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Invariant_persistent_homology_per_ARXIV.pdf
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📊 Size: 1.11 MB
📄 Pages: 6 pages
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Summary

Classical persistent homology is not suitable for studying the action of transformation groups different from the group of all self-homeomorphisms of a topological space. To obtain better lower bounds for the natural pseudo-distance associated with a group, G-invariant persistent homology is introduced, which adapts persistent homology to consider a set of chains invariant under the action of the group. This theory provides a positive lower bound for the pseudo-distance in cases where classical persistent homology cannot. The concept of G-invariant persistent homology is formalized, and its stability with respect to the natural pseudo-distance is proven, making it useful for shape comparison applications.

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Classical persistent homology is not suitable for studying the action of transformation groups different from the group of all self-homeomorphisms of a...

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  • File Format: PDF
  • File Size: 1.11 MB
  • Pages: 6
  • Language: EN
  • Total Downloads: 46
  • Last Updated: 2 months ago

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