分类能力 ,该文提出一种基于核函数的非线性感知器算法 ,简称核感知器算法 ,其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一种设计 .核感知器算法能够处理原始属性空间中线性不可分问题和高维特征空间中线性可分问题 .同时 ,文中详细分析了其算法与径向基函数神经网络、势函数方法和支持向量机等非线性算法的关系 .人工和实际数据的计算结果表明 :与线性感知器算法相比 ,核感知器算法可以有效地提高分类精度 .
This paper briefly reviews the perceptron algorithm and introduce its equivalent statement based on inner product. In order to enhance the classification ability of Rosenblatt's perceptron algorithm, authors generalize this algorithm by using kernel idea to yield a nonlinear perceptron algorithm based on kernels, e.g., kernel perceptron algorithm. It combines a simply iterative procedure with kernel functions to fulfill a design of nonlinear classifiers and can deal with the nonlinearly separable problems in the original attribute space and the linearly separable ones in the feature space. For the non separable cases, several heuristic strategies are suggested. Compared with other kernel machines such as SVM, KFD and KPCA, the algorithm structure of kernel perceptron algorithms is the simplest. This paper also analyzes the relation between the algorithm and radial basis function network, potential function method and support vector machine in detail. In the experiment aspects, the results of two artificial data and two benchmark databases are reported and analyzed. For the linear example, the classical and kernel perceptron methods both find the separated hyperplanes, which can classify all samples. About two spirals problem, the nonlinear decision plane obtained by kernel perceptron with radial basis function kernel can separate all samples lying in two spirals. For the image segmentation data, the correct rates of linear and kernel perceptron algorithm are 74.0% and 90.76% respectively. Since there exist 100 realizations in thyroid data set, the average error rate and variation from the linear perceptron are 14.23% and 5.74% respectively, while those from kernel one are 4.65% and 2.39%. Such experiment results show that kernel perceptron algorithm effectively improves the classification precision compared with the linear one.
出处
《计算机学报》
EI
CSCD
北大核心
2002年第7期689-695,共7页
Chinese Journal of Computers
基金
国家自然科学基金 (69885 0 0 4)资助
