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

The issue of determining the right number of clusters in K-Means has attracted considerable interest, especially in the recent years. Cluster intermix 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 cluster intermix. 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 by extracting anomalous patterns from the data one-by-one. We compare them with seven other methods, including Hartigan's rule, averaged Silhouette width and Gap statistic, under different between- and within-cluster spread-shape 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.