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Discovering Spatially Contiguous Clusters in Multivariate Geostatistical Data Through Spectral Clustering

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Advanced Data Mining and Applications (ADMA 2016)

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Abstract

Spectral clustering has recently become one of the most popular modern clustering algorithms for traditional data. However, the application of this clustering method on geostatistical data produces spatially scattered clusters, which is undesirable for many geoscience applications. In this work, we develop a spectral clustering method aimed to discover spatially contiguous and meaningful clusters in multivariate geostatistical data, in which spatial dependence plays an important role. The proposed spectral clustering method relies on a similarity measure built from a non-parametric kernel estimator of the multivariate spatial dependence structure of the data, emphasizing the spatial correlation among data locations. The capability of the proposed spectral clustering method to provide spatially contiguous and meaningful clusters is illustrated using the European Geological Surveys Geochemical database.

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References

  1. Allard, D.: Geostatistical classification and class kriging. J. Geog. Inf. Decis. Anal. 2, 87–101 (1998)

    Google Scholar 

  2. Allard, D., Guillot, G.: Clustering geostatistical data. In: Proceedings of the Sixth Geostatistical Conference (2000)

    Google Scholar 

  3. Allard, D., Monestiez, P.: Geostatistical segmentation of rainfall data. In: geoENV II: Geostatistics for Environmental Applications, pp. 139–150 (1999)

    Google Scholar 

  4. Ambroise, C., Dang, M., Govaert, G.: Clustering of spatial data by the EM algorithm. In: geoENV I: Geostatistics for Environmental Applications, pp. 493–504 (1995)

    Google Scholar 

  5. Bourgault, G., Marcotte, D., Legendre, P.: The multivariate (co)variogram as a spatial weighting function in classification methods. Math. Geol. 24(5), 463–478 (1992)

    Article  Google Scholar 

  6. Caliński, T., Harabasz, J.: A dendrite method for cluster analysis. Commun. Stat. 3(1), 1–27 (1974)

    MathSciNet  MATH  Google Scholar 

  7. Cao, Y., Chen, D.R.: Consistency of regularized spectral clustering. Appl. Comput. Harmonic Anal. 30(3), 319–336 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Charu, C., Chandan, K.: Data Clustering: Algorithms and Applications. Chapman and Hall/CRC, Boca Raton (2013)

    MATH  Google Scholar 

  9. Chilès, J.P., Delfiner, P.: Geostatistics: Modeling Spatial Uncertainty. Wiley, Hoboken (2012)

    Book  MATH  Google Scholar 

  10. Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via EM algorithm (with discussion). J. Roy. Stat. Soc. Ser. 39, 1–38 (1977)

    MathSciNet  MATH  Google Scholar 

  11. Filippone, M., Camastra, F., Masulli, F., Rovetta, S.: A survey of kernel and spectral methods for clustering. Pattern Recogn. 41(1), 176–190 (2008)

    Article  MATH  Google Scholar 

  12. Fouedjio, F.: A clustering approach for discovering intrinsic clusters in multivariate geostatistical data. In: Perner, P. (ed.) MLDM 2016. LNCS, vol. 9729, pp. 491–500. Springer, Switzerland (2016)

    Chapter  Google Scholar 

  13. Fouedjio, F.: A hierarchical clustering method for multivariate geostatistical data. Spatial Statistics (2016)

    Google Scholar 

  14. Guillot, G., Kan-King-Yu, D., Michelin, J., Huet, P.: Inference of a hidden spatial tessellation from multivariate data: application to the delineation of homogeneous regions in an agricultural field. J. Roy. Stat. Soc. Ser. C (Appl. Stat.) 55(3), 407–430 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Haas, T.C.: Lognormal and moving window methods of estimating acid deposition. J. Am. Stat. Assoc. 85(412), 950–963 (1990)

    Article  Google Scholar 

  16. Journel, A., Huijbregts, C.: Mining Geostatistics. Blackburn Press, New York (2003)

    Google Scholar 

  17. Kannan, R., Vempala, S., Vetta, A.: On clusterings: good, bad and spectral. J. ACM 51(3), 497–515 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lado, L., Hengl, T., Reuter, I.: Heavy metals in European soils: a geostatistical analysis of the FOREGS geochemical database. Geoderma 148(2), 189–199 (2008)

    Article  Google Scholar 

  19. Luxburg, U.V.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)

    Article  MathSciNet  Google Scholar 

  20. Luxburg, U.V., Belkin, M., Bousquet, O.: Consistency of spectral clustering. Ann. Stat. 36(2), 555–586 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  21. Luxburg, U.V., Bousquet, O., Belkin, M.: Limits of spectral clustering. In: Advances in Neural Information Processing Systems, pp. 857–864 (2004)

    Google Scholar 

  22. Nascimento, M.C., Carvalho, A.C.: Spectral methods for graph clustering – a survey. Eu. J. Oper. Res. 211(2), 221–231 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: Analysis and an algorithm. In: Advances in Neural Information Processing Systems, pp. 849–856. MIT Press (2001)

    Google Scholar 

  24. Olivier, M., Webster, R.: A geostatistical basis for spatial weighting in multivariate classification. Math. Geol. 21, 15–35 (1989)

    Article  Google Scholar 

  25. Pawitan, Y., Huang, J.: Constrained clustering of irregularly sampled spatial data. J. Stat. Comput. Simul. 73(12), 853–865 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  26. Romary, T., Ors, F., Rivoirard, J., Deraisme, J.: Unsupervised classification of multivariate geostatistical data: two algorithms. Comput. Geosci. 85, 96–103 (2015)

    Article  Google Scholar 

  27. Schaeffer, S.E.: Graph clustering. Comput. Sci. Rev. 1(1), 27–64 (2007)

    Article  MATH  Google Scholar 

  28. Theodoridis, S., Koutroumbas, K.: Pattern Recognition, 4th edn. Academic Press, New York (2009)

    MATH  Google Scholar 

  29. Tobler, W.R.: A computer movie simulating urban growth in the Detroit region. Econ. Geogr. 46, 234–240 (1970)

    Article  Google Scholar 

  30. Wand, M., Jones, C.: Kernel Smoothing. Monographs on Statistics and Applied Probability. Chapman & Hall, Sanford (1995)

    Book  Google Scholar 

  31. Zha, H., He, X., Ding, C., Gu, M., Simon, H.D.: Spectral relaxation for k-means clustering. In: Advances in Neural Information Processing Systems, pp. 1057–1064 (2001)

    Google Scholar 

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Correspondence to Francky Fouedjio .

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Fouedjio, F. (2016). Discovering Spatially Contiguous Clusters in Multivariate Geostatistical Data Through Spectral Clustering. In: Li, J., Li, X., Wang, S., Li, J., Sheng, Q. (eds) Advanced Data Mining and Applications. ADMA 2016. Lecture Notes in Computer Science(), vol 10086. Springer, Cham. https://doi.org/10.1007/978-3-319-49586-6_38

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  • DOI: https://doi.org/10.1007/978-3-319-49586-6_38

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