arXiv Open Access 2022

Reconstruction of univariate functions from directional persistence diagrams

Aina Ferrà Carles Casacuberta Oriol Pujol

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Abstrak

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.

Topik & Kata Kunci

math.AT cs.LG

Penulis (3)

Aina Ferrà

Carles Casacuberta

Oriol Pujol

Format Sitasi

APA MLA BibTeX

Ferrà, A., Casacuberta, C., Pujol, O. (2022). Reconstruction of univariate functions from directional persistence diagrams. https://arxiv.org/abs/2203.01894

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Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓