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

作者：Rizzi Romeo^*; Mahata Pritha; Mathieson Luke; Moscato Pablo

来源：PLos One, 2010, 5(12): e14067.

DOI：10.1371/journal.pone.0014067

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 hierarchal methods have in representing both intercluster differences and intracluster similarities.

• 出版日期2010-12-2
• 单位上海生物信息技术研究中心