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A relationist and descriptive approach to stationary time series

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00203217
Contributor : Vincent Vigneron <>
Submitted on : Wednesday, January 9, 2008 - 1:02:10 PM
Last modification on : Friday, February 12, 2021 - 9:11:29 AM
Long-term archiving on: : Tuesday, April 13, 2010 - 4:49:15 PM

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  • HAL Id : hal-00203217, version 1

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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⟩

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