Adaptación del método de agrupación k-medias para datos funcionales correlacionados espacialmente con aplicación a datos del índice de vegetación de diferencia normalizada de los páramos del Ecuador.

Abstract

Spatial dependence in environmental data is an influential criterion in clustering processes, as the results obtained provide relevant information. As classical methods do not take into account spatial dependence, the consideration of this structure produces unexpected results and clustering of curves that may not be similar in shape or behavior. In this work, clustering is performed using the modified k-means method for spatially correlated functional data applied to Normalized Difference Vegetation Index (NDVI) data from the moorlands of Ecuador. For this purpose, quality indices are implemented to obtain the appropriate number of groups. The methodology is based on a weighting of the distance matrix between the curves with the trace-variogram calculated with the coefficients of the base functions resulting from the smoothing of the data. For the validation of the method, some simulation scenarios are carried out, as well as a case of application to NDVI data; obtaining five latitudinally distributed regions.