The four cosmic tidal web elements from the $\beta$-skeleton

Precise cosmic web classification of observed galaxies in massive spectroscopic surveys can be either highly uncertain or computationally expensive. As an alternative, we explore a fast Machine Learning-based approach to infer the underlying dark matter tidal cosmic web environment of a galaxy distribution from its $\beta$-skeleton graph. We develop and test our methodology using the cosmological magnetohydrodynamic simulation Illustris-TNG at $z=0$. We explore three different tree-based machine-learning algorithms to find that a random forest classifier can best use graph-based features to classify a galaxy as belonging to a peak, filament or sheet as defined by the T-Web classification algorithm. The best match between the galaxies and the dark matter T-Web corresponds to a density field smoothed over scales of $2$ Mpc, a threshold over the eigenvalues of the dimensionless tidal tensor of $\lambda_{\rm{th}}=0.0$ and galaxy number densities around $8\times 10^{-3}$ Mpc$^{-3}$. This methodology results on a weighted F1 score of 0.728 and a global accuracy of 74\%. More extensive tests that take into account lightcone effects and redshift space distortions (RSD) are left for future work. We make one of our highest ranking random forest models available on a public repository for future reference and reuse.