Multidimensional persistent modules do not admit a concise representation analogous to that provided by persistence diagrams for real-valued functions. However, there is no obstruction for multidimensional persistent Betti numbers to admit one. Therefore, it is reasonable to look for a generalization of persistence diagrams concerning those properties that are related only to persistent Betti numbers. In this paper, the persistence space of a vector-valued continuous function is introduced to generalize the concept of persistence diagram in this sense. Furthermore, it is presented a method to visualize topological features of a shape via persistence spaces. Finally, it is shown that this method is resistant to perturbations of the input data.

The Persistence Space in Multidimensional Persistent Homology / Andrea, Cerri; Landi, Claudia. - ELETTRONICO. - 7749:(2013), pp. 180-191. ((Intervento presentato al convegno DGCI 2013 tenutosi a Seville (Spain) nel March 20-22, 2013 [10.1007/978-3-642-37067-0_16].

The Persistence Space in Multidimensional Persistent Homology

LANDI, Claudia
2013

Abstract

Multidimensional persistent modules do not admit a concise representation analogous to that provided by persistence diagrams for real-valued functions. However, there is no obstruction for multidimensional persistent Betti numbers to admit one. Therefore, it is reasonable to look for a generalization of persistence diagrams concerning those properties that are related only to persistent Betti numbers. In this paper, the persistence space of a vector-valued continuous function is introduced to generalize the concept of persistence diagram in this sense. Furthermore, it is presented a method to visualize topological features of a shape via persistence spaces. Finally, it is shown that this method is resistant to perturbations of the input data.
DGCI 2013
Seville (Spain)
March 20-22, 2013
7749
180
191
Andrea, Cerri; Landi, Claudia
The Persistence Space in Multidimensional Persistent Homology / Andrea, Cerri; Landi, Claudia. - ELETTRONICO. - 7749:(2013), pp. 180-191. ((Intervento presentato al convegno DGCI 2013 tenutosi a Seville (Spain) nel March 20-22, 2013 [10.1007/978-3-642-37067-0_16].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/929089
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