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

Abstract

We propose three completely data-driven methods for estimating the real cohomology groups H^k (X ; R) of a compact metric-measure space (X, d_X, _X) embedded in a metric-measure space (Y,d_Y,_Y), given a finite set of points S sampled from a uniform distrbution _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 R^n, where two of the three algorithms performed well.

Tasks

Reproductions