Advertisement

On Hard c-Means Using Quadratic Penalty-Vector Regularization for Uncertain Data

  • Yasunori Endo
  • Arisa Taniguchi
  • Aoi Takahashi
  • Yukihiro Hamasuna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6820)

Abstract

Clustering is one of the unsupervised classification techniques of the data analysis. Data are transformed from a real space into a pattern space to apply clustering methods. However, the data cannot be often represented by a point because of uncertainty of the data, e.g., measurement error margin and missing values in data. In this paper, we introduce quadratic penalty-vector regularization to handle such uncertain data into hard c-means (HCM) which is one of the most typical clustering algorithms. First, we propose a new clustering algorithm called hard c-means using quadratic penalty-vector regularization for uncertain data (HCMP). Second, we propose sequential extraction hard c-means using quadratic penalty-vector regularization (SHCMP) to handle datasets whose cluster number is unknown. Moreover, we verify the effectiveness of our propose algorithms through some numerical examples.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Miyamoto, S.: Introduction to Cluster Analysis. Morikita-Shuppan, Tokyo (1999) (in Japanese)Google Scholar
  2. 2.
    Endo, Y., Hasegawa, Y., Hamasuna, Y., Kanzawa, Y.: Fuzzy c-Means Clustering for uncertain Data using Quadratic Regularization of Penalty Vectors. Journal of Advance Computational Intelligence and Intelligent Informatics 15(1), 76–82 (2011)CrossRefGoogle Scholar
  3. 3.
    Endo, Y., Murata, R., Haruyama, H., Miyamoto, S.: Fuzzy c-Means for Data with Tolerance. In: Proc. 2005 International Symposium on Nonlinear Theory and Its Applications, pp. 345–348 (2005)Google Scholar
  4. 4.
    Murata, R., Endo, Y., Haruyama, H., Miyamoto, S.: On Fuzzy c-Means for Data with Tolerance. Journal of Advance Computational Intelligence and Intelligent Informatics 10(5), 673–681 (2006)CrossRefzbMATHGoogle Scholar
  5. 5.
    Kanzawa, Y., Endo, Y., Miyamoto, S.: Fuzzy c-Means Algorithms for Data with Tolerance based on Opposite Criterions. IEICE Trans. Fundamentals E90-A(10), 2194–2202 (2007)Google Scholar
  6. 6.
    Endo, Y., Hasegawa, Y., Hamasuna, Y., Miyamoto, S.: Fuzzy c-Means for Data with Rectangular Maximum Tolerance Range. Journal of Advanced Computational Intelligence and Intelligent Informatics 12(5), 461–466 (2008)CrossRefGoogle Scholar
  7. 7.
    Kanzawa, Y., Endo, Y., Miyamoto, S.: Fuzzy c-Means Algorithms for Data with Tolerance using Kernel Functions. IEICE Trans. Fundamentals E91-A(9), 2520–2534 (2008)CrossRefzbMATHGoogle Scholar
  8. 8.
    Hasegawa, Y., Endo, Y., Hamasuna, Y.: On Fuzzy c-Means for Data with Uncertainty using Spring Modulus. In: Proc. of SCIS & ISIS 2008 (2008)Google Scholar
  9. 9.
    Miyamoto, S., Arai, K.: Different Sequential Clustering Algorithms and Sequential Regression Models. In: Proc. of FUZZ-IEEE 2009 (2009)Google Scholar
  10. 10.
    MacQueen, J.B.: Some Methods of Classification and Analysis of Multivariate Observations. In: Proc. of 5th Berkeley Symposium on Math. Stat. and Prob., pp. 281–297 (1967)Google Scholar
  11. 11.
    Dave, R.N.: Characterization and Detection of Noise in Clustering. Pattern Recognition Letters 12, 657–664 (1991)Google Scholar
  12. 12.
    Dave, R.N., Krishnapuram, R.: Robust Clustering Methods: a Unified View. IEEE Trans. on Fuzzy Systems 5(2), 270–293 (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yasunori Endo
    • 1
  • Arisa Taniguchi
    • 2
  • Aoi Takahashi
    • 2
  • Yukihiro Hamasuna
    • 3
  1. 1.Department of Risk EngineeringUniversity of TsukubaTsukubaJapan
  2. 2.Graduate School of Systems and Information EngineeringUniversity of TsukubaTsukubaJapan
  3. 3.Department of InformaticsKinki UniversityHigashiosakaJapan

Personalised recommendations