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Abstract: One of the top ten most influential data mining algorithms, k-means, is known for being simple and scalable. However, it is sensitive to initialization of prototypes and requires that the number of clusters be specified in advance. This paper shows that evolutionary techniques conceived to guide the application of k-means can be more computationally efficient than systematic (i.e., repetitive) approaches that try to get around the above-mentioned drawbacks by repeatedly running the algorithm from different configurations for the number of clusters and initial positions of prototypes. To do so, a modified version of a (k-means based) fast evolutionary algorithm for clustering is employed. Theoretical complexity analyses for the systematic and evolutionary algorithms under interest are provided. Computational experiments and statistical analyses of the results are presented for artificial and text mining data sets. [ABSTRACT FROM AUTHOR]

A fuzzy extension of the Rand index [Rand, W.M., 1971. Objective criteria for the evaluation of clustering methods. J. Amer. Statist. Assoc. 846–850] is introduced in this paper. The Rand index is a traditional criterion for assessment and comparison of different results provided by classifiers and clustering algorithms. It is able to measure the quality of different hard partitions of a data set from a classification perspective, including partitions with different numbers of classes or clusters. The original Rand index is extended here by making it able to evaluate a fuzzy partition of a data set – provided by a fuzzy clustering algorithm or a classifier with fuzzy-like outputs – against a reference hard partition that encodes the actual (known) data classes. A theoretical formulation based on formal concepts from the fuzzy set theory is derived and used as a basis for the mathematical interpretation of the Fuzzy Rand Index proposed. The fuzzy counterparts of other (five) related indexes, namely, the Adjusted Rand Index of Hubert and Arabie, the Jaccard coefficient, the Minkowski measure, the Fowlkes–Mallows Index, and the Γ statistics, are also derived from this formulation. [Copyright &y& Elsevier]

Abstract: The present paper proposes a new cluster validity measure as an additional criterion to help the decision making process in fuzzy cluster analysis. This measure, named Fuzzy Silhouette, is a generalization to the fuzzy case of the Average Silhouette Width Criterion, originally conceived to assess crisp (non-fuzzy) data partitions. The Fuzzy Silhouette is more appealing than its crisp counterpart in the context of fuzzy cluster analysis since it makes explicit use of the fuzzy partition matrix provided by the clustering algorithm. In addition, it has been designed to improve performance of the original silhouette criterion in detecting regions with higher data density when the data set involves overlapping clusters. The performance of the Fuzzy Silhouette is evaluated and compared to that of five well-known cluster validity measures. Six data sets are used to illustrate different scenarios in which the proposed Fuzzy Silhouette performs similar to or better than these other criteria, thus becoming eligible to join a pool of measures to be used all together in fuzzy cluster analysis. [Copyright &y& Elsevier]