Improved Fréchet Distance for Time Series

Abstract

This paper focuses on the Fréchet distance introduced by Maurice Fréchet in 1906 to account for the proximity between curves (Fréchet (1906)). The major limitation of this proximity measure is that it is based on the closeness of the values independently of the local trends. To alleviate this set back, we propose a dissimilarity index extending the above estimates to include the information of dependency between local trends. A synthetic dataset is generated to reproduce and show the limited conditions for the Fréchet distance. The proposed dissimilarity index is then compared with the Fréchet estimate and results illustrating its efficiency are reported.