Frobenius correlation based u-shapelets discovery for time series clustering

Vanel Steve Siyou Fotso, Engelbert Mephu Nguifo, Philippe Vaslin

Abstract: Highlights • We review state of the art on similarity functions for uncertain time Series and evaluate them for the comparison of small, uncertain time series. • We introduce the Frobenius cOrrelation for uncertain Time series ushapelet discovery (FOTS), a new dissimilarity score based on local correlation, which has interesting properties useful for comparison of small, uncertain time series and that makes no assumption on the probability distribution of uncertainty in data. • We evaluate FOTS on 63 datasets on clustering task. • We put the source code at the disposal of the scientific community to allow extension of our work. Abstract An u-shapelet is a sub-sequence of a time series used for the clustering of time series datasets. The purpose of this paper is to discover u-shapelets on uncertain time series. To achieve this goal, 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 also well adapted to the comparison of short time series. The FOTS score is used with the Scalable Unsupervised Shapelet Discovery algorithm for the clustering of 63 datasets, and it has shown a substantial improvement in the quality of the clustering with respect to the Rand Index. This work defines a novel framework for the clustering of uncertain time series.