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# Dunn index

About: Dunn index is a(n) research topic. Over the lifetime, 150 publication(s) have been published within this topic receiving 24021 citation(s).

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TL;DR: A new graphical display is proposed for partitioning techniques, where each cluster is represented by a so-called silhouette, which is based on the comparison of its tightness and separation, and provides an evaluation of clustering validity.

Abstract: A new graphical display is proposed for partitioning techniques. Each cluster is represented by a so-called silhouette, which is based on the comparison of its tightness and separation. This silhouette shows which objects lie well within their cluster, and which ones are merely somewhere in between clusters. The entire clustering is displayed by combining the silhouettes into a single plot, allowing an appreciation of the relative quality of the clusters and an overview of the data configuration. The average silhouette width provides an evaluation of clustering validity, and might be used to select an ‘appropriate’ number of clusters.

10,821 citations

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TL;DR: A measure is presented which indicates the similarity of clusters which are assumed to have a data density which is a decreasing function of distance from a vector characteristic of the cluster which can be used to infer the appropriateness of data partitions.

Abstract: A measure is presented which indicates the similarity of clusters which are assumed to have a data density which is a decreasing function of distance from a vector characteristic of the cluster. The measure can be used to infer the appropriateness of data partitions and can therefore be used to compare relative appropriateness of various divisions of the data. The measure does not depend on either the number of clusters analyzed nor the method of partitioning of the data and can be used to guide a cluster seeking algorithm.

5,640 citations

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01 Jan 1973

TL;DR: Two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space; in both cases, the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the least squarederror criterion function.

Abstract: Two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space. In both cases, the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the least squared error criterion function. In the first case, the range of T consists largely of ordinary (i.e. non-fuzzy) partitions of X and the associated iteration scheme is essentially the well known ISODATA process of Ball and Hall. However, in the second case, the range of T consists mainly of fuzzy partitions and the associated algorithm is new; when X consists of k compact well separated (CWS) clusters, Xi , this algorithm generates a limiting partition with membership functions which closely approximate the characteristic functions of the clusters Xi . However, when X is not the union of k CWS clusters, the limi...

5,261 citations

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TL;DR: This article evaluates the performance of three clustering algorithms, hard K-Means, single linkage, and a simulated annealing (SA) based technique, in conjunction with four cluster validity indices, namely Davies-Bouldin index, Dunn's index, Calinski-Harabasz index, andA recently developed index I.

Abstract: In this article, we evaluate the performance of three clustering algorithms, hard K-Means, single linkage, and a simulated annealing (SA) based technique, in conjunction with four cluster validity indices, namely Davies-Bouldin index, Dunn's index, Calinski-Harabasz index, and a recently developed index I. Based on a relation between the index I and the Dunn's index, a lower bound of the value of the former is theoretically estimated in order to get unique hard K-partition when the data set has distinct substructures. The effectiveness of the different validity indices and clustering methods in automatically evolving the appropriate number of clusters is demonstrated experimentally for both artificial and real-life data sets with the number of clusters varying from two to ten. Once the appropriate number of clusters is determined, the SA-based clustering technique is used for proper partitioning of the data into the said number of clusters.

1,111 citations

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01 Aug 2012

TL;DR: This work compares the performances of eight well-known and widely used clustering validity indices and finds that the silhouette statistic index stands out in most of the data sets that are examined.

Abstract: Swarm intelligence has emerged as a worthwhile class of clustering methods due to its convenient implementation, parallel capability, ability to avoid local minima, and other advantages. In such applications, clustering validity indices usually operate as fitness functions to evaluate the qualities of the obtained clusters. However, as the validity indices are usually data dependent and are designed to address certain types of data, the selection of different indices as the fitness functions may critically affect cluster quality. Here, we compare the performances of eight well-known and widely used clustering validity indices, namely, the Calinski-Harabasz index, the CS index, the Davies-Bouldin index, the Dunn index with two of its generalized versions, the I index, and the silhouette statistic index, on both synthetic and real data sets in the framework of differential-evolution-particle-swarm-optimization (DEPSO)-based clustering. DEPSO is a hybrid evolutionary algorithm of the stochastic optimization approach (differential evolution) and the swarm intelligence method (particle swarm optimization) that further increases the search capability and achieves higher flexibility in exploring the problem space. According to the experimental results, we find that the silhouette statistic index stands out in most of the data sets that we examined. Meanwhile, we suggest that users reach their conclusions not just based on only one index, but after considering the results of several indices to achieve reliable clustering structures.

107 citations