Analýza časových řad pomocí vybraných shlukovacích metod

This bachelor project focuses on time series clustering methods with an emphasis on their application in climatology. The main objective is a methodological comparison of the classical k-means algorithm using Euclidean distance and a more advanced non-linear approach based on the Dynamic Time Warping metric combined with Dynamic Time Warping Barycenter Averaging. The research is divided into two phases. In the first phase, the algorithms are tested on controlled simulated data (including phase shifts, frequency changes, and the benchmark Cylinder-Bell-Funnel model), evaluating their accuracy using the Adjusted Rand Index. In the second phase, the tested models are applied to real global surface temperature measurements from the Berkeley Earth database. The thesis analyzes in detail the impact of data standardization and focuses on the geographical regionalization of climate as well as the detection of stochastic temperature extremes, specifically heat waves. The achieved results demonstrate that while Euclidean distance fails in the analysis of asynchronous deformations, the Dynamic Time Warping metric represents a highly robust tool for clustering shape-specific events independent of their phase shift.