Time dependent clustering of time series

In this work we consider the problem of clustering time series. Contrary to other works on this topic, our main concern is to let the most important observations, for instance the most recent, have a larger weight on the analysis. This is done by defining similarities measures between two time series, based on Pearson's correlation coefficient, which uses the notion of weighted mean and weighted covariance, where the weights increase monotonically with the time. We use these measures, which are metrics between time series, as a similarity or dissimilarity index between the $n$ time series to be clustered. We apply a very well known partitional method, the K-means, with some adaptations to make it able to choose the number of clusters