一种具有统计不相关性的最优边界鉴别向量集

为了解决现有维数约简算法受样本分布影响较大、不支持小样本学习等问题,在分析线性鉴别分析(LDA)中最优鉴别向量与支持向量机(SVM)中分类超平面法向量之间关系的基础上,基于统计不相关最优鉴别向量集优于正交最优鉴别向量集的事实,提出了通过对改进的SVM的二次优化问题进行递归求解来获取具有统计不相关性的最优边界鉴别向量集的算法,并使用核方法将其推广到可以解决非线性特征抽取问题.结果表明:在采用相同参数并使用k-最近邻分类器进行训练和测试的情况下,提出的算法对实际数据集Waveform,Heart,Diabetis的分类精度均高于SVM和RSVM,不会出现当抽取超过最优维数时随着抽取维数的增加分类精度反而降低的现象,体现了本算法在抽取不相关特征向量方面的有效性.

An Optimal Set of Uncorrelated Margin Discriminant Vectors

The usual dimensionality reduction algorithms were often affected by data distribu-tions, small size samples and others. In order to solve the problems mentioned above, an algo-rithm was proposed to obtain an optimal set of uncorrelated margin discriminant vectors by sol-ving the dual quadratic optimal problem of the modified support vector machine (SVM), which was based on the similarity between the optimal discriminant vector of linear discriminant anal-ysis (LDA) and the classification hyperplane normal vector of SVM, and the fact that the opti-mal set of uncorrelated discriminant vectors was superior to the optimal set of orthogonal dis-criminant vectors, then the algorithm was expanded to solve nonlinear feature extraction prob-lems using kernel technology. The results show that under the same parameters and k-nearest neighbor classifier for training and testing, the classification accuracy of the proposed algorithm is higher than that of SVM and recursive support vector machine(RSVM) for the public data sets Waveform, Heart, Diabetis, and doesn't appear that the classification accuracy becomes lower when the number of extraction dimensions is bigger than the optimal number, which re-flects its validity for extracting uncorrelated eigenvectors from the samples.