  Constructing reduced representations of high-dimensional systems is a
fundamental problem in physical chemistry. Many unsupervised machine learning
methods can automatically find such low-dimensional representations. However,
an often overlooked problem is what high-dimensional representation should be
used to describe systems before dimensionality reduction. Here, we address this
issue using a recently developed method called reweighted diffusion map [J.
Chem. Theory Comput. 2022, 18, 7179-7192]. We show how high-dimensional
representations can be quantitatively selected by exploring the spectral
decomposition of Markov transition matrices built from data obtained from
standard or enhanced sampling atomistic simulations. We demonstrate the
performance of the method in several high-dimensional examples.
