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.

Hierarchical Clustering Using the Arithmetic-Harmonic Cut: Complexity and Experiments

RIZZI, ROMEO;
2010

Abstract

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.
clustering; hierarchical clustering; arithmetic-harmonic cut; APX-hard; fixed-parameter tractable; approximation-algorithm; experimental evaluation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/435352
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