Linear Discriminant Analysis (LDA) has been widely applied in the field of face identification because of its simplicity and efficiency in capturing the most discriminant features. However LDA often fails when facing the change in illumination, pose or small training size. To overcome those difficulties, Principal Component Analysis (PCA), which recover the most descriptive/informative features in the reduced dimension feature space, are often used in preprocessing stage. Although there is a trend of preferring LDA over PCA in classification, it has been found that PCA may perform better than LDA in some cases, especially when the size of the training set is small. To better combine the merits of PCA and LDA, some rule-based parametric combination of PCA and LDA methods have been proposed. However in those methods the optimal parameter setting is not guaranteed and can only be approximated by exhaustive search. In this paper we propose a learning-based framework that can unify PCA and LDA in adaptively finding both discriminant and descriptive feature. To eliminate the parameter selection, we incorporate a non-linear boosting process to enhance a pool of hybrid classifiers and combine them into a more accurate one. To evaluate the performance of our boosted hybrid method, we compare it to state-of-the-art LDA variants and traditional PCA-LDA technique on three widely used face image benchmark databases. The experiment results show that our novel boosted hybrid discriminant analysis outperforms the other techniques and the best single hybrid classifier.
In content-based image retrieval (CBIR), in order to alleviate learning in the high-dimensional space, Fisher discriminant analysis (FDA) and multiple discriminant analysis (MDA) are commonly used to find an optimal discriminating subspace that the data are clustered in the reduced feature space, in which the probabilistic structure of the data could be simplified and captured by simpler model assumption, e.g., Gaussian mixtures. However, due to the two reasons (i) the real number of clases in the image database is usually unknown; and (ii) the image retrieval system acts as a classifier to divide the images into two classes, relevant and irrelevant, the effective dimension of projected subspace is usually one. In this paper, a novel hybrid feature dimension reduction techniqe is proposed to construct descriptive and discriminant features at the same time by maximizing the Rayleigh coefficient. The hybrid LDA and PCA analysis not only increases the effective dimension of the projected subspace, but also offers more flexibility and alternatives to LDA and PCA. Extensive tests on benchmark and real image databases have shown the superior performances of the hybrid analysis.