In this paper we introduce three methods for re-scaling data sets aiming at improving the likelihood of clustering validity indexes to return the true number of spherical Gaussian clusters with additional noise features. Our method obtains feature re-scaling factors taking into account the structure of a given data set and the intuitive idea that different features may have different degrees of relevance at different clusters. We experiment with the Silhouette (using squared Euclidean, Manhattan, and the pth power of the Minkowski distance), Dunn’s, Calinski–Harabasz and Hartigan indexes on data sets with spherical Gaussian clusters with and without noise features. We conclude that our methods indeed increase the chances of estimating the true number of clusters in a data set

In this paper we introduce a new hierarchical clustering algorithm called Ward _p . Unlike the original Ward, Ward _p generates feature weights, which can be seen as feature rescaling factors thanks to the use of the L _p norm. The feature weights are cluster dependent, allowing a feature to have different degrees of relevance at different clusters. We validate our method by performing experiments on a total of 75 real-world and synthetic datasets, with and without added features made of uniformly random noise. Our experiments show that: (i) the use of our feature weighting method produces results that are superior to those produced by the original Ward method on datasets containing noise features; (ii) it is indeed possible to estimate a good exponent p under a totally unsupervised framework. The clusterings produced by Ward _p are dependent on p. This makes the estimation of a good value for this exponent a requirement for this algorithm, and indeed for any other also based on the L _p norm.

This paper gives an experimentally supported review and comparison of several indices based on the conventional K-means inertia criterion for determining the number of clusters, $K$ , in datasets, using the popular Silhouette width index as a benchmark. Our experiments involve a novel version of the Elbow index, defined using values of $K$ two or three steps apart. We also discuss alternative ways of computing the inertia and summarizing its values. Even though there are no overall winners in our experiments, some of our results are very conclusive and can be used as a guide for indices determining the number of clusters in K-means.

© 2017 Elsevier B.V. Feature selection is a popular data pre-processing step. The aim is to remove some of the features in a data set with minimum information loss, leading to a number of benefits including faster running time and easier data visualisation. In this paper we introduce two unsupervised feature selection algorithms. These make use of a cluster-dependent feature-weighting mechanism reflecting the within-cluster degree of relevance of a given feature. Those features with a relatively low weight are removed from the data set. We compare our algorithms to two other popular alternatives using a number of experiments on both synthetic and real-world data sets, with and without added noisy features. These experiments demonstrate our algorithms clearly outperform the alternatives