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Fuzzy C-Means Algorithm Modification Based on Distance Measurement for River Water Quality
Corresponding Author(s) : Shofwatul ‘Uyun
Kinetik: Game Technology, Information System, Computer Network, Computing, Electronics, and Control,
Vol. 9, No. 3, August 2024
Abstract
River water quality could be determined by understanding the capacity of pollutants in a water body. Fuzzy C-Means (FCM) is one of the fuzzy clustering methods for determining river water quality by measuring water quality parameters, that is, dissolved oxygen (DO) and total dissolved solids (TDS). The FCM algorithm is an effective fuzzy clustering algorithm for grouping data but often produces local and inconsistent optimal solutions due to the partition matrix's random initialisation process. Therefore, this study proposes to modify the FCM algorithm to be precise in the partition matrix initialisation process using several distance concepts. The purpose of the proposed algorithm modification is to get more consistent FCM clustering results and minimise stop iterations. The validation process for the clustering results uses the FCM algorithm, and the FCM modification algorithm uses three parameters, namely the Partition Coefficient Index (PCI), Partition Entropy Index (PEI) and Silhouette Score (SS). The experiments were conducted with three replications and using various distance concepts. The results showed that the number of iterations stopped in the FCM algorithm has different values for PCI, PEI, SS, and stop iterations and objective functions in each trial. On the contrary, the FCM modification algorithm has consistent PCI, PEI, and SS values, and the number of iterations stops with fewer iterations. Therefore, the modified algorithm for initialising the partition matrix can be used in the fuzzy C-means clustering algorithm.
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- Pusat Pengolahan Data Kementerian Pekerjaan Umum Republik Indonesia, Buku Informasi Statistik Pekerjaan Umum. 2012.
- Menteri LIngkungan Hidup dan Kehutanan Republik Indonesia, “Peraturan Menteri Lingkungan Hidup dan Kehutanan Republik Indonesia Nomor 10 Tahun 2022.”
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- T. Garg, S. E. Hamilton, J. P. Hochard, E. P. Kresch, and J. Talbot, “(Not so) gently down the stream: River pollution and health in Indonesia,” J Environ Econ Manage, vol. 92, pp. 35–53, Nov. 2018. https://doi.org/10.1016/j.jeem.2018.08.011
- Z. Feng, R. Zhang, X. Liu, Q. Peng, and L. Wang, “Agricultural nonpoint source pollutant loads into water bodies in a typical basin in the middle reach of the Yangtze River,” Ecotoxicol Environ Saf, vol. 268, Dec. 2023. https://doi.org/10.1016/j.ecoenv.2023.115728
- C. Team et al., Fresh Water for the future, June. United Nations Environment Programme, 2012.
- A. Development Bank, “ADB Annual Report 2016,” 2016.
- D. Sutjiningsih, “Water Quality Index for Determining the Development Threshold of Urbanized Catchment Area in Indonesia,” International Journal of Technology, vol. 8, no. 1, p. 143, 2017. https://doi.org/10.14716/ijtech.v8i1.3971
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- K. K. Verma, B. M. Singh, and A. Dixit, “A review of supervised and unsupervised machine learning techniques for suspicious behavior recognition in intelligent surveillance system,” International Journal of Information Technology (Singapore), vol. 14, no. 1, pp. 397–410, Feb. 2022. https://doi.org/10.1007/s41870-019-00364-0
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- L. Zhu, “Selection of Multi-Level Deep Features via Spearman Rank Correlation for Synthetic Aperture Radar Target Recognition Using Decision Fusion,” IEEE Access, vol. 8, 2020. https://doi.org/10.1109/ACCESS.2020.3010969
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- H. Murfi, N. Rosaline, and N. Hariadi, “Deep autoencoder-based fuzzy c-means for topic detection,” Array, vol. 13, p. 100124, Mar. 2022. https://doi.org/10.1016/j.array.2021.100124
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- É. O. Rodrigues, “Combining Minkowski and Chebyshev: New distance proposal and survey of distance metrics using k-nearest neighbours classifier,” 2018. https://doi.org/10.1016/j.patrec.2018.03.021
- M. S. H. Ardani et al., “A new approach to signal filtering method using K-means clustering and distance-based Kalman filtering,” Sens Biosensing Res, vol. 38, Dec. 2022. https://doi.org/10.1016/j.sbsr.2022.100539
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- F. Farid and D. Rosadi, “Portfolio optimization based on self-organizing maps clustering and genetics algorithm,” International Journal of Advances in Intelligent Informatics, vol. 8, no. 1, pp. 33–44, Mar. 2022. https://doi.org/10.26555/ijain.v8i1.587
- A. E. Haryati, S. Surono, and S. Suparman, “Implementation of Minkowski-Chebyshev Distance in Fuzzy Subtractive Clustering,” EKSAKTA: Journal of Sciences and Data Analysis, pp. 82–87, Jun. 2021. https://doi.org/10.20885/eksakta.vol2.iss2.art1
- J. Li, J. Shao, W. Wang, and W. Xie, “An evolutional deep learning method based on multi-feature fusion for fault diagnosis in sucker rod pumping system,” Alexandria Engineering Journal, vol. 66, pp. 343–355, Mar. 2023. https://doi.org/10.1016/j.aej.2022.11.028
- N. Gueorguieva, I. Valova, and G. Georgiev, “M&MFCM: Fuzzy C-means Clustering with Mahalanobis and Minkowski Distance Metrics,” in Procedia Computer Science, Elsevier B.V., 2017, pp. 224–233. https://doi.org/10.1016/j.procs.2017.09.064
- E. Setyaningsih, N. Hidayat, U. Lestari, and A. Septiarini, “Modification OF K-Means and K-Mode Algorithms to Enhance the Performance of Clustering Student Learning Styles in the Learning Management System,” ICIC Express Letters, vol. 17, no. 1, pp. 49–59, Jan. 2023. https://doi.org/10.24507/icicel.17.01.49
References
Pusat Pengolahan Data Kementerian Pekerjaan Umum Republik Indonesia, Buku Informasi Statistik Pekerjaan Umum. 2012.
Menteri LIngkungan Hidup dan Kehutanan Republik Indonesia, “Peraturan Menteri Lingkungan Hidup dan Kehutanan Republik Indonesia Nomor 10 Tahun 2022.”
T. H. M. van Emmerik, S. Kirschke, L. J. Schreyers, S. Nath, C. Schmidt, and K. Wendt-Potthoff, “Estimating plastic pollution in rivers through harmonized monitoring strategies,” Mar Pollut Bull, vol. 196, Nov. 2023. https://doi.org/10.1016/j.marpolbul.2023.115503
T. Garg, S. E. Hamilton, J. P. Hochard, E. P. Kresch, and J. Talbot, “(Not so) gently down the stream: River pollution and health in Indonesia,” J Environ Econ Manage, vol. 92, pp. 35–53, Nov. 2018. https://doi.org/10.1016/j.jeem.2018.08.011
Z. Feng, R. Zhang, X. Liu, Q. Peng, and L. Wang, “Agricultural nonpoint source pollutant loads into water bodies in a typical basin in the middle reach of the Yangtze River,” Ecotoxicol Environ Saf, vol. 268, Dec. 2023. https://doi.org/10.1016/j.ecoenv.2023.115728
C. Team et al., Fresh Water for the future, June. United Nations Environment Programme, 2012.
A. Development Bank, “ADB Annual Report 2016,” 2016.
D. Sutjiningsih, “Water Quality Index for Determining the Development Threshold of Urbanized Catchment Area in Indonesia,” International Journal of Technology, vol. 8, no. 1, p. 143, 2017. https://doi.org/10.14716/ijtech.v8i1.3971
Y. Li et al., “Study on total phosphorus pollution load estimation and prevention and control countermeasures in Dongting Lake,” Energy Reports, vol. 9, pp. 294–305, Aug. 2023. https://doi.org/10.1016/j.egyr.2023.04.272
K. K. Verma, B. M. Singh, and A. Dixit, “A review of supervised and unsupervised machine learning techniques for suspicious behavior recognition in intelligent surveillance system,” International Journal of Information Technology (Singapore), vol. 14, no. 1, pp. 397–410, Feb. 2022. https://doi.org/10.1007/s41870-019-00364-0
Á. López-Oriona, J. A. Vilar, and P. D’Urso, “Hard and soft clustering of categorical time series based on two novel distances with an application to biological sequences,” Inf Sci (N Y), vol. 624, pp. 467–492, May 2023. https://doi.org/10.1016/j.ins.2022.12.065
Á. López-Oriona, P. D’Urso, J. A. Vilar, and B. Lafuente-Rego, “Quantile-based fuzzy C-means clustering of multivariate time series: Robust techniques,” International Journal of Approximate Reasoning, vol. 150, pp. 55–82, Nov. 2022. https://doi.org/10.1016/j.ijar.2022.07.010
L. Zhu, “Selection of Multi-Level Deep Features via Spearman Rank Correlation for Synthetic Aperture Radar Target Recognition Using Decision Fusion,” IEEE Access, vol. 8, 2020. https://doi.org/10.1109/ACCESS.2020.3010969
S. Subudhi and S. Panigrahi, “Use of optimized Fuzzy C-Means clustering and supervised classifiers for automobile insurance fraud detection,” Journal of King Saud University - Computer and Information Sciences, vol. 32, no. 5, 2020. https://doi.org/10.1016/j.jksuci.2017.09.010
N. Jafarzade et al., “Viability of two adaptive fuzzy systems based on fuzzy c means and subtractive clustering methods for modeling Cadmium in groundwater resources,” Heliyon, vol. 9, no. 8, Aug. 2023. https://doi.org/10.1016/j.heliyon.2023.e18415
A. Gupta, S. Datta, and S. Das, “Fuzzy Clustering to Identify Clusters at Different Levels of Fuzziness: An Evolutionary Multiobjective Optimization Approach,” IEEE Trans Cybern, vol. 51, no. 5, pp. 2601–2611, May 2021. https://doi.org/10.1109/TCYB.2019.2907002
A. S. Shirkhorshidi, T. Y. Wah, S. M. R. Shirkhorshidi, and S. Aghabozorgi, “Evolving Fuzzy Clustering Approach: An Epoch Clustering That Enables Heuristic Postpruning,” IEEE Transactions on Fuzzy Systems, vol. 29, no. 3, pp. 560–568, Mar. 2021. https://doi.org/10.1109/TFUZZ.2019.2956900
J. E. Nalavade and T. Senthil Murugan, “HRNeuro-fuzzy: Adapting neuro-fuzzy classifier for recurring concept drift of evolving data streams using rough set theory and holoentropy,” Journal of King Saud University - Computer and Information Sciences, vol. 30, no. 4, pp. 498–509, Oct. 2018. https://doi.org/10.1016/j.jksuci.2016.11.005
W. Yiping et al., “An improved multi-view collaborative fuzzy C-means clustering algorithm and its application in overseas oil and gas exploration,” J Pet Sci Eng, vol. 197, Feb. 2021. https://doi.org/10.1016/j.petrol.2020.108093
G. Wang, S. Guo, L. Han, Z. Zhao, and X. Song, “COVID-19 ground-glass opacity segmentation based on fuzzy c-means clustering and improved random walk algorithm,” Biomed Signal Process Control, vol. 79, Jan. 2023. https://doi.org/10.1016/j.bspc.2022.104159
Y. Huang, D. Chen, W. Zhao, and Y. Lv, “Fuzzy C-Means Clustering Based Deep Patch Learning With Improved Interpretability for Classification Problems,” IEEE Access, vol. 10, pp. 49873–49891, 2022. https://doi.org/10.1109/ACCESS.2022.3171109
H. Murfi, N. Rosaline, and N. Hariadi, “Deep autoencoder-based fuzzy c-means for topic detection,” Array, vol. 13, p. 100124, Mar. 2022. https://doi.org/10.1016/j.array.2021.100124
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,” International Journal of Fuzzy Systems, vol. 23, no. 1, pp. 139–144, Feb. 2021. https://doi.org/10.1007/s40815-020-00997-5
É. O. Rodrigues, “Combining Minkowski and Chebyshev: New distance proposal and survey of distance metrics using k-nearest neighbours classifier,” 2018. https://doi.org/10.1016/j.patrec.2018.03.021
M. S. H. Ardani et al., “A new approach to signal filtering method using K-means clustering and distance-based Kalman filtering,” Sens Biosensing Res, vol. 38, Dec. 2022. https://doi.org/10.1016/j.sbsr.2022.100539
Á. López-Oriona, J. A. Vilar, and P. D’Urso, “Quantile-based fuzzy clustering of multivariate time series in the frequency domain,” Fuzzy Sets Syst, vol. 443, pp. 115–154, Aug. 2022. https://doi.org/10.1016/j.fss.2022.02.015
F. Farid and D. Rosadi, “Portfolio optimization based on self-organizing maps clustering and genetics algorithm,” International Journal of Advances in Intelligent Informatics, vol. 8, no. 1, pp. 33–44, Mar. 2022. https://doi.org/10.26555/ijain.v8i1.587
A. E. Haryati, S. Surono, and S. Suparman, “Implementation of Minkowski-Chebyshev Distance in Fuzzy Subtractive Clustering,” EKSAKTA: Journal of Sciences and Data Analysis, pp. 82–87, Jun. 2021. https://doi.org/10.20885/eksakta.vol2.iss2.art1
J. Li, J. Shao, W. Wang, and W. Xie, “An evolutional deep learning method based on multi-feature fusion for fault diagnosis in sucker rod pumping system,” Alexandria Engineering Journal, vol. 66, pp. 343–355, Mar. 2023. https://doi.org/10.1016/j.aej.2022.11.028
N. Gueorguieva, I. Valova, and G. Georgiev, “M&MFCM: Fuzzy C-means Clustering with Mahalanobis and Minkowski Distance Metrics,” in Procedia Computer Science, Elsevier B.V., 2017, pp. 224–233. https://doi.org/10.1016/j.procs.2017.09.064
E. Setyaningsih, N. Hidayat, U. Lestari, and A. Septiarini, “Modification OF K-Means and K-Mode Algorithms to Enhance the Performance of Clustering Student Learning Styles in the Learning Management System,” ICIC Express Letters, vol. 17, no. 1, pp. 49–59, Jan. 2023. https://doi.org/10.24507/icicel.17.01.49