Are Easy Data Easy (for K-Means)
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This paper investigates the capability of correctly recovering well-separated clusters by various brands of the k-means algorithm. The concept of well-separatedness used here is derived directly from the common definition of clusters, which imposes an interplay between the requirements of within-cluster-homogenicity and between-clusters-diversity. Conditions are derived for a special case of well-separated clusters such that the global minimum of k-means cost function coincides with the well-separatedness. An experimental investigation is performed to find out whether or no various brands of k-means are actually capable of discovering well separated clusters. It turns out that they are not. A new algorithm is proposed that is a variation of k-means++ via repeated subsampling when choosing a seed. The new algorithm outperforms four other algorithms from k-means family on the task.
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