Comparing the morphology of molecular clouds without supervision

Abstract

Molecular clouds show complex structures reflecting their non-linear dynamics. Many studies investigating the bridge between their morphology and physical properties have shown the value of non-Gaussian higher-order statistics in capturing physical information. Yet, as this bridge is usually characterized in the supervised world of simulations, transferring it to observations can be hazardous, especially when the discrepancy between simulations and observations remains unknown. In this paper, we aim to identify relevant summary statistics, directly from the observation data. To do so, we developed a test to compare the informative power of two sets of summary statistics for a given unlabeled dataset. Contrary to supervised approaches, this test does not require knowledge of any class label or parameter associated with the data. Instead, it evaluates and compares the degeneracy levels of the summary statistics based on a notion of statistical compatibility. We applied this test to column density maps of 14 nearby molecular clouds observed by Herschel and iteratively compared different sets of typical summary statistics. We show that a standard Gaussian description of these clouds is highly degenerate but can be substantially improved when being estimated on the logarithm of the maps. This illustrates that low-order statistics, when properly used, remain very powerful. We further show that such descriptions still exhibit a small quantity of degeneracies, some of which are lifted by the higher-order statistics provided by reduced wavelet scattering transforms. These degeneracies quantitatively differ between observations and state-of-the-art simulations of dense cloud collapse, and they are not present for logFBM models. Finally, we show how to cooperatively use the summary statistics identified to build a morphological distance, which is evaluated visually and gives convincing results.