Hierarchical clustering with proximity metric derived from approximate reflectional symmetry

Authors:
Yong Zhang;Yun Wen Chen
Affiliations:
Department of Computer Science and Engineering, School of Information Science and Engineering, Fudan University, Shanghai, P.R. China;Department of Computer Science and Engineering, School of Information Science and Engineering, Fudan University, Shanghai, P.R. China
Venue:
FSKD'06 Proceedings of the Third international conference on Fuzzy Systems and Knowledge Discovery
Year:
2006

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Abstract

In order to address the problems arise from predefined similarity measure, learning similarity metric from data automatically has drawn a lot of interest. This paper tries to derive the proximity metric using reflectional symmetry information of the given data set. We first detect the hyperplane with highest degree of approximate reflectional symmetry measure among all the candidate hyper-planes defined by the principal axes and the centroid of the given data set. If the symmetry is prominent, then we utilize the symmetry information acquired to derive a retorted proximity metric which will be used as the input to the Complete-Link hierarchical clustering algorithm, otherwise we cluster the data set as usual. Through some synthetic data sets, we show empirically that the proposed algorithm can handle some difficult cases that cannot be handled satisfactorily by previous methods. The potential of our method is also illustrated on some real-world data sets.