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arXiv · 2203.01894

Reconstruction of univariate functions from directional persistence diagrams

Aina Ferrà·Carles Casacuberta·Oriol Pujol
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Abstract

We describe a method for approximating a single-variable function $f$ using persistence diagrams of sublevel sets of $f$ from height functions in different directions. We provide algorithms for the piecewise linear case and for the smooth case. Three directions suffice to locate all local maxima and minima of a piecewise linear continuous function from its collection of directional persistence diagrams, while five directions are needed in the case of smooth functions with non-degenerate critical points. Our approximation of functions by means of persistence diagrams is motivated by a study of importance attribution in machine learning, where one seeks to reduce the number of critical points of signal functions without a significant loss of information for a neural network classifier.

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Aina Ferrà, Carles Casacuberta, Oriol Pujol. 2022-03-03. Reconstruction of univariate functions from directional persistence diagrams. https://arxiv.org/abs/2203.01894

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