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A Novel Separating Hyperplane Classification Framework to Unify Nearest-class-model Methods for High-dimensional Data

Zhu, R., Wang, Z., Sogi, N., Fukui, K. and Xue, J-H. (2019). A Novel Separating Hyperplane Classification Framework to Unify Nearest-class-model Methods for High-dimensional Data. IEEE Transactions on Neural Networks and Learning Systems, doi: 10.1109/TNNLS.2019.2946967

Abstract

In this paper, we establish a novel separating hyperplane classification (SHC) framework to unify three nearest-classmodel 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 classification of highdimensional data. We first introduce the three nearest-classmodel 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 paper, through discovering the relationship between a convex cone and its polar cone. We then establish the new SHC framework to unify the nearest-classmodel 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 better performance than others on certain datasets. 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.

Publication Type: Article
Additional Information: © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Publisher Keywords: Classification, convex cone, convex hull, dual analysis, separating hyperplane, subspace
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments: Cass Business School > Actuarial Science & Insurance
URI: https://openaccess.city.ac.uk/id/eprint/23006
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