An objective approach to cluster validation

Abstract

Cluster validation is a major issue in cluster analysis. Many existing validity indices do not perform well when clusters overlap or there is significant variation in their covariance structure. The contribution of this paper is twofold. First, we propose a new validity index for fuzzy clustering. Second, we present a new approach for the objective evaluation of validity indices and clustering algorithms. Our validity index makes use of the covariance structure of clusters, while the evaluation approach utilizes a new concept of overlap rate that gives a formal measure of the difficulty of distinguishing between overlapping clusters. We have carried out experimental studies using data sets containing clusters of different shapes and densities and various overlap rates, in order to show how validity indices behave when clusters become less and less separable. Finally, the effectiveness of the new validity index is also demonstrated on a number of real-life data sets.

Towards a standard methodology to evaluate internal cluster validity indices

“…Little theoretic work has been published about the evaluation of cluster validity indices (Bouguessa et al, 2006) and, as a consequence there is a lack of standard procedures to evaluate CVIs. These procedures are desirable for several reasons: comparisons of evaluations are currently unfeasible due to the heterogeneity of the published evaluations; each researcher must design its own procedures so the same work is repeated unnecessarily; incorrect procedures are designed based on intuitions and feelings.…”

A Hierarchical Method for Determining the Number of Clusters

“…简称 CVI)是一类常见的指标,在为数众多的 CVI [6−13] 中,基于数据集几何结构的指标函数具有代表意义,它们考 虑了聚类的基本特征,即一个"好"的聚类结果应使得 k 个簇的簇内数据点是"紧凑"的,而不同簇的点之间是尽可 能"分离"的,指标量化聚类的簇内紧凑度和簇间分离度并组合二者 [6,7] ,代表性的指标包括 Xie-Beni 指标 [8] V xie 和 S.Wang-H.Sun-Q.Jiang 指标 [9] V wsj 等.对应于最大或最小指标值的 k 被认为是最佳聚类数 k * .其他类型的统计 指标包括 Gap statistic [2] 、信息熵 [3] 和 IGP(in-group proportion) [4] 等,其中,IGP 是一种新近提出的指标,它使用簇 内数据点的 in-group 比例来衡量聚类结果的质量,取得了优于现有其他指标的性能 [4] .…”

“…以上两式的定义原理如下:Scat 是簇内任意两个数据点之间距离的平方和;Sep 的原理是将每个簇看作是一 个大"数据点",大"数据点"间的"距离"通过簇间点对的平均距离来衡量.这样,Scat 和 Sep 保持了度量上的一致 性.另一方面,Scat 和 Sep 基于"点对"的平均距离定义,可用于度量非凸形簇结构的聚类质量.传统的基于几何结 构的聚类有效性指标(如 V xie [8] )通常基于簇质心(centroids)使用簇的平均半径和质心之间的距离来定义 Scat 和 [7] .…”

Fuzzy Cluster Validation Using the Partition Negentropy Criterion

“…This is the subject of cluster validation [3], whose objective is to provide a quality measure, or validity index, that allows to evaluate the results obtained by a clustering algorithm. Many cluster validity indices have been proposed in the literature, including geometric [4][5][6], probabilistic [7][8][9], graph theoretic [10], and visual [11,12] approaches.…”