Time series clustering by a robust autoregressive metric with application to air pollution

Abstract

In this paper, following a fuzzy approach and adopting an autoregressive parameterization, we propose a robust clustering model for classifying time series. In particular, by adopting a fuzzy\ud partitioning around medoids approach, the suggested clustering model is able to define the so-called medoid time series, which is a representative time series of each cluster, and the membership degrees of each time series to the different clusters. The robustness of the proposed clustering model is guaranteed by the adoption of a suitable robust metric for time series, i.e. the so-called exponential distance measure. In this way, the clustering model is able to tolerate the presence of outlier time series in the clustering process. In particular, it is capable of neutralizing and smoothing the disruptive effect of outlier time series, preserving the original clustering structure of the dataset, by assigning to outlier time series approximately the same membership degrees across clusters. To illustrate the usefulness and effectiveness of the suggested time series clustering model, a simulation study and an application to air pollution time series are carried out. Comparison with some existing clustering procedures suggested in the literature shows several advantages of the proposed model

GARCH-based robust clustering of time series

“…Time series are clustered by means of parameter estimates or by means of the residuals of the fitted models [19]. In this class, several time series clustering methods are based on the ARIMA representation of the time series (see, e.g., [16,17,[28][29][30][31][32][33][34]). Notice that most of these methods are devoted to capturing the structure of the mean of the process hypothesized as generator of the data, whereas little attention has been put on the variance.…”

Piecewise aggregate representations and lower-bound distance functions for multivariate time series

“…In this experiment, let the two functions perform on ASL dataset in which the lengths of MTS are different. The two parameters w and α used in the two functions are set to be w = [2,3,4,5,6,7,8] and α = [3,4,5,6,7,8,9,10]. Their tightness can be seen in Figs.…”

“…The tasks of time series data mining often combine some valid processes to improve the results [1,5,11]. Two kinds of the processes are the dimensionality reduction and distance function.…”

“…In views of the two kinds of dimensions, it is important to simultaneously reduce their dimensionality of MTS. In addition, some distance functions [3][4][5][6] are also designed to improve the quality of time series data mining. Some techniques of dimensionality reduction often combine with their corresponding distance functions [7][8][9] or correlations [10] for measuring the similarity between two different representations.…”

Fuzzy clustering with spatial–temporal information

“…Observed time series, or suitable transformations, are instead the segmentation data used in the observation-based approach (see, e.g., D'Urso, 2005a;Coppi et al, 2010, and references therein). In the last decade, different fuzzy clustering algorithms have been proposed for both univariate and multivariate time series (see, e.g., Coppi & D'Urso, 2002D'Urso, 2005b;D'Urso et al, 2015D'Urso et al, , 2016Vilar et al, 2017).…”