Discriminant analysis based on reliability of local neighborhood

Abstract

To obtain a compact and effective low-dimensional representation, recently, most existing discriminant manifold learning methods have integrated manifold learning into discriminant analysis (DA) for extracting the intrinsic structure of data. These methods learn two kinds of adjacency graphs, such as intrinsic graph and penalty graph, to characterize the similarity between samples from intraclass and the pseudo similarity of interclass. However, they treat every sample equally, which results in the following defects: (1) These methods cannot accurately characterize the marginal region among different classes only through penalty graphs. (2) They can not identify the noisy and outlier samples which reduce the robustness of these methods. To address these problems, we introduce an adaptive adjacency factor to perform the discriminative based reliability analysis for each sample. By integrating the adjacency factor into discriminant manifold learning methods, we propose a novel method for DA namely discriminant analysis based on reliability of local neighborhood (DA-RoLN). We mainly have three contributions in this paper: (1) By the introduction of adjacency factor, sample points can be divided into three parts: intraclass samples, marginal samples, and outliers. Therefore, DA-RoLN emphasizes the effect of valid samples and filters the influence of outliers. (2) We adaptively calculate the adjacency factor in low-dimensional space, thus, the margin between different classes in low-dimensional space is emphasized. (3) An iterative algorithm is developed to solve the objective function of DA-RoLN, and it is easy to solve with a low computational cost. Extensive experimental results show the effectiveness of DA-RoLN.