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Noise-resistant fuzzy clustering algorithm

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Abstract

The main objective of Fuzzy C-means (FCM) algorithm is to group data into some clusters based on their similarities and dissimilarities. However, noise and outliers affect the performance of the algorithm that results in misplaced cluster centers. Although several corrections are made in the algorithm to tackle this problem but the algorithm is not improved effectively and still suffers from the same problem. Noise-resistant FCM (nrFCM) algorithm is proposed in this work to improve the performance of the FCM algorithm when dealing with noise and outliers. The nrFCM algorithm eliminates the effects of noise and outliers on the cluster centers by introducing a function of distance instead of the distance itself into the objective function of the FCM algorithm. It is shown that the nrFCM algorithm is significantly more accurate than the FCM algorithm and noise and outliers cannot impair its accuracy. However, its runtime is higher than that of the FCM algorithm because of nonlinear update equation for cluster centers.

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References

  • Ahmed T, Mohamed B, Abdelkader C (2015) Nonlinear system identification using clustering algorithm based on kernel method and particle swarm optimization. Int J Uncertain Fuzziness Knowl-Based Syst 23(5):667–683

    MathSciNet  MATH  Google Scholar 

  • Aladag CH, Yolcu U, Egrioglu E, Dalar AZ (2012) A new time invariant fuzzy time series forecasting method based on particle swarm optimization. Appl Soft Comput 12(10):3291–3299

    Google Scholar 

  • Amezcua J, Melin P (2019) A new fuzzy learning vector quantization method for classification problems based on a granular approach. Granul Comput 4:197–209

    Google Scholar 

  • Anderson D, Bezdek J, Popescu M, Keller J (2010) Comparing fuzzy, probabilistic, and possibilistic partitions. IEEE Trans Fuzzy Syst 18(5):906–917

    Google Scholar 

  • Antonelli M, Ducange P, Lazzerini B, Marcelloni F (2016) Multi-objective evolutionary design of granular rule-based classifiers. Granul Comput 1:37–58

    Google Scholar 

  • Apolloni B, Bassis S, Rota J, Galliani GL, Gioia M, Ferrari L (2016) A neurofuzzy algorithm for learning from complex granules. Granul Comput 1:225–246

    Google Scholar 

  • Askari S (2017a) A novel and fast MIMO fuzzy inference system based on a class of fuzzy clustering algorithms with interpretability and complexity analysis. Expert Syst Appl 84:301–322

    Google Scholar 

  • Askari S (2017b) Oil reservoirs classification using fuzzy clustering. Int J Eng 30(9):1391–1400

    Google Scholar 

  • Askari S, Montazerin N (2015) A high-order multi-variable Fuzzy Time Series forecasting algorithm based on fuzzy clustering. Expert Syst Appl 42(4):2121–2135

    Google Scholar 

  • Askari S, Montazerin N, Fazel Zarandi MH (2015a) A clustering based forecasting algorithm for multivariable fuzzy time series using linear combinations of independent variables. Appl Soft Comput 35:151–160

    Google Scholar 

  • Askari S, Montazerin N, Fazel Zarandi MH (2015b) Forecasting semi-dynamic response of natural gas networks to nodal gas consumptions using genetic fuzzy systems. Energy 83:252–266

    Google Scholar 

  • Askari S, Montazerin N, Fazel Zarandi MH (2016a) High frequency modeling of natural gas networks from low frequency nodal meter readings using time series disaggregation. IEEE Trans Ind Inf 12(1):136–147

    Google Scholar 

  • Askari S, Montazerin N, Fazel Zarandi MH (2016b) Gas networks simulation from disaggregation of low frequency nodal gas consumption. Energy 112:1286–1298

    Google Scholar 

  • Askari S, Montazerin N, Fazel Zarandi MH, Hakimi E (2017a) Generalized entropy based possibilistic fuzzy c-means for clustering noisy data and its convergence proof. Neurocomputing 219:186–202

    Google Scholar 

  • Askari S, Montazerin N, Fazel Zarandi MH (2017b) Generalized possibilistic fuzzy c-means with novel cluster validity indices for clustering noisy data. Appl Soft Comput 53:262–283

    Google Scholar 

  • Askari S, Montazerin N, Fazel Zarandi MH (2020) Modeling energy flow in natural gas networks using time series disaggregation and fuzzy systems tuned by particle swarm optimization. Appl Soft Comput 92:106332

    Google Scholar 

  • Aydav PSS, Minz S (2020) Granulation-based self-training for the semi-supervised classification of remote-sensing images. Granular Computing 5:309–327

    Google Scholar 

  • Beliakov G, Li G, Vu HQ, Wilkin T (2015) Characterizing compactness of geometrical clusters using fuzzy measures. IEEE Trans Fuzzy Syst 23(4):1030–1043

    Google Scholar 

  • Bezdek JC, Ehrlich R, Full W (1984) FCM: the fuzzy c-means clustering algorithm. Comput Geosci 10(2–3):191–203

    Google Scholar 

  • Bouzbida M, Hassine L, Chaari A (2017) Robust kernel clustering algorithm for nonlinear system identification. Math Probl Eng 2017:1–11

    MathSciNet  MATH  Google Scholar 

  • Chen SM, Chang YC (2010) Multi-variable fuzzy forecasting based on fuzzy clustering and fuzzy rule interpolation techniques. Inf Sci 180(24):4772–4783

    MathSciNet  Google Scholar 

  • Chen SM, Chen SW (2014) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and the probabilities of trends of fuzzy logical relationships. IEEE Trans Cybern 45(3):391–403

    Google Scholar 

  • Chen SM, Chen SW (2015) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and the probabilities of trends of fuzzy logical relationships. IEEE Trans Cybern 45(3):391–403

    Google Scholar 

  • Chen SM, Jian WS (2017) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups, similarity measures and PSO techniques. Inf Sci 391–392:65–79

    Google Scholar 

  • Chen SM, Phuong BDH (2017) Fuzzy time series forecasting based on optimal partitions of intervals and optimal weighting vectors. Knowl-Based Syst 118:204–216

    Google Scholar 

  • Chen SM, Tanuwijaya K (2011a) Fuzzy forecasting based on high-order fuzzy logical relationships and automatic clustering techniques. Expert Syst Appl 38(12):15425–15437

    Google Scholar 

  • Chen SM, Tanuwijaya K (2011b) Multivariate fuzzy forecasting based on fuzzy time series and automatic clustering techniques. Expert Syst Appl 38(8):10594–10605

    Google Scholar 

  • Chen SM, Wang NY (2010) Fuzzy forecasting based on fuzzy-trend logical relationship groups. IEEE Trans Syst Man Cybern Part B (Cybern) 40(5):1343–1358

    Google Scholar 

  • Chen L, Chen CLP, Lu M (2011) A multiple-kernel fuzzy c-means algorithm for image segmentation. IEEE Trans Syst Man Cybern Part B (Cybern) 41(5):1263–1274

    Google Scholar 

  • Chen SM, Chu HP, Sheu TW (2012) TAIEX forecasting using fuzzy time series and automatically generated weights of multiple factors. IEEE Trans Syst Man Cybern Part A: Syst Hum 42(6):1485–1495

    Google Scholar 

  • Chen SM, Manalu GMT, Pan JS, Liu HC (2013) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and particle swarm optimization techniques. IEEE Trans Cybern 43(3):1102–1117

    Google Scholar 

  • Chen SM, Zou XY, Gunawan GC (2019a) Fuzzy time series forecasting based on proportions of intervals and particle swarm optimization techniques. Inf Sci 500:127–139

    MathSciNet  Google Scholar 

  • Chen J, Li Y, Yang X, Zhao S, Zhang Y (2019b) VGHC: a variable granularity hierarchical clustering for community detection. Granul Comput. https://doi.org/10.1007/s41066-019-00195-1

    Article  Google Scholar 

  • Cheng CH, Cheng GW, Wang JW (2008) Multi-attribute fuzzy time series method based on fuzzy clustering. Expert Syst Appl 34(2):1235–1242

    MathSciNet  Google Scholar 

  • Chintalapudi KK, Kam M (1998) A noise-resistant fuzzy C means algorithm for clustering. IEEE World Congr Comput Intell. https://doi.org/10.1109/FUZZY.1998.686334

    Article  Google Scholar 

  • Ciucci D (2016) Orthopairs and granular computing. Granular. Computing 1:159–170

    Google Scholar 

  • Dubois D, Prade H (2016) Bridging gaps between several forms of granular computing. Granul Comput 1:115–126

    Google Scholar 

  • Duru O, Bulut E (2014) A non-linear clustering method for fuzzy time series: histogram damping partition under the optimized cluster paradox. Appl Soft Comput 24:742–748

    Google Scholar 

  • Egrioglu E, Aladag CH, Yolcu U, Uslu VR, Erilli NA (2011) Fuzzy time series forecasting method based on Gustafson-Kessel fuzzy clustering. Expert Syst Appl 38(8):10355–10357

    Google Scholar 

  • Filippone M, Masulli F, Rovetta S (2010) Applying the possibilistic c-means algorithm in kernel-induced spaces. IEEE Trans Fuzzy Syst 18(3):572–584

    Google Scholar 

  • Gosain A, Dahiya S (2016) Performance analysis of various fuzzy clustering algorithms: a review. Proc Comput Sci 79:100–111

    Google Scholar 

  • Groll L, Jakel J (2005) A new convergence proof of fuzzy C-means. IEEE Trans Fuzzy Syst 13(3):717–720

    Google Scholar 

  • Hathaway RJ, Bezdek JC (2001) Fuzzy C-means clustering of incomplete data. IEEE Trans Syst Man Cybern Part B (Cybern) 31(5):735–744

    Google Scholar 

  • Havens T, Bezdek J, Leckie C, Hall L, Palaniswami M (2012) Fuzzy c-means algorithms for very large data. IEEE Trans Fuzzy Syst 20(6):1130–1146

    Google Scholar 

  • Kalist V, Ganesan P, Sathish BS, Jenitha JMM, Shaik KB (2015) Possibilistic-fuzzy C-means clustering approach for the segmentation of satellite images in HSL color space. Proc Comput Sci 57:49–56

    Google Scholar 

  • Kaur P, Gosain A (2010) Density-oriented approach to identify outliers and get noiseless clusters in fuzzy C-means. IEEE Int Conf Fuzzy Syst. https://doi.org/10.1109/FUZZY.2010.5584592

    Article  Google Scholar 

  • Koutroumbas KD, Xenaki SD, Rontogiannis AA (2018) On the convergence of the sparse possibilistic c-means algorithm. IEEE Trans Fuzzy Syst 26(1):324–337

    Google Scholar 

  • Krishnapuram R, Keller J (1993) A possibilistic approach to clustering. IEEE Trans Fuzzy Syst 1(2):98–110

    Google Scholar 

  • Krishnapuram R, Keller J (1996) The possibilistic c-means algorithm: insights and recommendations. IEEE Trans Fuzzy Syst 4(3):385–393

    Google Scholar 

  • Krisnapuram R, Frigui H, Nasroui O (1995a) Fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation-Part I. IEEE Trans Fuzzy Syst 3(1):29–43

    Google Scholar 

  • Krisnapuram R, Frigui H, Nasroui O (1995b) Fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation-Part II. IEEE Trans Fuzzy Syst 3(1):44–60

    Google Scholar 

  • Lei T, Jia X, Zhang Y, He L, Meng H, Nandi AK (2018) Significantly fast and robust fuzzy c-means clustering algorithm based on morphological reconstruction and membership filtering. IEEE Trans Fuzzy Syst 26(5):3027–3041

    Google Scholar 

  • Li ST, Cheng YC (2010) A stochastic HMM-based forecasting model for fuzzy time series. IEEE Trans Syst Man Cybern Part B (Cybern) 40(5):1255–1266

    Google Scholar 

  • Lingras P, Haider F, Triff M (2016) Granular meta-clustering based on hierarchical, network, and temporal connections. Granul Comput 1:71–92

    Google Scholar 

  • Liu H, Cocea M (2017) Granular computing-based approach for classification towards reduction of bias in ensemble learning. Granul Comput 2:131–139

    Google Scholar 

  • Liu H, Cocea M (2019) Nature-inspired framework of ensemble learning for collaborative classification in granular computing context. Granul Comput 4:715–724

    Google Scholar 

  • Liu H, Zhang L (2018) Fuzzy rule-based systems for recognition-intensive classification in granular computing context. Granul Comput 3:355–365

    Google Scholar 

  • Liu Z, Xu S, Zhang Y, Chen CLP (2014) A multiple-feature and multiple-kernel scene segmentation algorithm for humanoid robot. IEEE Trans Cybern 44(11):2232–2240

    Google Scholar 

  • Livi L, Sadeghian A (2016) Granular computing, computational intelligence, and the analysis of non-geometric input spaces. Granul Comput 1:13–20

    Google Scholar 

  • Loia V, D’Aniello G, Gaeta A, Orciuoli F (2016) Enforcing situation awareness with granular computing: a systematic overview and new perspectives. Granul Comput 1:127–143

    Google Scholar 

  • Maji P, Pal SK (2007) Rough set based generalized fuzzy c-means algorithm and quantitative indices. IEEE Trans Syst Man Cybern Part B (Cybern) 37(6):1529–1540

    Google Scholar 

  • Makrogiannis S, Economou G, Fotopoulos S, Bourbakis NG (2005) Segmentation of color images using multiscale clustering and graph theoretic region synthesis. IEEE Trans Syst Man Cybern Part A: Syst Hum 35(2):224–238

    Google Scholar 

  • Martino FD, Sessa S (2020) Extended Gustafson-Kessel granular hotspot detection. Granul Comput 5:85–95

    Google Scholar 

  • Ozdemir D, Akarun L (2011) Fuzzy algorithms for combined quantization and dithering. IEEE Trans Image Process 10(6):923–931

    MATH  Google Scholar 

  • Pal NR, Pal K, Keller JM, Bezdek JC (2005) A possibilistic fuzzy C-means clustering algorithm. IEEE Trans Fuzzy Syst 13(4):517–530

    Google Scholar 

  • Peters G, Weber R (2016) DCC: a framework for dynamic granular clustering. Granul Comput 1:1–11

    Google Scholar 

  • Song Y, Zhang G, Lu H, Lu J (2019) A noise-tolerant fuzzy c-means based drift adaptation method for data stream regression. IEEE Int Conf Fuzzy Syst. https://doi.org/10.1109/FUZZ-IEEE.2019.8859005

    Article  Google Scholar 

  • Srinivasan T, Palanisamy B (2015) Scalable clustering of high-dimensional data technique using SPCM with ant colony optimization intelligence. Sci World J 2015:1–5

    Google Scholar 

  • Tolias YA, Panas SM (1998) Image segmentation by a fuzzy clustering algorithm using adaptive spatially constrained membership functions. IEEE Trans Syst Man Cybern Part A: Syst Hum 28(3):359–369

    Google Scholar 

  • Tung WL, Quek C (2004) Falcon: neural fuzzy control and decision systems using FKP and PFKP clustering algorithms. IEEE Trans Syst Man Cybern Part B (Cybern) 34(1):686–695

    Google Scholar 

  • Wang G, Yang J, Xu J (2017) Granular computing: from granularity optimization to multi-granularity joint problem solving. Granul Comput 2:105–120

    Google Scholar 

  • Wang Q, Wang X, Fang C, Yang W (2020) Robust fuzzy c-means clustering algorithm with adaptive spatial & intensity constraint and membership linking for noise image segmentation. Appl Soft Comput 92:106318

    Google Scholar 

  • Wong WK, Bai E, Chu AWC (2010) Adaptive time-variant models for fuzzy-time-series forecasting. IEEE Trans Syst Man Cybern Part B (Cybern) 40(6):1531–1542

    Google Scholar 

  • Wu F, Yan S, Smith JS, Zhang B (2019) Deep multiple classifier fusion for traffic scene recognition. Granul Comput. https://doi.org/10.1007/s41066-019-00182-6

    Article  Google Scholar 

  • Xie Z, Wang S, Zhang DY, Chung FL, Hanbin (2007) Image segmentation using the enhanced possibilistic clustering method. Inf Technol J 6(4):541–546

    Google Scholar 

  • Zeng S, Chen SM, Teng MO (2019) Fuzzy forecasting based on linear combinations of independent variables, subtractive clustering algorithm and artificial bee colony algorithm. Inf Sci 484:350–366

    Google Scholar 

  • Zhang Q, Chen Z (2014) A distributed weighted possibilistic C-means algorithm for clustering incomplete big sensor data. Int J Distrib Sens Netw 2014:1–14

    Google Scholar 

  • Zhang JS, Leung YW (2004) Improved possibilistic C-means clustering algorithms. IEEE Trans Fuzzy Syst 12(2):209–217

    Google Scholar 

  • Zhang M, Hall LO, Goldgof DB (2002) A generic knowledge-guided image segmentation and labeling system using fuzzy clustering algorithms. IEEE Trans Syst Man Cybern Part B (Cybern) 32(5):571–582

    Google Scholar 

  • Zhang Y, Huang D, Ji M, Xie F (2011) Image segmentation using PSO and PCM with Mahalanobis distance. Expert Syst Appl 38(7):9036–9040

    Google Scholar 

  • Zhang Q, Yang LT, Chen Z, Xia F (2017a) A high-order possibilistic c-means algorithm for clustering incomplete multimedia data. IEEE Syst J 11(4):2160–2169

    Google Scholar 

  • Zhang Q, Yang LT, Chen Z, Li P (2017b) PPHOPCM: privacy preserving high-order possibilistic C-means algorithm for big data clustering with cloud computing. IEEE Trans Big Data. https://doi.org/10.1109/TBDATA.2017.2701816

    Article  Google Scholar 

  • Zhang C, Gao R, Qin H, Feng X (2019a) Three-way clustering method for incomplete information system based on set-pair analysis. Granul Comput. https://doi.org/10.1007/s41066-019-00197-z

    Article  Google Scholar 

  • Zhang Q, Yang LT, Castiglione A, Peng ZC (2019b) Secure weighted possibilistic C-means algorithm on cloud for clustering big data. Inf Sci 479:515–525

    Google Scholar 

  • Zhu L, Chung FL, Wang S (2009) Generalized fuzzy c-means clustering algorithm with improved fuzzy partitions. IEEE Trans Syst Man Cybern Part B (Cybern) 39(3):578–591

    Google Scholar 

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  1. Mechanical Engineering Department, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran, 1591634311, Iran

    S. Askari

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Askari, S. Noise-resistant fuzzy clustering algorithm. Granul. Comput. 6, 815–828 (2021). https://doi.org/10.1007/s41066-020-00230-6

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