In-The-Limit Clustering Axioms
| Autor: | Robert A. Kłopotek, Mieczyslaw A. Klopotek |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
education.field_of_study
Computer science Population k-means clustering Axiomatic system Consistency (knowledge bases) Mathematics::Logic TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS Limit (mathematics) Isomorphism Cluster analysis education Mathematical economics Axiom |
| Zdroj: | Artificial Intelligence and Soft Computing ISBN: 9783030615338 ICAISC (2) |
| Popis: | The paper studies the major reason for the contradictions in the Kleinberg’s axiomatic system for clustering [9]. We found that the so-called consistency axiom is the single source of problems because it creates new clusters instead of preserving the existent ones. Furthermore, this axiom contradicts the practice that data to be clustered is a sample of the actual population to be clustered. We correct this axiom to fit this requirement. It turns out, however, that the axiom is then too strong and implies isomorphism. Therefore we propose to relax it by allowing for centric consistency and demonstrate that under centric consistency, the axiomatic framework is not contradictory anymore. The practical gain is the availability of true cluster preserving operators. |
| Databáze: | OpenAIRE |
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