Singularity Problem Of Scatter Matrix Research Articles

Integrating Discriminant and Descriptive Information for Dimension Reduction and Classification

In this paper, a novel hybrid dimension reduction technique for classification is proposed based on the hybrid analysis of principal component analysis (PCA) and linear discriminant analysis (LDA). LDA is known for capturing the most discriminant features of the data in the projected space while PCA is known for preserving the most descriptive ones after projection. Our hybrid technique integrates discriminant and descriptive information and finds a richer set of alternatives beyond LDA and PCA in a 2-D parametric space, which fits a specific classification task and data distribution better. Theoretical study shows that our technique also alleviates the singularity problem of scatter matrix, which is caused by small training set, and increases the effective dimension of the projected subspace. In order to find the hybrid features adaptively and avoid exhaustive parameter searching, we further propose a boosted hybrid analysis method that incorporates a nonlinear boosting process to enhance a set of hybrid classifiers and combine them into a more accurate one. Compared with the other techniques that aim at combining PCA and LDA, our approaches are novel because our method finds alternatives to LDA and PCA in a 2-D parameter space and the boosting process provides enhancement and robust combination of the classifiers. Extensive experiments are conducted on benchmark and real image databases to compare our proposed methods with the state-of-the-art linear and nonlinear discriminant analysis techniques. The results show the superior performance of our hybrid analysis methods