Multidimensional persistent homology is stable

Cerri, Andrea ; Di Fabio, Barbara ; Ferri, Massimo ; Frosini, Patrizio ; Landi, Claudia (2009) Multidimensional persistent homology is stable. p. 14. DOI 10.6092/unibo/amsacta/2603.

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Multidimensional persistence studies topological features of shapes by analyzing the lower level sets of vector-valued functions. The rank invariant completely determines the multidimensional analogue of persistent homology groups. We prove that multidimensional rank invariants are stable with respect to function perturbations. More precisely, we construct a distance between rank invariants such that small changes of the function imply only small changes of the rank invariant. This result can be obtained by assuming the function to be just continuous. Multidimensional stability opens the way to a stable shape comparison methodology based on multidimensional persistence.

Document type
Monograph (Technical Report)
Cerri, Andrea
Di Fabio, Barbara
Ferri, Massimo
Frosini, Patrizio
Landi, Claudia
Multidimensional persistence, persistence diagram, size function, Cech homology, foliation
Deposit date
03 Aug 2009
Last modified
16 May 2011 12:10

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