Stable Comparison of Multidimensional Persistent Homology Groups with Torsion

  title={Stable Comparison of Multidimensional Persistent Homology Groups with Torsion},
  author={P. Frosini},
  journal={Acta Applicandae Mathematicae},
  • P. Frosini
  • Published 2010
  • Mathematics, Computer Science
  • Acta Applicandae Mathematicae
  • The present lack of a stable method to compare persistent homology groups with torsion is a relevant problem in current research about Persistent Homology and its applications in Pattern Recognition. In this paper we introduce a pseudo-distance dT that represents a possible solution to this problem. Indeed, dT is a pseudo-distance between multidimensional persistent homology groups with coefficients in an Abelian group, hence possibly having torsion. Our main theorem proves the stability of the… CONTINUE READING
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