On the strong consistency of feature-weighted k-means clustering in a nearmetric space

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Research Article

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Weighted k-means (WK-means) is a well-known method for automated feature weight learning in a conventional k-means clustering framework. In this paper, we analytically explore the strong consistency of the WK-means algorithm under independent and identically distributed sampling of the data points. The choice of dissimilarity measure plays a key role in data partitioning and detecting the inherent groups existing in a dataset. We propose a proof of strong consistency of the WK-means algorithm when the dissimilarity measure used is assumed to be a nearmetric. The proof can be further extended to those dissimilarity measures which are an increasing function of a nearmetric. Through detailed experiments, we demonstrate that WK-means-type algorithms, equipped with a nearmetric, can be pretty effective especially when some of the features are unimportant in revealing the cluster structure of the dataset.



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