Abstract
This paper introduces a method for clustering spatially dependent functional data. The idea is to consider the contribution of each curve to the spatial variability. Thus, we define a spatial dispersion function associated to each curve and perform a k-means like clustering algorithm. The algorithm is based on the optimization of a fitting criterion between the spatial dispersion functions associated to each curve and the representative of the clusters. The performance of the proposed method is illustrated by an application on real data and a simulation study.
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Caballero, W., Giraldo, R., Mateu, J.: A universal kriging approach for spatial functional data. Stoch. Environ. Res. Risk Assess. 27(7), 1553–1563 (2013)
Calinski, T., Harabasz, J.: A dendrite method for cluster analysis. Commun. Stat. 3(1), 2279–2280 (1974)
Celeux G., Diday E., Govaert G., Lechevallier Y., Ralambondrainy H.: Classification automatique des donnees: environnement statistique et informatique. Dunod (1989)
de Boor, C.: A Practical Guide to Splines. Springer, New York (1978)
Davies, D.L., Bouldin, D.W.: A cluster separation measure. IEEE Trans. Pattern Anal. Mach. Intell. PAMI–1(2), 224–227 (1979)
Delicado, P., Giraldo, R., Comas, C., Mateu, J.: Statistics for spatial functional data: some recent contributions. Environmetric 21, 224–239 (2010)
Diday, E.: La methode des Nuees dynamiques. Revue de Stat. Appl. 19(2), 19–34 (1971)
Ferraty, F., Vieu, P.: NonParametric Functional Data Analysis Theory and Practice. Springer Series in Statistics. Springer, New York (2006)
Giraldo, R., Delicado, P., Comas, C., Mateu, J.: Hierarchical clustering of spatially correlated functional data. Stat. Neerl. 66, 403–421 (2011)
Giraldo, R., Delicado, P., Mateu, J.: Ordinary kriging for function-valued spatial data. Environ. Ecol. Stat. 18, 411–426 (2011)
Giraldo, R., Delicado, P., Mateu, J.: Continuous time-varying kriging for spatial prediction of functional data: an environmental application. J. Agric. Biol. Environ. Stat. 15(1), 66–82 (2010)
Haggarty, R., Miller, C., Scott, E.M.: Spatially weighted functional clustering of river network data. J. R. Stat. Soc. Ser. C 64, 491–506 (2015)
Hennig, C., Lin, C.-J.: Flexible parametric bootstrap for testing homogeneity against clustering and assessing the number of clusters. Stat. Comput. 25, 821–833 (2015)
Journel, A.G., Huijbregts, ChJ: Mining Geostatistics. The Blackburn Press, New York (2004)
Jiang, H., Serban, N.: Clustering random curves under spatial interdependence: classification of service accessibility. Technometrics 54, 108–119 (2010)
Ramsay, J.E., Silverman, B.W.: Functional Data Analysis, 2nd edn. Springer, New York (2005)
Rand, W.M.: Objective criteria for the evaluation of clustering methods. J. Am. Stat. Assoc. 66(336), 846–850 (1971)
Romano E., Balzanella A., Verde R.: Clustering Spatio-functional data: a model-based approach. Studies in Classification, Data Analysis, and Knowledge Organization Springer, Berlin-Heidelberg, New York (2010a)
Romano, E., Balzanella, A., Verde, R.: A new regionalization method for spatially dependent functional data based on local variogram models: an application on environmental data. In: Atti delle XLV Riunione Scientifica della Societá Italiana di Statistica Universitá degli Studi di Padova Padova. CLEUP, Padova (2010)
Romano, E., Mateu, J., Giraldo, R.: On the performance of two clustering methods for spatial functional data. AStA Adv. Stat. Anal. 99(4), 467–492 (2015)
Romano E., Verde R.: Clustering geostatistical functional data. Advanced Statistical Methods for the analysis of large data-sets, series Studies in Theoretical and Applied Statistics, A. Di Ciaccio, M. Coli, J.M. Angulo (eds.), Springer, Berlin (2011)
Rouseeuw, P.J.: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20(1), 53–65 (1987)
Sun, Y., Genton, M.G.: Adjusted functional boxplots for spatio-temporal data visualization and outlier detection. Environmetrics 23, 54–64 (2012)
Sun, Y., Li, B., Genton, M. G.: Geostatistics for large datasets. In: Space-Time Processes and Challenges Related to Environmental Problems, E. Porcu, J. M. Montero, M. Schlather (eds), Springer, Vol. 207, Chapter 3, pp. 55–77 (2012)
Secchi, P., Vantini, S., Vitelli, V.: Bagging Voronoi classifiers for clustering spatial functional data. Int. Giornal Appl. Earth Observ. Geoinf. 22, 53–64 (2012)
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Romano, E., Balzanella, A. & Verde, R. Spatial variability clustering for spatially dependent functional data. Stat Comput 27, 645–658 (2017). https://doi.org/10.1007/s11222-016-9645-2
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DOI: https://doi.org/10.1007/s11222-016-9645-2