Hierarchical Clustering with Proximity Metric Derived from Approximate Reflectional Symmetry

  • Yong Zhang
  • Yun Wen Chen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4223)


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.


Rand Index Locally Linear Embedding Partitional Cluster Approximate Symmetry Proximity Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Blake, L., Merz, J.: UCI repository of machine learning databases (1998),
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    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)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    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)Google Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    Xu, R., Wunsch, D.: Survey of clustering algorithms. IEEE Transactions on Neural Networks 16(3), 645–678 (2005)CrossRefGoogle Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    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)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yong Zhang
    • 1
  • Yun Wen Chen
    • 1
  1. 1.Department of Computer Science and Engineering, School of Information Science and EngineeringFudan UniversityShanghaiP.R. China

Personalised recommendations