A Novel Separating Hyperplane Classification Framework to Unify Nearest-Class-Model Methods for High-Dimensional Data

In this article, we establish a novel separating hyperplane classification (SHC) framework to unify three nearest-class-model methods for high-dimensional data: the nearest subspace method (NSM), the nearest convex hull method (NCHM), and the nearest convex cone method (NCCM). Nearest-class-model methods are an important paradigm for the classification of high-dimensional data. We first introduce the three nearest-class-model methods and then conduct dual analysis for theoretically investigating them, to understand deeply their underlying classification mechanisms. A new theorem for the dual analysis of NCCM is proposed in this article by discovering the relationship between a convex cone and its polar cone. We then establish the new SHC framework to unify the nearest-class-model methods based on the theoretical results. One important application of this new SHC framework is to help explain empirical classification results: why one class model has a better performance than others on certain data sets. Finally, we propose a new nearest-class-model method, the soft NCCM, under the novel SHC framework to solve the overlapping class model problem. For illustrative purposes, we empirically demonstrate the significance of our SHC framework and the soft NCCM through two types of typical real-world high-dimensional data: the spectroscopic data and the face image data.