On Rough Set Based Non Metric Model

  • Yasunori Endo
  • Ayako Heki
  • Yukihiro Hamasuna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7647)


Non metric model is a kind of clustering method in which belongingness or the membership grade of each object to each cluster is calculated directly from dissimilarities between objects and cluster centers are not used.

By the way, the concept of rough set is recently focused. Conventional clustering algorithms classify a set of objects into some clusters with clear boundaries, that is, one object must belong to one cluster. However, many objects belong to more than one cluster in real world, since the boundaries of clusters overlap with each other. Fuzzy set representation of clusters makes it possible for each object to belong to more than one cluster. On the other hand, the fuzzy degree sometimes may be too descriptive for interpreting clustering results. Rough set representation could handle such cases. Clustering based on rough set representation could provide a solution that is less restrictive than conventional clustering and less descriptive than fuzzy clustering.

This paper shows two type of Rough set based Non Metric model (RNM). One algorithm is Rough set based Hard Non Metric model (RHNM) and the other is Rough set based Fuzzy Non Metric model (RFNM). In the both algorithms, clusters are represented by rough sets and each cluster consists of lower and upper approximation. Second, the proposed methods are kernelized by introducing kernel functions which are a powerful tool to analize clusters with nonlinear boundaries


Kernel Function Cluster Center Lower Approximation High Dimensional Feature Space Membership Grade 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yasunori Endo
    • 1
    • 4
  • Ayako Heki
    • 2
  • Yukihiro Hamasuna
    • 3
  1. 1.Faculty of Eng., Info. and Sys.University of TsukubaTsukubaJapan
  2. 2.Graduate School of Sys. and Info. Eng.University of TsukubaTsukubaJapan
  3. 3.Department of InformaticsKinki UniversityOsakaJapan
  4. 4.International Institute for Applied Systems Analysis (IIASA)LaxenburgAustria

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