Frobenius correlation based u-shapelets discovery for time series clustering

An u-shapelet is a sub-sequence of a time series used for clustering a time series dataset. The problem we are interested in this paper is how to discover u-shapelets on uncertain time series? To answer this question, we propose a dissimilarity score called FOTS whose computation is based on the eigenvector decomposition and the comparison of the autocorrelation matrices of the time series. This score is robust to the presence of uncertainty ; it is not very sensitive to transient changes; it allows capturing complex relationships between time series such as oscillations and trends, and it is adapted to the comparison of shorts time series. The FOTS score is used with the Scalable Unsu-pervised Shapelet Discovery algorithm for the clustering of 17 literature datasets, and it shows a substantial improvement in the quality of the clustering (Rand Index). This work defines a framework for the clustering of uncertain time series.