Descripción del método mean shift para análisis de datos espaciales

Abstract

The Alternative Energies and Environment Research Group (GEAA) belonging to Escuela Superior Politécnica de Chimborazo (ESPOCH) is currently working on the clustering of meteorological data in order to understand the weather patterns of the Andean region of Ecuador. In this context, within ESPOCH, there is no accessible and detailed documentation on a specific clustering method for this purpose. Therefore, the aim of this study was to carry out a theoretical-practical documentary research, in which the Mean Shift clustering method, its theoretical foundations and its implementation in spatial temperature data in the Sierra region of Ecuador are described. Thus, a qualitative and quantitative methodological design with descriptive scope was used. Consequently, a bibliographic document containing 3 chapters was obtained, the first chapter described tools of Functional Analysis and Probability Theory such as the Windows Parzen technique and the density function estimator, the second chapter established the estimation of the multivariate density function and the localization of maxima through the gradient of a density function, and the convergence criteria by means of theorems. Finally, in the third chapter, the Mean shift method was implemented to the minimum temperature variable of the CNRM Atmospheric Circulation model during the 2020-2050 period, using the Sklearn library in Python. The obtained clusters reflect a direct dependence with the bandwidth. It is recommended to carry on with the research on mathematical theory of the optimal bandwidth choice, since it is a being a field which is under active research.