On the Consistency of k-means++ algorithm

Kłopotek, Mieczysław A.

doi:10.3233/fi-2020-1909

Cited by 3 publications

(1 citation statement)

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“…The k-means like algorithms are of interest not only because their efficiency, but also due to interesting theoretical property like consistency in the limit for growing sample sizes [12], applicability of kernel-trick for Euclidean [11] and non-Euclidean space [16], existence of cluster-preserving transformations [13], possibility to check clusterability [14], applicability in label-free test set evaluations [22], privacy preserving [26] and many other [10], [17], [15]. Therefore, intense studies of k-means family are vital.…”

Section: Previous Workmentioning

confidence: 99%

On Probabilistic k-Richness of the k-Means Algorithms

Kłopotek

2019

Machine Learning, Optimization, and Data Science

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This paper investigates the capability of correctly recovering well-separated clusters by various brands of the kmeans 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 withincluster-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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