A new ranking method for principal components analysis and its application to face image analysis

In this work, we investigate a new ranking method for principal component analysis (PCA). Instead of sorting the principal components in decreasing order of the corresponding eigenvalues, we propose the idea of using the discriminant weights given by separating hyperplanes to select among the principal components the most discriminant ones. The method is not restricted to any particular probability density function of the sample groups because it can be based on either a parametric or non-parametric separating hyperplane approach. In addition, the number of meaningful discriminant directions is not limited to the number of groups, providing additional information to understand group differences extracted from high-dimensional problems. To evaluate the discriminant principal components, separation tasks have been performed using face images and three different databases. Our experimental results have shown that the principal components selected by the separating hyperplanes allow robust reconstruction and interpretation of the data, as well as higher recognition rates using less linear features in situations where the differences between the sample groups are subtle and consequently most difficult for the standard and state-of-the-art PCA selection methods.