To solve the problem of multimodal data classification, the idea of localization is introduced into discriminant analysis, known as local discriminant analysis. In this paper, we first illustrated, by some synthetic data as examples, the drawbacks of LFDA and MFA, two recently proposed and successfully used local linear discriminant analysis methods. We then proposed a new local discriminant projection method to overcome the drawback of LFDA and MFA that neighbor relationships between samples of different classes are not fully taken into consideration. The underlying idea of the new method, different from LFDA and MFA, is that the desired projection should make neighbors of the same class close and neighbors of different classes apart. Based on this idea, we proposed two optimal functions, one is represented by the sum of squared distance between samples, the other is represented by within class scatter and between class scatter. Analyses and comparisons on the two optimal functions are also included in this paper. Experiment results show that the new method overcomes the shortcomings of LFDA and MFA, and achieves good performance on the synthetic data, USPS, UCI standard handwriting digital data sets and IDA standard data sets.%为解决多模数据的分类问题,局部化思想被引入到判别分析中,称为局部判别分析.该文以人工数据为例深入分析了近年来提出的较为成功的两种局部线性判别分析方法:LFDA(Local Fisher Discriminant Analysis)和MFA(Marginal Fisher Analysis)的不足.为克服这两种方法中没有充分考虑异类样本近邻关系的缺点,文中提出了一种新的局部判别投影方法.该方法采用与LFDA和MFA不同的局部化方法,其基本思想是寻找投影方向使同类近邻样本在投影后尽量紧凑,而异类近邻样本在投影后尽量分开.针对该思想,文中提出了两种优化目标(一种用样本间距离平方和来表示,另一种用样本类内与类间散度来表示)并做了分析和比较.实验结果表明,该文方法有效地克服了LFDA和MFA存在的固有问题,在人工数据集、UCI、USPS手写数字标准数据集和IDA标准数据集上均取得较好效果.
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