Title: Reducing dendrogram instability using clustering based on indiscernibility and indiscernibility level

Authors: R.B. Fajriya Hakim; Subanar Seno; Edi Winarko

Addresses: Statistics Department, Faculty of Mathematics and Natural Sciences, Universitas Islam Indonesia, Jalan Kaliurang KM 14.5 Sleman, Jogjakarta 55584, Indonesia. ' Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, Jogjakarta 55528, Indonesia. ' Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, Jogjakarta 55528, Indonesia

Abstract: The notions of indiscernibility and discernibility are the core concept of classical rough sets to cluster similarities and differences of data objects. In this paper, we use a new method of clustering data based on the combination of indiscernibility (quantitative indiscernibility relation) and its indiscernibility level. The indiscernibility level quantify the indiscernibility of pair of objects among other objects in information systems and this level represent the granularity of pair of objects in information system. For comparison to the new method, the following four clustering methods were selected and evaluated on a simulation dataset: average-, complete- and single-linkage agglomerative hierarchical clustering and Ward|s method. The result of this paper shows that the four methods of hierarchical clustering yield dendrogram instability that gives different solution under permutation of input order of data object while the new method reduces dendrogram instability.

Keywords: rough sets; hierarchical clustering; indiscernibility level; dendrogram instability.

DOI: 10.1504/IJGCRSIS.2011.043365

International Journal of Granular Computing, Rough Sets and Intelligent Systems, 2011 Vol.2 No.2, pp.87 - 106

Available online: 26 Oct 2011 *

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