Cross Concept Local Fisher Discriminant Analysis for Image Classification

Abstract

Distance metric learning is widely used in many visual computing methods, especially image classification. Among various metric learning approaches, Fisher Discriminant Analysis (FDA) is a classical metric learning approach utilizing the pair-wise semantic similarity and dissimilarity in image classification. Moreover, Local Fisher Discriminant Analysis (LFDA) takes advantage of local data structure in FDA and achieves better performance. Both FDA and LFDA can only deal with images with simple concept relations, where images either belong to the same concept category or come from different categories. However, in real application scenarios, images usually contain multiple concepts, and relations of concepts and images are complex. In this paper, to improve the flexibility of LFDA on the complex image-concept relations, we propose a new pairwise constraints method called Cross Concept Local Fisher Discriminant Analysis (C²LFDA) for image classification. By considering the cross concept images as a special case of within-class samples, C²LFDA models the semantic relations of images for distance metric learning under the framework of LFDA. We calculate within-class and between-class scatter matrix based on the proposed re-weighting scheme and local manifold structure. By solving the objective function of discriminant analysis using the proposed scheme, a set of projected representation is obtained to better reflect the complex semantic relations among images. Experimental evaluations and comparisons show the effectiveness of the proposed method.