Horizon Visibility Graphs and Time Series Merge Trees are Dual

Autor:	Stephen, Colin
Rok vydání:	2019
Předmět:	Physics - Data Analysis Statistics and Probability Computer Science - Computational Geometry Nonlinear Sciences - Chaotic Dynamics
Druh dokumentu:	Working Paper
Popis:	In this paper we introduce the horizon visibility graph, a simple extension to the popular horizontal visibility graph representation of a time series, and show that it possesses a rigorous mathematical foundation in computational algebraic topology. This fills a longstanding gap in the literature on the horizontal visibility approach to nonlinear time series analysis which, despite a suite of successful applications across multiple domains, lacks a formal setting in which to prove general properties and develop natural extensions. The main finding is that horizon visibility graphs are dual to merge trees arising naturally over a filtered complex associated to a time series, while horizontal visibility graphs are weak duals of these trees. Immediate consequences include availability of tree-based reconstruction theorems, connections to results on the statistics of self-similar trees, and relations between visibility graphs and the emerging field of applied persistent homology. Comment: 6 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1906.08825 Zobrazit plný text záznamu View this record from Arxiv