%0 Conference Proceedings
%T k-means Cluster Shape Implications
%+ Polska Akademia Nauk = Polish Academy of Sciences = Académie polonaise des sciences (PAN)
%+ Cardinal Stefan Wyszyński University (UKSW)
%A Kłopotek, Mieczysław, A.
%A Wierzchoń, Sławomir, T.
%A Kłopotek, Robert, A.
%Z Part 2: Clustering/Unsupervised Learning/Analytics
%< avec comité de lecture
%@ 978-3-030-49160-4
%( Artificial Intelligence Applications and Innovations
%B 16th IFIP International Conference on Artificial Intelligence Applications and Innovations (AIAI)
%C Neos Marmaras, Greece
%Y Ilias Maglogiannis
%Y Lazaros Iliadis
%Y Elias Pimenidis
%I Springer International Publishing
%3 IFIP Advances in Information and Communication Technology
%V AICT-583
%N Part I
%P 107-118
%8 2020-06-05
%D 2020
%R 10.1007/978-3-030-49161-1_10
%K Cluster shape
%K Motion-consistency
%K Outer-consistency
%K Incremental clustering
%K Perfect cluster separation
%K Clusterability
%Z Computer Science [cs]Conference papers
%X 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.
%G English
%Z TC 12
%Z WG 12.5
%2 https://inria.hal.science/hal-04050593/document
%2 https://inria.hal.science/hal-04050593/file/497040_1_En_10_Chapter.pdf
%L hal-04050593
%U https://inria.hal.science/hal-04050593
%~ IFIP
%~ IFIP-AICT
%~ IFIP-TC
%~ IFIP-WG
%~ IFIP-TC12
%~ IFIP-AIAI
%~ IFIP-WG12-5
%~ IFIP-AICT-583