Journal of the Korea Society of Computer and Information (한국컴퓨터정보학회논문지)

Korean Society of Computer Information (한국컴퓨터정보학회)
권호 표지
DOI QR코드

DOI QR Code

An Extension of Possibilistic Fuzzy C-means using Regularization

Regularization을 이용한 Possibilistic Fuzzy C-means의 확장

  • Received : 2010.01.05
  • Accepted : 2010.01.26
  • Published : 2010.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

Fuzzy c-means (FCM) and possibilistic c-means (PCM) are the two most well-known clustering algorithms in fuzzy clustering area, and have been applied in many applications in their original or modified forms. However, FCM's noise sensitivity problem and PCM's overlapping cluster problem are also well known. Recently there have been several attempts to combine both of them to mitigate the problems and possibilistic fuzzy c-means (PFCM) showed promising results. In this paper, we proposed a modified PFCM using regularization to reduce noise sensitivity in PFCM further. Regularization is a well-known technique to make a solution space smooth and an algorithm noise insensitive. The proposed algorithm, PFCM with regularization (PFCM-R), can take advantage of regularization and further reduce the effect of noise. Experimental results are given and show that the proposed method is better than the existing methods in noisy conditions.

Fuzzy c-means(FCM)와 possibilistic c-means(PCM)는 퍼지 클러스터링 영역에서 대표적인 두 가지 방법으로 많은 패턴 인식 문제들에 성공적으로 활용되어져 왔다. 하지만 이들 방법 역시 잡음 민감성과 중첩 클러스터 문제를 가지고 있다. 이들 문제점을 극복하기 위해, 최근 두 방법을 결합하려는 시도가 있어왔고, possibilistic fuzzy c-means(PFCM)는 FCM과 PCM을 목적 함수 단계에서 통합함으로써 두 방법이 가지는 문제점을 완화시키는 성공적인 결과를 보여주었다. 이 논문에서는 PFCM에 regularization을 도입함으로써 PFCM의 잡음 민감성을 한층 더 줄여줄 수 있는 향상된 PFCM을 소개한다. Regularization은 해공간을 평탄화 함으로써 잡음의 영향을 줄이는 대표적인 방법 중 하나이다. 제안한 방법은 PFCM의 장점과 더불어 regularization에 의해 잡음의 영향을 더욱 줄일 수 있으며, 이는 실험을 통해 확인할 수 있다.

Keywords

References

  1. L. A. Zadeh, "Fuzzy sets," Information and Control, Vol. 8, No. 3, pp. 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X
  2. J. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, New York, Springer, 1981.
  3. R. Krishnapuram and J. Keller, "A possibilistic approach to clustering," IEEE Transactions on Fuzzy Systems, Vol. 1, No. 2, pp. 98-110, 1993. https://doi.org/10.1109/91.227387
  4. N. R. Pal, K. Pal, J. M. Keller, and J. C. Bezdek, "A possibilistic fuzzy c-means clustering algorithm," IEEE Transactions on Fuzzy Systems, Vol. 13, No. 4, pp. 517-530, 2005. https://doi.org/10.1109/TFUZZ.2004.840099
  5. J. S. Zhang and Y. W. Leung, "Improved possibilistic c-means clustering algorithms," IEEE Transactions on Fuzzy Systems, Vol. 12, No. 2, pp. 209-217, 2004. https://doi.org/10.1109/TFUZZ.2004.825079
  6. N. R. Pal, K. Pal, and J. Bezdek, "A mixed c-means clustering model," Proceedings of 6th IEEE International Conference on Fuzzy Systems, July 1997, pp. 11-21, 1997.
  7. A. Tikhonov, "On solving incorrectly posed problems and method of regularization," Dokl. Acad. Nauk USSR, Vol. 151, pp. 501-504, 1963.
  8. R. Li and M. Mukaidono, "A maximum entropy approach to fuzzy clustering," Proceedings of 4th IEEE International Conference on Fuzzy Systems, March 1995, pp. 2227-2232, 1995.
  9. S. Miyamoto and K. Umayahara, "Fuzzy clustering by quadratic regularization," Proceedings of 4th IEEE International Conference on Fuzzy Systems, March 1998, pp. 1394-1399, 1998.
  10. D. Ozdemir and L. Akarun, "A fuzzy algorithm for color quantization of images," Pattern Recognition, Vol. 35, No. 8, pp. 1785-1791, 2002. https://doi.org/10.1016/S0031-3203(01)00170-4
  11. J. Yu and M. S. Yang, "A generalized fuzzy clustering regularization model with optimality tests and model complexity analysis," IEEE Transactions on Fuzzy Systems, Vol. 15, No. 5, pp. 904-915, 2007. https://doi.org/10.1109/TFUZZ.2006.889957
  12. P. C. Hansen, "Analysis of discrete ill-posed problems by means of the L-curve," SIAM Review, Vol. 34, No. 4, pp. 561-580, 1992. https://doi.org/10.1137/1034115
  13. D. K. Stando and M. Rudnicki, "Regularization parameter selection in discrete ill-posed problems - the use of the U-curve," International Journal of Applied Mathematics and Computer Science, Vol. 17, No. 2, pp. 157-164, 2007. https://doi.org/10.2478/v10006-007-0014-3
  14. C. W. Hsu, C. C. Chang, and C. J. Lin, "A practical guide to support vector classification," Technical Report, 2003, Department of Computer Science, National Taiwan University, Taipei, Taiwan.

Cited by

  1. A Context-Aware Information Service using FCM Clustering Algorithm and Fuzzy Decision Tree vol.16, pp.7, 2013, https://doi.org/10.9717/kmms.2013.16.7.810
  2. An Improved Clustering Method with Cluster Density Independence vol.20, pp.12, 2010, https://doi.org/10.9708/jksci.2015.20.12.015
  3. 밀도에 무관한 클러스터링 기법의 개선 vol.21, pp.5, 2010, https://doi.org/10.6109/jkiice.2017.21.5.967