一种两阶段判别分析方法

A Two-stage Discriminant Analysis Method

为了解决LDA对复杂分布数据的表达问题,本文提出了一种新的非参数形式的散度矩阵构造方法。该方法能更好的刻画分类边界信息,并保留更多对分类有用的信息。同时针对小样本问题中非参数结构形式的类内散度矩阵可能奇异,提出了一种两阶段鉴别分析方法对准则函数进行了最优化求解。该方法通过奇异值分解把人脸图像投影到混合散度矩阵的主元空间,使类内散度矩阵在投影空间中是非奇异的,通过CS分解,从理论上分析了同时对角化散度矩阵的求解,并证明了得到的投影矩阵满足正交约束条件。在ORL,Yale和Yale B人脸库上测试的结果显示,改进的算法在性能上优于PCA+LDA,ULDA和OLDA等子空间方法。

In order to tackle the problem of representing the distribution of complicated data using LDA, this paper proposes a novel method for constructing the non-parametric scatter matrix. Compared to classical LDA, our method can describe the classification boundary in a better way while preserving more useful information for classification. Since the non-parametric within-class scatter matrix may be singular for small sample-size problem, we propose a two-stage discriminant analysis method to optimize the criterion function. The human face images are projected onto the principal component subspace of the mixture scatter matrix via SVD so that the within-class scatter matrix in the projection subspace is singular. Via CS decomposition, we theoretically analyze the problem of solving the diagonal scatter matrix and prove that the projection matrix satisfies the orthogonally constraint. The experimental results on three face databases, i.e., the ORL database, the Yale database and the Yale B database, demonstrate the improvement of the proposed method over the traditional subspace methods.