Local dual-graph discriminant classifier for binary classification

Abstract

Graph-based methods mine the potential structural information of data by constructing various graphs that positively affect the classifiers when dealing with classification problems. However, traditional graph-based classifiers are the most common single-graph classifiers and minimize only intra-class compactness, where inter-class separability is replaced by other factors. To consider real inter-class separability, we introduce a novel local dual-graph structure that can fully mine the geometric distribution of data by simultaneously maximizing the inter-class separability and minimizing the intra-class compactness. This local dual-graph structure reflects the relationship between samples and their neighbors and hence avoids the negative impact of outliers on the construction of graphs. Furthermore, a novel classifier called the local dual-graph discriminant classifier (LDGDC) is proposed using a local dual-graph structure. Originally, LDGDC is designed to perform the following optimization: minimization of the 2-norm regularization of model coefficients and intra-class compactness, and maximization of the inter-class separability, which is a non-convex optimization problem. To facilitate the solution, we transform the original non-convex problem of LDGDC into a convex problem. Finally, experiments were conducted on several public datasets, and the results demonstrate the effectiveness and robustness of the proposed LDGDC.