On the Discrepancy between Kleinberg’s Clustering Axioms and k-Means Clustering Algorithm Behavior

This paper performs an investigation of Kleinberg’s axioms (from both an intuitive and formal standpoint) as they relate to the well-known k -mean clustering method. The axioms, as well as a novel variations thereof, are analyzed in Euclidean space. A few natural properties are proposed, resulting i...

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Bibliographic Details
Published in:Machine learning 2023-07, Vol.112 (7), p.2501-2553
Main Authors: Kłopotek, Mieczysław Alojzy, Kłopotek, Robert Albert
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Axioms
Cluster analysis
Clustering
Computer Science
Consistency
Control
Datasets
Euclidean geometry
Euclidean space
Machine Learning
Mechatronics
Natural Language Processing (NLP)
Robotics
Simulation and Modeling
Vector quantization
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Summary:This paper performs an investigation of Kleinberg’s axioms (from both an intuitive and formal standpoint) as they relate to the well-known k -mean clustering method. The axioms, as well as a novel variations thereof, are analyzed in Euclidean space. A few natural properties are proposed, resulting in k -means satisfying the intuition behind Kleinberg’s axioms (or, rather, a small, and natural variation on that intuition). In particular, two variations of Kleinberg’s consistency property are proposed, called centric consistency and motion consistency. It is shown that these variations of consistency are satisfied by k-means.
ISSN:0885-6125
1573-0565
DOI:10.1007/s10994-023-06308-x