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Conference Papers Year : 2020

k-means Cluster Shape Implications

Abstract

We present a novel justification why k-means clusters should be (hyper)ball-shaped ones. We show that the clusters must be ball-shaped to attain motion-consistency. If clusters are ball-shaped, one can derive conditions under which two clusters attain the global optimum of k-means. We show further that if the gap is sufficient for perfect separation, then an incremental k-means is able to discover perfectly separated clusters. This is in conflict with the impression left by an earlier publication by Ackerman and Dasgupta. The proposed motion-transformations can be used to the new labeled data for clustering from existent ones.
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hal-04050593 , version 1 (29-03-2023)

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Mieczysław A. Kłopotek, Sławomir T. Wierzchoń, Robert A. Kłopotek. k-means Cluster Shape Implications. 16th IFIP International Conference on Artificial Intelligence Applications and Innovations (AIAI), Jun 2020, Neos Marmaras, Greece. pp.107-118, ⟨10.1007/978-3-030-49161-1_10⟩. ⟨hal-04050593⟩
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