无监督模式下统计不相关最佳鉴别平面

统计不相关最佳鉴别平面是一种重要的特征抽取方法，在模式识别领域中具有广泛的应用。然而，统计不相关最佳鉴别平面是基于Fisher准则和总体散布矩阵共轭正交条件的，需要通过样本类别信息计算Fisher最佳鉴别矢量，因而只能用于有监督模式。提出了一种将统计不相关最佳鉴别平面扩展到无监督模式下的方法，其基本思想是将模糊概念引入Fisher线性判别分析，通过对模糊Fisher准则的优化，在无监督模式下计算出最佳鉴别矢量及模糊散布矩阵，再根据共轭正交约束条件，求得第二条最佳鉴别矢量，进而获得一种基于无监督统计不相关最佳鉴别平面的特征抽取方法。对UCI数据集及CMU-PIE人脸数据库进行实验，结果表明，在样本类别信息缺失的情况下，该方法尽管无法具有与有监督模式下的统计不相关最佳鉴别平面特征抽取方法同样的性能，但当类别差异较大时，能够抽取有利于分类的统计不相关特征，获得优于主成分分析与独立成分分析等常见无监督特征抽取方法的性能。

Uncorrelated optimal discriminant plane in unsupervised pattern

Uncorrelated optimal discriminant plane is an important feature extraction method and has been wildly used in the pattern recognition field. However, uncorrelated optimal discriminant plane is based on Fisher criterion function and the conjugated orthogonal constraint of the total class scatter matrix. It needs the class information to calculate the Fisher optimal discriminant vector. Thus, it can only be used in supervised pattern. A new method was presented to extend uncorrelated optimal discriminant plane to unsupervised pattern. The basic idea was to introduce the fuzzy concept into Fisher linear discriminant analysis and used the defined fuzzy Fisher criterion function as its optimized objective to figure out an optimal discriminant vector and fuzzy scatter matrixes in unsupervised pattern. In the conjugated orthogonal constraint of the fuzzy total class scatter matrix, the second discriminant vector which maximized the fuzzy Fisher criterion can be obtained. Thus, a new feature extraction method based on unsupervised uncorrelated optimal discriminant plane was proposed. The experimental results for UCI datasets and CMU-PIE face database demonstrate that although this method is unable to surpass traditional uncorrelated optimal discriminant plane, it can extract the uncorrelated features for classification and is superior to the common unsupervised feature extraction methods such as principal component analysis and independent component analysis when the between-class difference is big.