Hierarchical clustering using the arithmetic-harmonic cut: complexity and experiments.
Clustering, particularly hierarchical clustering, is an important method for understanding and analysing data across a wide variety of knowledge domains with notable utility in systems where the data can be classified in an evolutionary context. This paper introduces a new hierarchical clustering pr...
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| Auteurs principaux: | , , , |
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| Format: | article |
| Langue: | EN |
| Publié: |
Public Library of Science (PLoS)
2010
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| Sujets: | |
| Accès en ligne: | https://doaj.org/article/3d1c06c6ca0b43f78298ded6d8916924 |
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| Résumé: | Clustering, particularly hierarchical clustering, is an important method for understanding and analysing data across a wide variety of knowledge domains with notable utility in systems where the data can be classified in an evolutionary context. This paper introduces a new hierarchical clustering problem defined by a novel objective function we call the arithmetic-harmonic cut. We show that the problem of finding such a cut is NP-hard and APX-hard but is fixed-parameter tractable, which indicates that although the problem is unlikely to have a polynomial time algorithm (even for approximation), exact parameterized and local search based techniques may produce workable algorithms. To this end, we implement a memetic algorithm for the problem and demonstrate the effectiveness of the arithmetic-harmonic cut on a number of datasets including a cancer type dataset and a corona virus dataset. We show favorable performance compared to currently used hierarchical clustering techniques such as k-Means, Graclus and Normalized-Cut. The arithmetic-harmonic cut metric overcoming difficulties other hierarchical methods have in representing both intercluster differences and intracluster similarities. |
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