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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; 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 10.1109/tnnls.2019.2946967. (In press). Green open access

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Abstract

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.

Type: Article
Title: A Novel Separating Hyperplane Classification Framework to Unify Nearest-Class-Model Methods for High-Dimensional Data
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/tnnls.2019.2946967
Publisher version: https://doi.org/10.1109/tnnls.2019.2946967
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Classification, convex cone, convex hull, dual analysis, separating hyperplane, subspace.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10085621
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