支持向量和多中心点：非线性聚类的两大方法

Support Vector and Multi-Exemplar: Two Main Approaches for Nonlinear Clustering

摘要: 作为数据挖掘的基础方法之一，数据聚类被广泛应用各个不同领域，例如计算机科学、医学、社会科学和经济学等。根据类的样本点的分布，数据聚类问题通常可以划分成线性可分聚类和非线性可分聚类。由于现实世界的数据分布流形的复杂性，非线性聚类是最流行和最被广泛研究的聚类问题之一。本文首先从四个角度对非线性聚类的近期工作做一个简要的综述，包括基于核的聚类算法、多中心点聚类算法、基于图的聚类算法以及基于支持向量的聚类算法。接着，我们将特别地介绍我们在非线性聚类研究方面的两个主要工作，分别是位置正则化的支持向量聚类(PSVC)以及多中心点近邻传播算法(MEAP)。我们将介绍这些方法的优势与局限性，同时指出未来的研究方向。

Abstract:  

As a fundamental method for data mining, data clustering has been widely used in various fields such as computer science, medical science, social science and economics. According to the data distribution of clusters, the data clustering problem can be categorized into linearly separable clustering and nonlinearly separable clustering. Due to the complex manifold of the real-world data, nonlinearly separable clustering is one of the most popular and widely studied clustering problems. In this paper, we will first make a brief survey on the recent research works in nonlinear clustering, from four perspectives, namely, kernel-based clustering, multi-exemplar clustering, graph-based clustering and support vector-based clustering. Then, we will particularly introduce our two research works in nonlinear clustering, namely, position regularized support vector clustering (PSVC) and multi-exemplar affinity propagation (MEAP). We will analyze their merits and limitations and point out the future research directions.