Intelligent Choice of the Number of Clusters in K-Means Clustering: An Experimental Study with Different Cluster Spreads

Abstract

The issue of determining "the right number of clusters" in K-Means has attracted considerable interest, especially in the recent years. Cluster overlap appears to be a factor most affecting the clustering results. This paper proposes an experimental setting for comparison of different approaches at data generated from Gaussian clusters with the controlled parameters of between-and within-cluster spread to model different cluster overlaps. The setting allows for evaluating the centroid recovery on par with conventional evaluation of the cluster recovery. The subjects of our interest are two versions of the "intelligent" K-Means method, ik-Means, that find the right number of clusters one-by-one extracting "anomalous patterns" from the data. We compare them with seven other methods, including Hartigan's rule, averaged Silhouette width and Gap statistic, under six different between-and within-cluster spreadshape conditions. There are several consistent patterns in the results of our experiments, such as that the right K is reproduced best by Hartigan's rule -but not clusters or their centroids. This leads us to propose an adjusted version of iK-Means, which performs well in the current experiment setting.

Examination of European Union economic cohesion: A cluster analysis approach

“…To eliminate both problems repeated clustering is necessary (typically 25 runs are used). The most suitable number of clusters can be determined by various criteria such as elbow (bend) rule, Hartigan index, Gap statistics, average silhouette, Aikake information criterion, etc., see Meloun and Militký (2006) or Chiang and Mirkin (2009).…”

“…Hartigan (1975), Meloun and Militký (2006) or Chiang and Mirkin (2009). This method enables to divide objects into clusters (groups) where the division is based on objects' similarity or proximity, which is appropriate for the presented study, as k-means clustering will result in a set of (small) groups of countries with similar economic development in examined period.…”

A Clustering-Based Approach to Reduce Feature Redundancy

“…Some of which have been target of research effort for a long time. For instance, K-Means requires K (the number of clusters in Y ) to be known beforehand, and the clustering produced by K-Means can be heavily affected by the initial centroids used in its first step [3], [5], [24], [30], [33], [35].…”

“…Among the many algorithms addressing these two interrelated issues, intelligent K-Means (iK-Means) seems quite successful [5], [7], [28]. This algorithm finds the clusters in a data set by extracting one anomalous pattern at a time, as per below.…”

Applying subclustering and Lp distance in Weighted K-Means with distributed centroids

“…The choice of the range, rather than of the standard deviation in (16) has yet another interesting characteristic: unlike the latter, the former is not biased towards unimodal distributions [21,6]. Consider the following example of two features, a being unimodal and b being bimodal.…”