Journal of the Korea Institute of Information and Communication Engineering (한국정보통신학회논문지)

The Korea Institute of Information and Commucation Engineering (한국정보통신학회)
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Improved Density-Independent Fuzzy Clustering Using Regularization

레귤러라이제이션 기반 개선된 밀도 무관 퍼지 클러스터링

  • Han, Soowhan (Department of Applied Software Engineering, Dong-eui University) ;
  • Heo, Gyeongyong (Department of Electronic Engineering, Dong-eui University)
  • Received : 2019.09.23
  • Accepted : 2019.10.19
  • Published : 2020.01.31
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Abstract

Fuzzy clustering, represented by FCM(Fuzzy C-Means), is a simple and efficient clustering method. However, the object function in FCM makes clusters affect clustering results proportional to the density of clusters, which can distort clustering results due to density difference between clusters. One method to alleviate this density problem is EDI-FCM(Extended Density-Independent FCM), which adds additional terms to the objective function of FCM to compensate for the density difference. In this paper, proposed is an enhanced EDI-FCM using regularization, Regularized EDI-FCM. Regularization is commonly used to make a solution space smooth and an algorithm noise insensitive. In clustering, regularization can reduce the effect of a high-density cluster on clustering results. The proposed method converges quickly and accurately to real centers when compared with FCM and EDI-FCM, which can be verified with experimental results.

FCM(Fuzzy C-Means)으로 대표되는 퍼지 클러스터링은 간단하면서도 효율적인 클러스터링 방법이지만, FCM에서 사용하는 목적 함수에서는 밀도가 높은 클러스터가 클러스터링 결과에 많은 영향을 미치도록 함으로써 클러스터 사이의 밀도 차에 의해 클러스터링 결과에 왜곡이 발생할 수 있다. 이러한 밀도 문제를 완화하는 방법의 하나로 FCM의 목적 함수에 밀도 차이를 보정할 수 있는 항을 추가한 EDI-FCM(Extended Density-Independent FCM)이 있다. 이 논문에서는 레귤러라이제이션을 이용하여 EDI-FCM을 보완한 Regularized EDI-FCM을 제안한다. 레귤러라이제이션은 해공간을 평탄화하고 잡음 민감성을 줄이기 위해 흔히 사용되는 방법으로, 클러스터링에서는 특정 클러스터가 클러스터링 결과에 미치는 영향을 줄이는 역할을 한다. 제안하는 방법은 FCM이나 EDI-FCM과 비교했을 때 실제 클러스터 중심에 빠르고 정확하게 수렴한다는 것을 실험 결과를 통해 확인할 수 있다.

Keywords

References

  1. J. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, New York, Springer, 1981.
  2. B. H. Yoo, W. W. Kim, and G. Heo, "An Improved Clustering Method with Cluster Density Independence," Journal of the Korea Society of Computer and Information, vol. 20, no. 12, pp. 15-20, Dec. 2015. https://doi.org/10.9708/jksci.2015.20.12.015
  3. S. H. Kim, and G. Heo, "Improvement on Density Independent Clustering Method," Journal of the Korea Institute of Information and Communication Engineering, vol. 21, no. 5, pp. 967-973, May. 2017. https://doi.org/10.6109/jkiice.2017.21.5.967
  4. X. Chang, Q. Wang, Y. Liu, and Y. Wang, "Sparse Regularization in Fuzzy c-Means for High-Dimensional Data Clustering," IEEE Transactions on Cybernetics, vol. 47, no. 9, pp. 2616-2627, Sep. 2017. https://doi.org/10.1109/TCYB.2016.2627686
  5. J. Nayak, "Fuzzy C-means(FCM) Clustering Algorithm: A Decade Review from 2000 to 2014," Systems and Technologies, vol. 32, no. 2, pp. 133-179, Dec. 2014.
  6. M. Fuhry, and L. Reichel, "A new Tikhonov regularization method," Numerical Algorithms, vol. 59, no. 3, pp. 433-445, Mar. 2012. https://doi.org/10.1007/s11075-011-9498-x
  7. S. Susan, P. Sharawat, S. Singh, R. Meena, A. Verma, and M. Kumar, "Fuzzy C-means with non-extensive entropy regularization," in Proceedings of 2015 IEEE International Conference on Signal Processing, Informatics, Communication and Energy Systems, Kozhikode, India, pp. 1-5, 2015.
  8. Y. Kanzawa, "Power-regularized fuzzy clustering for spherical data," Journal of Advanced Computational Intelligence and Intelligent Informatics, vol. 22, no. 2, pp. 163-171, Mar. 2018. https://doi.org/10.20965/jaciii.2018.p0163
  9. E. Yasunori, T. Isao, H. Yukihiro, and M. Sadaaki, "Kernelized fuzzy c-means clustering for uncertain data using quadratic penalty-vector regularization with explicit mappings," in Proceedings of 2011 IEEE International Conference on Fuzzy Systems, Taipei, Taiwan, pp. 804-809, 2011.