A recent result on size functions is extended to higher homology modules: the persistent homology based on a multidimensional measuring function is reduced to a 1-dimensional one. This leads to a stable distance for multidimensional persistent homology. Some reflections on i-essentiality of homological critical values conclude the paper.
One-dimensional reduction of multidimensional persistent homology / Cagliari F.; Di Fabio B.; Ferri M.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 138:(2010), pp. 3003-3017. [10.1090/S0002-9939-10-10312-8]
One-dimensional reduction of multidimensional persistent homology
CAGLIARI, FRANCESCA;DI FABIO, BARBARA;FERRI, MASSIMO
2010
Abstract
A recent result on size functions is extended to higher homology modules: the persistent homology based on a multidimensional measuring function is reduced to a 1-dimensional one. This leads to a stable distance for multidimensional persistent homology. Some reflections on i-essentiality of homological critical values conclude the paper.File in questo prodotto:
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