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: 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, 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 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.