A new topological entropy-based approach for measuring similarities among piecewise linear functions

In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing the comparison between discrete piecewise linear functions. The comparison is certi ed by the stability theorem for persistent entropy. The theorem is used in the implementat...

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Detalles Bibliográficos
Autores: Rucco, Matteo, González Díaz, Rocío, Jiménez Rodríguez, María José, Atienza Martínez, María Nieves, Cristalli, Cristina, Concettoni, Enrico, Ferrante, Andrea, Merelli, Emanuela
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2017
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/87688
Acceso en línea:https://hdl.handle.net/11441/87688
https://doi.org/10.1016/j.sigpro.2016.12.006
Access Level:acceso abierto
Palabra clave:Piecewise linear functions
Noisy signals
Persistent homology
Persistent Entropy
Supervised classi cation
Descripción
Sumario:In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing the comparison between discrete piecewise linear functions. The comparison is certi ed by the stability theorem for persistent entropy. The theorem is used in the implementation of a new algorithm. The algorithm transforms a discrete piecewise linear function into a ltered simplicial complex that is analyzed with persistent homology and persistent entropy. Persistent entropy is used as discriminant feature for solving the supervised classi cation problem of real long length noisy signals of DC electrical motors. The quality of classi cation is stated in terms of the area under receiver operating characteristic curve (AUC=94.52%)