Orhan KESEMEN
(Karadeniz Teknik Üniversitesi)
Özge TEZEL
(Karadeniz Teknik Üniversitesi)
Eda ÖZKUL
(Karadeniz Teknik Üniversitesi)
Buğra Kaan TİRYAKİ
(Karadeniz Teknik Üniversitesi)
Yıl: 2020Cilt: 28Sayı: 1ISSN: 1300-0632 / 1300-0632Sayfa Aralığı: 140 - 152İngilizce

68 0
Fuzzy c-Means Directional Clustering (FCMDC) algorithm using trigonometric approximation
Cluster analysis is widely used in data analysis. Statistical data analysis is generally performed on thelinear data. If the data has directional structure, classical statistical methods cannot be applied directly to it. Thisstudy aims to improve a new directional clustering algorithm which is based on trigonometric approximation. Thetrigonometric approximation is used for both descriptive statistics and clustering of directional data. In this paper, thefuzzy clustering algorithms (FCD and FCM4DD) improved for directional data and the proposed method are carried outon some numerical and real data examples, and the simulation results are presented. Consequently, these results indicatethat the fuzzy c-means directional clustering algorithm gives the better results from the points of the mean square errorand the standard deviation for cluster centers.
Fen > Mühendislik > Bilgisayar Bilimleri, Yapay Zeka
Fen > Mühendislik > Bilgisayar Bilimleri, Sibernitik
Fen > Mühendislik > Bilgisayar Bilimleri, Donanım ve Mimari
Fen > Mühendislik > Bilgisayar Bilimleri, Bilgi Sistemleri
Fen > Mühendislik > Bilgisayar Bilimleri, Yazılım Mühendisliği
Fen > Mühendislik > Bilgisayar Bilimleri, Teori ve Metotlar
Fen > Mühendislik > Mühendislik, Elektrik ve Elektronik
DergiAraştırma MakalesiErişime Açık
  • [1] Mooney JA, Helms PJ, Jolliffe IT. Fitting mixtures of von Mises distributions: a case study involving sudden infant death syndrome. Computational Statistics & Data Analysis 2003; 41: 505-513.
  • [2] Carta JA, Bueno C, Ramirez P. Statistical modelling of directional wind speeds using mixtures of von Mises distributions: case study. Energy Conversion and Management 2008; 49 (5): 897-907. doi: 10.1016/j.enconman.2007.10.017
  • [3] Lee A. Circular data. Wiley Interdisciplinary Reviews: Computational Statistics 2010; 2 (4): 477-486. doi: 10.1002/wics.98
  • [4] Abraham C, Molinari N, Servien R. Unsupervised clustering of multivariate circular data. Statistics in Medicine 2013; 32 (8): 1376-1382. doi: 10.1002/sim.5589
  • [5] Chen L, Singh VP, Guo S, Fang B, Liu P. A new method for identification of flood seasons using directional statistics. Hydrological Sciences Journal 2013; 58 (1): 28-40. doi: 10.1080/02626667.2012.743661
  • [6] Tasdan F, Cetin M. A simulation study on the influence of ties on uniform scores test for circular data. Journal of Applied Statistics 2014; 41 (5): 1137-1146. doi: 10.1080/02664763.2013.862224
  • [7] Abuzaid AH. Analysis of mother’s day celebration via circular statistics. The Philippine Statistician 2012; 61 (2): 39-52.
  • [8] Yang MS, Pan JA. On fuzzy clustering of directional data. Fuzzy Set and Systems 1997; 91 (3): 319-326. doi: 10.1016/S0165-0114(96)00157-1
  • [9] von Mises R. Uber die die ”Ganzzahligkeit” der atomgewicht und verwandte fragen. Physikal 1918; 19: 490-500 (in German).
  • [10] Kesemen O, Tezel Ö, Özkul E. Fuzzy c-means clustering algorithm for directional data (FCM4DD). Expert Systems with Applications 2016; 58: 76-82. doi: 10.1016/j.eswa.2016.03.034
  • [11] Hamilton LJ. Characterising spectral sea wave conditions with statistical clustering of actual spectra. Applied Ocean Research 2010; 32 (3): 332-342. doi: 10.1016/j.apor.2009.12.003
  • [12] Pewsey A, Neuhäuser M, Ruxton GD. Circular statistics in R. New York, NY, USA: Oxford University Press, 2013.
  • [13] Bellasio R. Analysis of wind data for airport runway design. Journal of Airline and Airport Management 2014; 4 (2): 97-116. doi: 10.3926/jairm.26
  • [14] Maruotti A. Analyzing longitudinal circular data by projected normal models: a semi-parametric approach based on finite mixture models. Environmental and Ecological Statistics 2016; 23 (2): 257-277. doi: 10.1007/s10651-015- 0338-3
  • [15] Patterson TA, Parton A, Langrock R, Blackwell PG, Thomas L et al. Statistical modelling of individual animal movement: an overview of key methods and a discussion of practical challenges. AStA Advances in Statistical Analysis 2017; 101 (4): 399-438. doi: 10.1007/s10182-017-0302-7
  • [16] Roy A, Pal A, Garain U. JCLMM: A finite mixture model for clustering of circular-linear data and its application to psoriatic plaque segmentation. Pattern Recognition 2017; 66 (4): 160-173. doi: 10.1016/j.patcog.2016.12.016
  • [17] Mastrantonio G, Pollice A, Fedele F. Distributions-oriented wind forecast verification by a hidden Markov model for multivariate circular-linear data. Stochastic Environmental Research and Risk Assessment 2018; 32 (1): 169-181. doi: 10.1007/s00477-017-1416-x
  • [18] Luengo-Sanchez S, Larrañaga P, Bielza C. A directional-linear bayesian network and its application for clustering and simulation of neural somas. IEEE Access 2019; 7 (1): 69907-69921. doi: 10.1109/ACCESS.2019.2918494
  • [19] Euán C, Sun Y. Directional spectra-based clustering for visualizing patterns of ocean waves and winds. Journal of Computational and Graphical Statistics 2019; 1-15. doi: 10.1080/10618600.2019.1575745
  • [20] Mastrantonio G, Lasinio GJ, Maruotti A, Calise G. Invariance properties and statistical inference for circular data. Statistica Sinica 2019; 29 (1): 67-80.
  • [21] Chang-Chien SJ, Hung WL, Yang MS. On mean shift-based clustering for circular data. Soft Computing 2012; 16 (6): 1043-1060. doi: 10.1007/s00500-012-0802-z
  • [22] Batschelet E. Circular Statistics in Biology. New York, NY, USA: Academic Press, 1981.
  • [23] Fisher NI. Statistical Analysis of Circular Data. New York, NY, USA: Cambridge University Press, 1993.
  • [24] Mardia KV, Jupp PE. Directional Statistics. New York, NY, USA: Wiley, 2000.
  • [25] Ackermann H. A note on circular nonparametrical classification. Biometrical Journal 1997; 39 (5): 577-587. doi: 10.1002/bimj.4710390506
  • [26] Lund U. Cluster analysis for directional data. Communications in Statistics-Simulation and Computation 1999; 28 (4): 1001-1009. doi: 10.1080/03610919908813589
  • [27] Höppner F, Klawonn F, Kruse R, Runkler T. Fuzzy Cluster Analysis. Chichester, UK: Wiley, 2000.
  • [28] Bezdek JC. Pattern Recognition with Fuzzy Objective Function Algorithms. New York, NY, USA: Plenum Press, 1981.
  • [29] Pal NR, Bezdek JC. On cluster validity for the fuzzy c-means model. IEEE Transactions on Fuzzy systems 1995; 3 (3): 370-379. doi: 10.1109/91.413225
  • [30] Stephens MA. Techniques for Directional Data. Stanford, CA, USA: Stanford University, 1969.
  • [31] Best DJ, Fisher NI. Efficient simulation of the von mises distribution. Journal of the Royal Statistical Society. Series C(Applied Statistics) 1979; 28 (2): 152-157. doi: 10.2307/2346732
  • [32] Kesemen O, Tezel Ö, Özkul E, Tiryaki BK, Ağayev E. A comparison of validity indices on fuzzy c-means clustering algorithm for directional data. In: IEEE 2017 25th Signal Processing and Communications Applications Conference (SIU); Antalya, Turkey; 2017. pp. 1-4. doi: 10.1109/SIU.2017.7960557

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