One-Dimensional Reduction of Multidimensional Persistent Homology

Cagliari, Francesca ; Di Fabio, Barbara ; Ferri, Massimo (2008) One-Dimensional Reduction of Multidimensional Persistent Homology. DOI 10.6092/unibo/amsacta/2632.
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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 reflec- tions on i-essentiality of homological critical values conclude the paper.

Document type
Monograph (Technical Report)
Cagliari, Francesca
Di Fabio, Barbara
Ferri, Massimo
Size function, measuring function, rank invariant, pattern recognition, i-essentiality
Deposit date
23 Sep 2009 09:14
Last modified
16 May 2011 12:11

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