基于径向基函数网络估计密度函数的数据分类

Data classification based on density function estimated by radial basis function

针对样本总体分布已知的分类问题,提出了一种新的分类方法.通过非线性映射将训练样本映射到高维特征空间,基于向量投影法从训练样本中选择边界向量,运用多维二叉树搜索法确定每个边界向量同类中的k近邻,运用统计理论中的大数定理估计样本的类条件概率密度函数,由边界向量与相应的密度函数构成新的训练样本对.对每一类数据建立一个径向基函数(RBF)网络,以相应类的边界向量作为中心,通过训练以RBF网络来估计样本的类条件概率密度,并采用基于最小错误率的贝叶斯决策来实现分类.对机器学习数据的仿真研究结果表明该方法具有与支持向量机(SVM)相似的识别率,并且能快速有效地实现多类分类.

A new method was proposed for classification of samples with known distribution. A nonlinear function was used to map the input to a higher-dimensional space, vectors near the boundaries were pre-extracted from the training samples based on vector projection, and searching based on the multi-dimension binary tree was implemented to get the k nearest vectors of each boundary vector. By the law of large numbers in statistics, the value of the class-conditional probability density function of a sample was estimated. A new training data set was composed of boundary vectors and their corresponding density function. A radial basis function （RBF） network was constructed with the boundary vectors as the network centers to approximate the class-conditional probability density function of each class of objects in the training data set. The classification conformed to the minimum error rate of the Bayesian decision rule. Simulation results of machine learning data sets showed that the proposed algorithm has the same level of accuracy with the support vector machines （SVM） in data classification, and can quickly and effectively classify data with more than two classes of objects.