What to expect from dynamical modelling of cluster haloes II.
  Investigating dynamical state indicators with Random Forest
  We investigate the importances of various dynamical features in predicting
the dynamical state (DS) of galaxy clusters, based on the Random Forest (RF)
machine learning approach. We use a large sample of galaxy clusters from the
Three Hundred Project of hydrodynamical zoomed-in simulations, and construct
dynamical features from the raw data as well as from the corresponding mock
maps in the optical, X-ray, and Sunyaev-Zel'dovich (SZ) channels. Instead of
relying on the impurity based feature importance of the RF algorithm, we
directly use the out-of-bag (OOB) scores to evaluate the importances of
individual features and different feature combinations. Among all the features
studied, we find the virial ratio, $\eta$, to be the most important single
feature. The features calculated directly from the simulations and in
3-dimensions carry more information on the DS than those constructed from the
mock maps. Compared with the features based on X-ray or SZ maps, features
related to the centroid positions are more important. Despite the large number
of investigated features, a combination of up to three features of different
types can already saturate the score of the prediction. Lastly, we show that
the most sensitive feature $\eta$ is strongly correlated with the well-known
half-mass bias in dynamical modelling. Without a selection in DS, cluster halos
have an asymmetric distribution in $\eta$, corresponding to an overall positive
half-mass bias. Our work provides a quantitative reference for selecting the
best features to discriminate the DS of galaxy clusters in both simulations and
observations.
