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arXiv · 2411.19894

Noncommutative Model Selection and the Data-Driven Estimation of Real Cohomology Groups

Araceli Guzmán-Tristán·Antonio Rieser·Eduardo Velázquez-Richards
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Abstract

We propose three completely data-driven methods for estimating the real cohomology groups $H^k (X ; \mathbb{R})$ of a compact metric-measure space $(X, d_X, \mu_X)$ embedded in a metric-measure space $(Y,d_Y,\mu_Y)$, given a finite set of points $S$ sampled from a uniform distrbution $\mu_X$ on $X$, possibly corrupted with noise from $Y$. We present the results of several computational experiments in the case that $X$ is embedded in $\mathbb{R}^n$, where two of the three algorithms performed well.

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Araceli Guzmán-Tristán, Antonio Rieser, Eduardo Velázquez-Richards. 2024-11-29. Noncommutative Model Selection and the Data-Driven Estimation of Real Cohomology Groups. https://arxiv.org/abs/2411.19894

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