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On the stability of persistent entropy and new summary functions for TDA
March 22, 2018 Β· Declared Dead Β· π Pattern Recognition
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Authors
N. Atienza, R. Gonzalez-Diaz, M. Soriano-Trigueros
arXiv ID
1803.08304
Category
cs.IT: Information Theory
Citations
97
Venue
Pattern Recognition
Last Checked
4 months ago
Abstract
Persistent homology and persistent entropy have recently become useful tools for patter recognition. In this paper, we find requirements under which persistent entropy is stable to small perturbations in the input data and scale invariant. In addition, we describe two new stable summary functions combining persistent entropy and the Betti curve. Finally, we use the previously defined summary functions in a material classification task to show their usefulness in machine learning and pattern recognition.
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