Noise fuzzy clustering of time series by autoregressive metric

Abstract

We propose a robust fuzzy clustering model for classifying time series, considering the autoregressive metric based. In particular, we suggest a clustering procedure which:\ud 1) considers an autoregressive parameterization of the time series, capable of representing a large class of time series; 2) inherits the benefits of the partitioning around medoids approach,\ud classifying time series in classes characterized by prototypal observed time series (the “medoid” time series), which synthesize the structural information of each cluster; 3) inherits the benefits of the fuzzy approach, capturing the vague (fuzzy) behaviour of particular time series, such as “middle” time series (time series with middle features in respect of the considered clusters in all time period) and “switching” time series (time series with a pattern\ud typical of a given cluster during a certain time period and a completely different pattern, similar to another cluster, in another time period); 4) is capable of suitably neutralizing the negative influence of the presence of “outlier” time series in the clustering procedure, i.e., the “outlier” time series are classified in the so-called “noise cluster” and therefore cluster structure is not altered. To illustrate the effectiveness of the proposed model, a simulation study and an application to real time series are carried out

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

“…[25,26]); 2) feature-based clustering: in this case, the methods are based on features derived for the time series (see, e.g., [27][28][29][30][31]); 3) model-based clustering: these methods are based on parameters estimates of model fitted to the time series (e.g. ARMA or ARIMA models) (see, e.g., [2,3]). In this paper, we adopt the model-based approach.…”

“…For comparison purposes, we have considered the non-robust AR-FCMdC model [3] and the robust ARbased Fuzzy C-Medoids Clustering with Noise Cluster model (AR-FCMdC-NC) [2]. We have also drawn a comparison between the fuzzy approach and the crisp approach, by considering the crisp versions of AR-FCMdC and AR-FCMdC-NC, i.e.…”

“…The higher this value, the better the classification performance of the model considered. We have chosen this strategy to be consistent with that used by D'Urso et al [2,3]. To assign each time series to a specific cluster we have set cut-off values.…”

“…Notice that the fuzzy approach also allow us to identify peculiar patterns of time series, like switching time series, i.e. time series showing a pattern typical of a given cluster during a certain time period, and a completely different pattern (representative of another cluster) in another time period [2,3]. For detailed discussions on the benefits connected to autoregressive model-based clustering approach, fuzzy methodology, partitioning around medoids procedure see D'Urso et al [2,3].…”

“…time series showing a pattern typical of a given cluster during a certain time period, and a completely different pattern (representative of another cluster) in another time period [2,3]. For detailed discussions on the benefits connected to autoregressive model-based clustering approach, fuzzy methodology, partitioning around medoids procedure see D'Urso et al [2,3]. We observe that the fuzzy approach has been employed for clustering/classification of sequences in other research areas, for instance in computational biology [4][5][6][7][8][9][10][11][12][13][14][15].…”