Distâncias adaptativas e kernelizadas aplicadas a agrupamento de séries temporais tipo intervalo

Abstract

The task of clustering is part of everyday life and human nature. The literature that deals with clustering provides techniques, metrics and algorithms to accomplish this task. In particular, the clustering of observed data over time and in the form of intervals represents a challenge, with new methods being proposed for this purpose. The advantage of adaptive distances is that they assign different weights to the variables of clusters, and an algorithm that succeeds in adapting to this can bring results far superior to algorithms that treat all variables in the same way, with the same level of importance. Moreover, kernelization makes it possible to work with data in a new space, different from the original space, where the groups will present a better separation. The objective of this work is to consider new distances for the KMeans method in the clustering of interval time series. We will use adaptive distances and distances calculated through the kernelization of the metric and the feature space. To validate the proposed algorithms, we performed a study with time series generated from the parameters of Space-Time Autoregressive (STAR) models, using Monte Carlo simulations as well as real data. The comparison will take place through external and internal indices. The results obtained in the simulations demonstrate that the proposed algorithms performed better than the existing methods. The application to real data considered cryptocurrency series and traditional indices such as gold, oil, stock exchanges, among others. The results point to insights that can be used for future work in machine learning and economics.