A relationist and descriptive approach to stationary time series

Aurélien Hazan (1) , Vincent Vigneron (1)

1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes

With the objective of questioning the foundings of network modeling in complex systems sciences, this article addresses the issue of building discrete topological spaces from continuous data measured on a complex system thanks to sta- tistical inference, then to characterize the obtained space. We first take the example of graphs to underline the sensitivity of graph properties to thresholding. Then we put forward a possible way to cope with that drawback thanks to a multilevel point of view. We extend results to n-ary relations thanks to simplicial complexes, and to statistical independence before characterizing the obtained space with simplicial homology, in a threshold-independent manner.

Mots clés: knowledge representation; random graph; binary relations; correlation; independence; simplicial complex; persistent homology

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Aurélien Hazan, Vincent Vigneron. A relationist and descriptive approach to stationary time series. European Conference on Complex Systems (ECCS07), Oct 2007, Dresden, Germany. pp.00. ⟨hal-00203217⟩