On the stability of persistent entropy and new summary functions for TDA
Persistent entropy is a topological statistic for data sets defined using the concepts of persistent homology and Shannon entropy. It has been successfully applied to images analysis and signal processing but its formal properties do not seem to be well known so far. The aim of this paper is to find the requirements under which persistent entropy is stable to small perturbations in the input data and scale-invariant. In addition, two new stable summary functions based on persistent entropy are provided. Their usefulness for pattern recognition is also shown.
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Information Theory
Information Theory
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