Point Symmetry-Based Distance Measures and Their Applications to Clustering

  • Sanghamitra Bandyopadhyay
  • Sriparna Saha


This chapter presents some symmetry-based distances used for clustering a given data set. In recent years some symmetry-based similarity measurements have been developed. The definitions of these measures and their advantages and disadvantages are elaborately described in the first part of this chapter. In the second part, a recently developed genetic algorithm-based clustering technique, named GAPS, that uses a symmetry-based distance for assignment of points to different clusters and for fitness computation is elaborately described. Kd-tree-based nearest neighbor search is further used to reduce the time complexity of computing symmetry-based distance. A time complexity analysis of this algorithm is provided. The convergence proof of the GAPS clustering technique is also established in the present chapter. Results on a wide range of data sets show that GAPS is able to detect any type of clusters, irrespective of their geometrical shape and overlapping nature, as long as they possess the characteristic of symmetry. GAPS is compared with some existing symmetry-based clustering techniques for several artificial and real-life data sets.


Cluster Center Cluster Technique Query Point Cluster Assignment Stochastic Matrice 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sanghamitra Bandyopadhyay
    • 1
  • Sriparna Saha
    • 2
  1. 1.Machine Intelligence UnitIndian Statistical InstituteKolkataIndia
  2. 2.Dept. of Computer ScienceIndian Institute of TechnologyPatnaIndia

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