Belief C-Means: An extension of Fuzzy C-Means algorithm in belief functions framework
Belief C-Means: An extension of Fuzzy C-Means algorithm in belief functions framework
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Belief C-Means：模糊 C-Means 算法在置信函数框架中的扩展
DOI：
10.1016/j.patrec.2011.10.011
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发表时间：
2012-02-01
影响因子：
5.1
通讯作者：
Pan, Quan
中科院分区：
文献类型：
--
作者：
Liu, Zhun-ga;Dezert, Jean;Pan, Quan
著名的数据聚类模糊 C 均值 (FCM) 算法已扩展到证据 C 均值 (ECM) 算法，以便在具有数据信用分区的置信函数框架中工作。根据数据聚类问题，在某些情况下，ECM 给出的聚类的某些重心可能会变得非常接近，这可能会对数据聚类的 ECM 性能造成严重问题。为了解决这个问题，我们在本文中引入了不精确聚类的概念。我们的方法的原则是考虑位于特定类（集群）重心中间的对象必须以相同的信念提交给每个特定集群，而不是像 ECM 算法中经典的那样属于不精确的元集群。远离两个（或多个）特定簇中心且难以区分的异常值对象将被归入由这些特定簇组成的不精确簇（分离的元簇）。本文提出的新 Belief C-Means (BCM) 算法遵循这个非常简单的原理。在BCM中，每个对象的特定簇的置信质量是根据对象与其所属簇中心之间的距离来计算的。在确定元簇的置信质量时，将考虑对象与特定簇的中心之间的距离以及这些中心之间的距离。与 ECM 的做法相反，我们在 BCM 算法中不使用元簇的重心。在本文中，我们还提供了几个示例来说明 BCM 的兴趣，并展示其与基于 FCM 和 ECM 的聚类技术的主要区别。皇冠版权所有 (C) 2011 由 Elsevier B.V. 出版。保留所有权利。
The well-known Fuzzy C-Means (FCM) algorithm for data clustering has been extended to Evidential C-Means (ECM) algorithm in order to work in the belief functions framework with credal partitions of the data. Depending on data clustering problems, some barycenters of clusters given by ECM can become very close to each other in some cases, and this can cause serious troubles in the performance of ECM for the data clustering. To circumvent this problem, we introduce the notion of imprecise cluster in this paper. The principle of our approach is to consider that objects lying in the middle of specific classes (clusters) barycenters must be committed with equal belief to each specific cluster instead of belonging to an imprecise meta-cluster as done classically in ECM algorithm. Outliers object far away of the centers of two (or more) specific clusters that are hard to be distinguished, will be committed to the imprecise cluster (a disjunctive meta-cluster) composed by these specific clusters. The new Belief C-Means (BCM) algorithm proposed in this paper follows this very simple principle. In BCM, the mass of belief of specific cluster for each object is computed according to distance between object and the center of the cluster it may belong to. The distances between object and centers of the specific clusters and the distances among these centers will be both taken into account in the determination of the mass of belief of the meta-cluster. We do not use the barycenter of the meta-cluster in BCM algorithm contrariwise to what is done with ECM. In this paper we also present several examples to illustrate the interest of BCM, and to show its main differences with respect to clustering techniques based on FCM and ECM. Crown Copyright (C) 2011 Published by Elsevier B.V. All rights reserved.