Stable Comparison of Multidimensional Persistent Homology Groups with Torsion
@article{Frosini2010StableCO, title={Stable Comparison of Multidimensional Persistent Homology Groups with Torsion}, author={Patrizio Frosini}, journal={Acta Applicandae Mathematicae}, year={2010}, volume={124}, pages={43-54} }
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…
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