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The Persistence Space in Multidimensional Persistent Homology

  • Andrea Cerri
  • Claudia Landi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7749)

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.

Keywords

Topological Feature Homology Class Lower Dimensional Space Persistent Homology Multidimensional Analogue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andrea Cerri
    • 1
    • 3
  • Claudia Landi
    • 2
    • 3
  1. 1.IMATI – CNRGenovaItalia
  2. 2.DISMIUniversità di Modena e Reggio EmiliaItalia
  3. 3.ARCESUniversità di BolognaItalia

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