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On mean shift-based clustering for circular data

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Abstract

Cluster analysis is a useful tool for data analysis. Clustering methods are used to partition a data set into clusters such that the data points in the same cluster are the most similar to each other and the data points in the different clusters are the most dissimilar. The mean shift was originally used as a kernel-type weighted mean procedure that had been proposed as a clustering algorithm. However, most mean shift-based clustering (MSBC) algorithms are used for numeric data. The circular data that are the directional data on the plane have been widely used in data analysis. In this paper, we propose a MSBC algorithm for circular data. Three types of mean shift implementation procedures with nonblurring, blurring and general methods are furthermore compared in which the blurring mean shift procedure is the best and recommended. The proposed MSBC for circular data is not necessary to give the number of cluster. It can automatically find a final cluster number with good clustering centers. Several numerical examples and comparisons with some existing clustering methods are used to demonstrate its effectiveness and superiority of the proposed method.

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References

  • Banerjee A, Dhillon IS, Ghosh J, Sra S (2005) Clustering on the unit hypersphere using von Mises-Fisher distributions. J Mach Learn Res 6:1345–1382

    MathSciNet  MATH  Google Scholar 

  • Bartels R (1984) Estimation in a bidirectional mixture of von Mises distributions. Biometrics 40:777–784

    Article  Google Scholar 

  • Carta C, Bueno JA, Ramirez P (2008) Statistical modeling of directional wind speeds using mixtures of von Mises distributions. Energy Conserv Manage 49:897–907

    Article  Google Scholar 

  • Chang-Chien SJ, Yang MS, Hung WL (2010) Mean shift-based clustering for directional data. In: Proceedings of third international workshop on advanced computational intelligence, pp 367–372

  • Cheng Y (1995) Mean shift, mode seeking, and clustering. IEEE Trans Pattern Anal Mach Intell 17:790–799

    Article  Google Scholar 

  • Comaniciu D, Meer P (2002) Mean shift: a robust approach toward feature space analysis. IEEE Trans Pattern Anal Mach Intell 24:603–619

    Article  Google Scholar 

  • Corcoran J, Chhetri P, Stimson R (2009) Using circular statistics to explore the geography of the journey to work. Papers Reg Sci 88:119–132

    Article  Google Scholar 

  • Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines. Cambridge University Press, Cambridge

    Google Scholar 

  • Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm (with discussion). J Roy Stat Soc Ser B 39:1–38

    MathSciNet  MATH  Google Scholar 

  • Dortet-Bernadet JL, Wicker N (2008) Model-based clustering on the unit sphere with an illustration using gene expression profiles. Biostatistics 9(1):66–80

    Article  MATH  Google Scholar 

  • Fashing M, Tomasi C (2005) Mean shift is a bound optimization. IEEE Trans Pattern Anal Mach Intell 27:471–474

    Article  Google Scholar 

  • Filippone M, Camastra F, Masulli F, Rovetta S (2008) A survey of kernel and spectral methods for clustering. Pattern Recogn 41:176–190

    Article  MATH  Google Scholar 

  • Fisher NI (1993) Statistical analysis of circular data. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Fukunaga K, Hostetler LD (1975) The estimation of the gradient of a density function with applications in pattern recognition. IEEE Trans Inf Theory 21:32–40

    Article  MathSciNet  MATH  Google Scholar 

  • Gao KS, Chia F, Krantz I, Nordin P, Machin D (2006) On the application of the von Mises distribution and angular regression methods to investigate the seasonality of disease onset. Stat Med 25:1593–1618

    Article  MathSciNet  Google Scholar 

  • Kobayashi T, Otsu N (2010) Von Mises-Fisher mean shift for clustering on a hypersphere. In: Proceedings of the 20th international conference on pattern recognition, ICPR 2010, pp 2130–2133

  • Lee A (2010) Circular data, WIREs. Comput Stat 2:477–486

    Google Scholar 

  • Mardia KV (1972) Statistics of directional data. Academic Press, London

    MATH  Google Scholar 

  • Mardia KV, Jupp PE (2000) Directional statistics. Wiley, New York

    MATH  Google Scholar 

  • Mardia KV, Sutton TW (1975) On the modes of a mixture of two von Mises distributions. Biometrika 62:699–701

    Article  MathSciNet  MATH  Google Scholar 

  • McGraw T, Vemuri BC, Yezierski B, Mareci T (2006) Von Mises-fisher mixture model of the diffusion ODF. In: Proceedings of the 3rd IEEE international symposium on biomedical imaging: from Nano to Macro, pp 65–68

  • McLachlan GJ, Basford KE (1988) Mixture models: inference and applications to clustering. Marcel Dekker, NY

    MATH  Google Scholar 

  • Mooney JA, Helms PJ, Jolliffe IT (2003) Fitting mixtures of von Mises distributions: a case study involving sudden infant death syndrome. Comput Stat Data Anal 41:505–513

    Article  MathSciNet  Google Scholar 

  • Schölkopf B, Smola A, Müller K (1998) Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput 10:1299–1319

    Article  Google Scholar 

  • Silverman BW (1998) Density estimation for statistics and data analysis. Chapman and Hall, New York

    Google Scholar 

  • Spurr BD, Koutbeiy MA (1991) A comparison of various methods for estimating the parameters in mixtures of von Mises distributions. Commun Stat Simul Comput 20:725–741

    Article  MathSciNet  MATH  Google Scholar 

  • Stephens MA (1969) Techniques for directional data. Tech. Report #150, Department of Statistics, Stanford University, Stanford

  • Thang ND, Chen L, Chan CK (2008) Feature reduction using mixture model of directional distributions. In: Proceedings of the 10th international conference on control, automation, robotics and vision, ICARCV, pp 2208–2212

  • Vapnik VN (1998) Statistical learning theory. Wiley, New York

    MATH  Google Scholar 

  • Von Mises R (1918) Uber die die “Ganzzahligkeit” der Atomgewicht und verwandte Fragen. Physikal Z 19:490–500

    Google Scholar 

  • Watson GS, Williams EJ (1956) On the construction of significance tests on the circle and the sphere. Biometrika 43:344–352

    MathSciNet  MATH  Google Scholar 

  • Wu KL, Yang MS (2007) Mean shift-based clustering. Pattern Recogn 40:3035–3052

    Article  MATH  Google Scholar 

  • Yang MS, Pan JA (1997) On fuzzy clustering of directional data. Fuzzy Sets Syst 91:319–326

    Article  MATH  Google Scholar 

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Acknowledgments

The authors would like to thank the anonymous referees for their helpful comments in improving the presentation of this paper. This work was supported in part by the National Science Council of Taiwan, under Grant NSC-99-2118-M-033-004-MY2.

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Authors and Affiliations

  1. Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, 32023, Taiwan

    Shou-Jen Chang-Chien & Miin-Shen Yang

  2. Department of Applied Mathematics, National Hsinchu University of Education, Hsin-Chu, Taiwan

    Wen-Liang Hung

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  1. Shou-Jen Chang-Chien
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  2. Wen-Liang Hung
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  3. Miin-Shen Yang
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Correspondence to Miin-Shen Yang.

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Chang-Chien, SJ., Hung, WL. & Yang, MS. On mean shift-based clustering for circular data. Soft Comput 16, 1043–1060 (2012). https://doi.org/10.1007/s00500-012-0802-z

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