COMPARISON OF FUZZY SUBTRACTIVE CLUSTERING AND FUZZYC-MEANS
DOI:
https://doi.org/10.21107/kursor.v11i1.254Keywords:
Clustering, Fuzzy Clustering, Fuzzy C-Means, Fuzzy Subtractive Clustering, Principal Component AnalysisAbstract
Multivariate statistics have related problems with large data dimensions. One method that can be used is principal component analysis (PCA). Principal component analysis (PCA) is a technique used to reduce data dimensions consisting of several dependent variables while maintaining variance in the data. PCA can be used to stabilize measurements in statistical analysis, one of which is cluster analysis. Fuzzy clustering is a method of grouping based on membership values ​​that includes fuzzy sets as a weighting basis for grouping. In this study, the fuzzy clustering method used is Fuzzy Subtractive Clustering (FSC) and Fuzzy C-Means (FCM) with a combination of the Minkowski Chebysev distance. The purpose of this study was to compare the cluster results obtained from the FSC and FCM using the DBI validity index. The results obtained indicate that the results of clustering using FCM are better than the FSC.
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References
[1] Y. Aït-Sahalia and D. Xiu, “Principal Component Analysis of High-Frequency Data,†J. Am. Stat. Assoc., vol. 114, no. 525, pp. 287–303, Jan. 2019, doi: 10.1080/01621459.2017.1401542.
[2] A. Matuschek et al., “Analysis of parathyroid graft rejection suggests alloantigen-specific production of nitric oxide by iNOS-positive intragraft macrophages.,†Transpl. Immunol., vol. 21, no. 4, pp. 183–191, Sep. 2009, doi: 10.1016/j.trim.2009.04.004.
[3] I.T. Jolliffe, Principal Component Analysis, 2nd ed. New York: Springer-Verlag, 2002.
[4] G. Gan, C. Ma, and J. Wu, Data Clustering: Theory, Algorithms, and Applications. Society for Industrial and Applied Mathematics, 2007.
[5] A. C. Rencher and W. F. Christensen, Methods of Multivariate Analysis. Wiley, 2012.
[6] J. S. R. Jang, C. T. Sun, and E. Mizutani, “Neuro-Fuzzy and Soft Computing-A Computational Approach to Learning and Machine Intelligence [Book Review],†IEEE Trans. Automat. Contr., vol. 42, no. 10, pp. 1482–1484, Oct. 1997, doi: 10.1109/TAC.1997.633847.
[7] S. Kusumadewi and H. Purnomo, “Aplikasi Logika Fuzzy untuk Pendukung Keputusan, vol. II,†Yogyakarta Graha Ilmu, 2013.
[8] J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms. Boston, MA: Springer US, 1981.
[9] L. Zhang, M. Luo, J. Liu, Z. Li, and Q. Zheng, “Diverse fuzzy c-means for image clustering,†Pattern Recognit. Lett., vol. 130, pp. 275–283, 2020, doi: https://doi.org/10.1016/j.patrec.2018.07.004.
[10] W. Qiao and Z. Yang, “An Improved Dolphin Swarm Algorithm Based on Kernel Fuzzy C-Means in the Application of Solving the Optimal Problems of Large-Scale Function,†IEEE Access, vol. 8, pp. 2073–2089, 2020, doi: 10.1109/ACCESS.2019.2958456.
[11] Y. Karuna, S. Saladi, and C. V. Narasimhulu, “Segmentation of tumor using PCA based modified fuzzy C means algorithms on MR brain images,†Int. J. Imaging Syst. Technol., vol. 30, Jun. 2020, doi: 10.1002/ima.22451.
[12] P. Upadhyay and C. Nagpal, “PCA-Aided FCM Identifies Stressful Events of Sleep EEG Under Hot Environment,†IETE J. Res., pp. 1–14, Jun. 2020, doi: 10.1080/03772063.2020.1782273.
[13] G. Zhao, L. Zhang, C. Tang, W. Hao, and Y. Luo, “Clustering of AE signals collected during torsional tests of 3D braiding composite shafts using PCA and FCM,†Compos. Part B Eng., vol. 161, pp. 547–554, 2019, doi: https://doi.org/10.1016/j.compositesb.2018.12.145.
[14] I. D. Widodo, “Fuzzy subtractive clustering based prediction model for brand association analysis,†MATEC Web Conf., vol. 154, p. 01082, Feb. 2018, doi: 10.1051/matecconf/201815401082.
[15] S. K. Chandar, “Stock market prediction using subtractive clustering for a neuro fuzzy hybrid approach,†Cluster Comput., vol. 22, no. S6, pp. 13159–13166, Nov. 2019, doi: 10.1007/s10586-017-1321-6.
[16] E. S. Abdolkarimi and M. R. Mosavi, “Wavelet-adaptive neural subtractive clustering fuzzy inference system to enhance low-cost and high-speed INS/GPS navigation system,†GPS Solut., vol. 24, no. 2, p. 36, Apr. 2020, doi: 10.1007/s10291-020-0951-y.
[17] K. Benmouiza and A. Cheknane, “Clustered ANFIS network using fuzzy c-means, subtractive clustering, and grid partitioning for hourly solar radiation forecasting,†Theor. Appl. Climatol., vol. 137, no. 1–2, pp. 31–43, Jul. 2019, doi: 10.1007/s00704-018-2576-4.
[18] H. Chen and C. Li, “Comprehensive Service Level Analysis of Online Taxi Drivers Based on Fuzzy Clustering Combined with Principal Component Analysis,†in Proceedings of the 2019 4th International Conference on Humanities Science and Society Development (ICHSSD 2019), 2019, pp. 577–583, doi: 10.2991/ichssd-19.2019.116.
[19] É. O. Rodrigues, “Combining Minkowski and Chebyshev: New distance proposal and survey of distance metrics using k-nearest neighbours classifier,†Pattern Recognit. Lett., vol. 110, pp. 66–71, 2018, doi: https://doi.org/10.1016/j.patrec.2018.03.021.
[20] S. Surono and R. D. A. Putri, “Optimization of Fuzzy C-Means Clustering Algorithm with Combination of Minkowski and Chebyshev Distance Using Principal Component Analysis,†Int. J. Fuzzy Syst., 2020, doi: 10.1007/s40815-020-00997-5.
[21] R. A. Johnson and D. W. Wichern, “Applied multivariate statistical analysis,†Statistics (Ber)., vol. 6215, no. 10, p. 10, 2015.
[22] V. Gaspersz, “Teknik analisis dalam penelitian percobaan,†Tarsito. Bandung, vol. 718, 1995.
[23] R. Gustriansyah, N. Suhandi, and F. Antony, “Clustering optimization in RFM analysis Based on k-Means,†Indones. J. Electr. Eng. Comput. Sci., vol. 18, no. 1, p. 470, Apr. 2020, doi: 10.11591/ijeecs.v18.i1.pp470-477.
[24] K. Rezaei and H. Rezaei, “New distance and similarity measures for hesitant fuzzy soft sets,†Iran. J. Fuzzy Syst., vol. 16, no. 6, pp. 159–176, 2019.
[2] A. Matuschek et al., “Analysis of parathyroid graft rejection suggests alloantigen-specific production of nitric oxide by iNOS-positive intragraft macrophages.,†Transpl. Immunol., vol. 21, no. 4, pp. 183–191, Sep. 2009, doi: 10.1016/j.trim.2009.04.004.
[3] I.T. Jolliffe, Principal Component Analysis, 2nd ed. New York: Springer-Verlag, 2002.
[4] G. Gan, C. Ma, and J. Wu, Data Clustering: Theory, Algorithms, and Applications. Society for Industrial and Applied Mathematics, 2007.
[5] A. C. Rencher and W. F. Christensen, Methods of Multivariate Analysis. Wiley, 2012.
[6] J. S. R. Jang, C. T. Sun, and E. Mizutani, “Neuro-Fuzzy and Soft Computing-A Computational Approach to Learning and Machine Intelligence [Book Review],†IEEE Trans. Automat. Contr., vol. 42, no. 10, pp. 1482–1484, Oct. 1997, doi: 10.1109/TAC.1997.633847.
[7] S. Kusumadewi and H. Purnomo, “Aplikasi Logika Fuzzy untuk Pendukung Keputusan, vol. II,†Yogyakarta Graha Ilmu, 2013.
[8] J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms. Boston, MA: Springer US, 1981.
[9] L. Zhang, M. Luo, J. Liu, Z. Li, and Q. Zheng, “Diverse fuzzy c-means for image clustering,†Pattern Recognit. Lett., vol. 130, pp. 275–283, 2020, doi: https://doi.org/10.1016/j.patrec.2018.07.004.
[10] W. Qiao and Z. Yang, “An Improved Dolphin Swarm Algorithm Based on Kernel Fuzzy C-Means in the Application of Solving the Optimal Problems of Large-Scale Function,†IEEE Access, vol. 8, pp. 2073–2089, 2020, doi: 10.1109/ACCESS.2019.2958456.
[11] Y. Karuna, S. Saladi, and C. V. Narasimhulu, “Segmentation of tumor using PCA based modified fuzzy C means algorithms on MR brain images,†Int. J. Imaging Syst. Technol., vol. 30, Jun. 2020, doi: 10.1002/ima.22451.
[12] P. Upadhyay and C. Nagpal, “PCA-Aided FCM Identifies Stressful Events of Sleep EEG Under Hot Environment,†IETE J. Res., pp. 1–14, Jun. 2020, doi: 10.1080/03772063.2020.1782273.
[13] G. Zhao, L. Zhang, C. Tang, W. Hao, and Y. Luo, “Clustering of AE signals collected during torsional tests of 3D braiding composite shafts using PCA and FCM,†Compos. Part B Eng., vol. 161, pp. 547–554, 2019, doi: https://doi.org/10.1016/j.compositesb.2018.12.145.
[14] I. D. Widodo, “Fuzzy subtractive clustering based prediction model for brand association analysis,†MATEC Web Conf., vol. 154, p. 01082, Feb. 2018, doi: 10.1051/matecconf/201815401082.
[15] S. K. Chandar, “Stock market prediction using subtractive clustering for a neuro fuzzy hybrid approach,†Cluster Comput., vol. 22, no. S6, pp. 13159–13166, Nov. 2019, doi: 10.1007/s10586-017-1321-6.
[16] E. S. Abdolkarimi and M. R. Mosavi, “Wavelet-adaptive neural subtractive clustering fuzzy inference system to enhance low-cost and high-speed INS/GPS navigation system,†GPS Solut., vol. 24, no. 2, p. 36, Apr. 2020, doi: 10.1007/s10291-020-0951-y.
[17] K. Benmouiza and A. Cheknane, “Clustered ANFIS network using fuzzy c-means, subtractive clustering, and grid partitioning for hourly solar radiation forecasting,†Theor. Appl. Climatol., vol. 137, no. 1–2, pp. 31–43, Jul. 2019, doi: 10.1007/s00704-018-2576-4.
[18] H. Chen and C. Li, “Comprehensive Service Level Analysis of Online Taxi Drivers Based on Fuzzy Clustering Combined with Principal Component Analysis,†in Proceedings of the 2019 4th International Conference on Humanities Science and Society Development (ICHSSD 2019), 2019, pp. 577–583, doi: 10.2991/ichssd-19.2019.116.
[19] É. O. Rodrigues, “Combining Minkowski and Chebyshev: New distance proposal and survey of distance metrics using k-nearest neighbours classifier,†Pattern Recognit. Lett., vol. 110, pp. 66–71, 2018, doi: https://doi.org/10.1016/j.patrec.2018.03.021.
[20] S. Surono and R. D. A. Putri, “Optimization of Fuzzy C-Means Clustering Algorithm with Combination of Minkowski and Chebyshev Distance Using Principal Component Analysis,†Int. J. Fuzzy Syst., 2020, doi: 10.1007/s40815-020-00997-5.
[21] R. A. Johnson and D. W. Wichern, “Applied multivariate statistical analysis,†Statistics (Ber)., vol. 6215, no. 10, p. 10, 2015.
[22] V. Gaspersz, “Teknik analisis dalam penelitian percobaan,†Tarsito. Bandung, vol. 718, 1995.
[23] R. Gustriansyah, N. Suhandi, and F. Antony, “Clustering optimization in RFM analysis Based on k-Means,†Indones. J. Electr. Eng. Comput. Sci., vol. 18, no. 1, p. 470, Apr. 2020, doi: 10.11591/ijeecs.v18.i1.pp470-477.
[24] K. Rezaei and H. Rezaei, “New distance and similarity measures for hesitant fuzzy soft sets,†Iran. J. Fuzzy Syst., vol. 16, no. 6, pp. 159–176, 2019.
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