Ricerc@Sapienza

Robustness to the presence of outliers in time series clustering is addressed. Assuming that the clustering principle is to group realizations of series generated from similar dependence structures, three robust versions of a fuzzy C-medoids model based on comparing sample quantile autocovariances are proposed by considering, respectively, the so-called metric, noise, and trimmed approaches. Each method achieves its robustness against outliers in different manner.

The detection of patterns in multivariate time series is a relevant task, especially for large datasets. In this paper, four clustering models for multivariate time series are proposed, with the following characteristics. First, the Partitioning Around Medoids (PAM) framework is considered. Among the different approaches to the clustering of multivariate time series, the observation-based is adopted. To cope with the complexity of the features of each multivariate time series and the associated assignment uncertainty a fuzzy clustering approach is adopted.

In this paper a Self-Organizing Map (SOM) robust to the presence of outliers, the Smoothed SOM (S-SOM), is proposed. S-SOM improves the properties of input density mapping, vector quantization, and clustering of the standard SOM in the presence of outliers by upgrading the learning rule in order to smooth the representation of outlying input vectors onto the map. The upgrade of the learning rule is based on the complementary exponential distance between the input vector and its closest codebook. The convergence of the S-SOM to a stable state is proved.