基于最大散度差鉴别准则的自适应分类算法

首先证明了,当类内散布矩阵非奇异时,特定参数值c0下最大散度差的最优鉴别方向等同于Fisher最优鉴别方向;其次,给出了最大散度差分类算法的识别率随参数C变化的曲线.该曲线通常为一脉冲曲线.随着参数C的增大,识别率也逐渐增大.当参数C增大到c0时,识别率达到最大值.另外,以往的研究成果表明:当类内散布矩阵奇异时,最大散度差鉴别准则逐步逼近大间距线性投影准则.而且,随着参数C的不断增大,最大散度差分类算法的识别率也单调增大并最终稳定到大间距线性投影分类算法的识别率上.为此,我们提出了基于最大散度差鉴别准则的自适应分类算法.新算法可以根据训练样本的特性(类内散布矩阵是否奇异)自动选择恰当的参数C.在UCI机器学习数据库上的6个数据集以及AR人脸图像数据库上的测试结果表明,自适应最大散度差分类算法具有良好的分类性能.

Adaptive Classification Algorithm Based on Maximum Scatter Difference Discriminant Criterion

In this paper we first prove that the optimal discriminant direction of Maximum scatter difference(MSD)discriminant criterion with a certain value co is equivalent to the optimal Fisher discriminant direction.Second,sample recognition rate curves of MSD are illustrated.The recognition rate curve is usually a pulse curve when the within-class scatter matrix is nonsingnlar.With the increase of parameter C,the recognition rate of MSD also increases.The recognition rate of MSD achieves its maximum when C is equal to c_0.In addition,former study showed that,when the within-class scatter matrix is singular,MSD criterion is approaching the large margin linear projection criterion as parameter C increases. Moreover,the recognition rate curve of MSD is non-decreasing.Thus,an adaptive classifica- tion algorithm based on maximum scatter difference discriminant criterion is proposed based on these facts.The new algorithm can tune parameter C automatically according to the characteristics of training samples.Experiment conducted on 6 datasets from UCI Machine Learning Repository and AR face database demonstrates that the adaptive classification algorithm for maximum scatter difference has good classification property.