Trendlets: A novel probabilistic representational structures for clustering the time series data

Time series data is a sequence of values recorded systematically over a period which are mostly used for prediction, clustering, and analysis. The two essential features of a time series data are trend and seasonality. Preprocessing of the time series data is necessary for performing prediction tasks. In most of the cases, the trend and the seasonality are removed before applying the regression algorithms. The accuracy of such algorithms depends upon the functions used for the removal of trend and seasonality. Clustering of an unlabeled time series data with the presence of trend and seasonality is challenging. In this paper, we propose a probabilistic representational learning method for grouping the time series data. We introduce five terminologies in our method of clustering namely the trendlets, uplets, downlets, equalets and trendlet string. These elements are the representational building blocks of our proposed method. Experiments on the proposed algorithm are performed with the renewable energy data on the electricity supply system of continental Europe which includes the demand and inflow of renewable energy for the term 2012 to 2014 and UCR-2018 time series archive containing 128 datasets. We compared our proposed representational method with various clustering algorithms using the silhouette score. Mini-batch k-means and agglomerative hierarchical clustering algorithms show better performance in terms of quality, logical accordance with data and time taken for clustering.