Wavelet-based self-organizing maps for classifying multivariate time series

Following a nonparametric approach, we suggest a time-series clustering method. Our clustering approach combines the benefits connected to the interpretative power of the nonparametric representation of the time series, and the clustering and vector quantization informational gain produced by the adopted unsupervised neural networks technique, enhanced with the self-organizing maps ordering and topological preservation abilities. The proposed clustering method takes into account a composite wavelet-based information of the multivariate time series by adding to the information connected to the wavelet variance, namely the influence of variability of individual univariate components of them ultivariate time series across scales, the information associated to wavelet correlation, represented by the interaction between pairs of univariate components of the multivariate time series at each scale, and then suitably tuning the combination of these pieces of information. In order to assess the effectiveness of the proposed clustering approach, a simulation study and an empirical application are shown.