Are Easy Data Easy (for K-Means)
This addresses the problem of cluster recovery in data analysis, particularly for users relying on k-means, but is incremental as it modifies an existing method.
The paper investigates whether k-means algorithms can correctly recover well-separated clusters, finding that they generally fail, and proposes a new algorithm based on k-means++ with repeated subsampling that outperforms four other k-means variants.
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 {sub}sampling when choosing a seed. The new algorithm outperforms four other algorithms from $k$-means family on the task.