The dynamics of physical
systems that require high-dimensional
representation can often be captured in a few meaningful degrees of
freedom called collective variables (CVs). However, identifying CVs
is challenging and constitutes a fundamental problem in physical chemistry.
This problem is even more pronounced when CVs need to provide information
about slow kinetics related to rare transitions between long-lived
metastable states. To address this issue, we propose an unsupervised
deep-learning method called spectral map. Our method constructs slow
CVs by maximizing the spectral gap between slow and fast eigenvalues
of a transition matrix estimated by an anisotropic diffusion kernel.
We demonstrate our method in several high-dimensional reversible folding
processes.