Aplicaciones de modelos lineales de corregionalización : Clustering para datos funcionales espacialmente correlacionado.

Abstract

The classification of spatially correlated functional data involves a comprehensive approach tailored to the unique characteristics of this data type. This approach aims to facilitate the identification of spatially homogeneous groups within specific locations. The methodology employed initiates by smoothing the observed data utilizing Fourier bases. These bases offer valuable properties for data analysis. By leveraging these properties and utilizing the resultant coefficients obtained from the smoothing process, a dissimilarity matrix between the data curves is computed. This dissimilarity matrix is then integrated into the calculation of both the semivariogram and the multivariate variogram, depending on the circumstances of the analysis. These variograms serve as crucial tools for understanding spatial relationships and variabilities within the dataset. The analysis in focus centers around eight climatological stations located in Quito, namely San Antonio, Cotocollao, Carapungo, Belisario, Centro, Guamaní, Los Chillos, and Tumbaco. The variables of interest include average temperature and total precipitation, measured over the 24-hour period of each day throughout the year 2023. Additionally, real variables recorded at these climatological stations, as well as simulated variables generated through the METEO project, are taken into consideration. This comprehensive dataset forms the basis for the subsequent comparison and evaluation of three clustering methodologies. The primary objective of this comparative analysis is to determine which clustering methodology best suits the presented dataset. This evaluation not only addresses the classification of spatially correlated functional data but also serves to compare the efficacy of the proposed methodologies against traditional approaches. Ultimately, the aim is to design a spatial correlation model capable of effectively establishing groupings of the simulated variables, thereby enhancing our understanding of the underlying spatial patterns and relationships within the dataset. Through this rigorous methodology, researchers can gain deeper insights into the complex dynamics of spatially correlated functional data, thus contributing to advancements in the field of spatial data analysis and modeling.