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

• URL: http://arxiv.org/abs/2411.19894v1
• Date: Fri, 29 Nov 2024 17:58:45 GMT
• Title: Noncommutative Model Selection and the Data-Driven Estimation of Real Cohomology Groups
• Authors: Araceli Guzmán-Tristán, Antonio Rieser, Eduardo Velázquez-Richards,
• Abstract summary: We propose three data-driven methods for estimating the real cohomology groups $Hk (X ; mathbbR)$ of a compact metric-measure space.<n>We present the results of several computational experiments in the case that $X$ is embedded in $mathbbRn$, where two of the three algorithms performed well.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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