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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >A Novel Separating Hyperplane Classification Framework to Unify Nearest-Class-Model Methods for High-Dimensional Data
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A Novel Separating Hyperplane Classification Framework to Unify Nearest-Class-Model Methods for High-Dimensional Data

机译：一种新型分离超平面分类框架，为高维数据统一最近的级模型方法

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摘要

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.
机译：在本文中，我们建立了一个新型分离超平面分类（SHC）框架，统一了三个最近的高维数据模型方法：最近的子空间方法（NSM），最近的凸船用方法（NCHM）和最近的凸锥法（NCCM）。最近的类模型方法是高维数据分类的重要范式。我们首先介绍了三种最近的类模型方法，然后对理论调查它们进行双重分析，深入了解其潜在的分类机制。本文通过发现凸锥和其极性锥之间的关系，在本文中提出了NCCM双分析的新定理。然后，我们建立新的SHC框架以统一基于理论结果的最近级模型方法。这个新的SHC框架的一个重要应用是帮助解释经验分类结果：为什么一个类模型在某些数据集上的其他型号比其他模型更好。最后，我们提出了一种新的最近级模型方法，软核心剧本，在新的SHC框架下解决了重叠的类模型问题。出于说明性目的，我们通过两种类型的典型实世界高维数据和面部图像数据证明了SHC框架和软NCCM对软NCCM的重要性：光谱数据和面部图像数据。

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