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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blake, L., Merz, J.: UCI repository of machine learning databases (1998), http://www.ics.uci.edu/~mlearn/MLRepository.html
Sun, C., Sherrah, J.: 3D symmetry detection using the extended Gaussian image. IEEE Transactions on Pattern Analysis and Machine Intelligence 19(2), 164–168 (1997)
Colliot, O., Tuzikov, A., Cesar, R., Bloch, I.: Approximate reflectional symmetries of fuzzy objects with an application in model-based object recognition. Fuzzy Set and Systems 147, 141–163 (2004)
Corsini, P., Lazzerini, B., Marcelloni, F.: A fuzzy relational clustering algorithm based on a dissimilarity measure extracted from data. IEEE Transactions on Systems, Man and Cybernetics, Part B 34(1), 775–781 (2004)
Klein, O., Kamvar, S.O., Manning, C.: From instance-level constraints to space-level constraints: Making the most of prior knowledge in data clustering. In: Proceedings of the Nineteenth International Conference on Machine Learning, pp. 307–314 (2002)
Su, M., Chou, C.-H.: A modified version of the k-means algorithm with a distance based on cluster symmetry. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(6), 674–680 (2001)
Xu, R., Wunsch, D.: Survey of clustering algorithms. IEEE Transactions on Neural Networks 16(3), 645–678 (2005)
Wagstaff, K., Cardie, C., Rogers, S., Schroedl, S.: Constrained k-means clustering with background knowledge. In: Proceedings of the Eighteenth International Conference on Machine Learning, pp. 577–584 (2001)
Xing, E.P., Ng, A.Y., Jordan, M.I., Russell, S.: Distance metric learning, with application to clustering with side-information. Advances in Neural Information Processing Systems 15, 505–512 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, Y., Chen, Y.W. (2006). Hierarchical Clustering with Proximity Metric Derived from Approximate Reflectional Symmetry. In: Wang, L., Jiao, L., Shi, G., Li, X., Liu, J. (eds) Fuzzy Systems and Knowledge Discovery. FSKD 2006. Lecture Notes in Computer Science(), vol 4223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11881599_9
Download citation
DOI: https://doi.org/10.1007/11881599_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-45916-3
Online ISBN: 978-3-540-45917-0
eBook Packages: Computer ScienceComputer Science (R0)