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Descripción

Persistence modules are algebraic constructs that can be used to describe the shape of an object starting from a geometric representation of it. As shape descriptors, persistence modules are not complete, that is they may not distinguish non-equivalent shapes. In this paper we show that one reason for this is that homomorphisms between persistence modules forget the geometric nature of the problem. Therefore we introduce geometric homomorphisms between persistence modules, and show that in some cases they perform better. A combinatorial structure, the $H_0$-tree, is shown to be an invariant for geometric isomorphism classes in the case of persistence modules obtained through the 0th persistent homology functor.

Pertenece a

AMS Acta  

Autor(es)

Cagliari, Francesca -  Ferri, Massimo -  Gualandri, Luciano -  Landi, Claudia - 

Id.: 61651097

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveMAT/03 Geometria - 

Tipo de recurso: Articolo  -  PeerReviewed  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] http://amsacta.unibo.it/4313/

Fecha de contribución: 29-jul-2015

Contacto:

Localización:
* Cagliari, Francesca ; Ferri, Massimo ; Gualandri, Luciano ; Landi, Claudia (2012) Persistence modules, shape description, and completeness. Springer LNCS, 7309 . pp. 148-156.

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