  Using random walk sampling methods for feature learning on networks, we
develop a method for generating low-dimensional node embeddings for directed
graphs and identifying transition states of stochastic chemical reacting
systems. We modified objective functions adopted in existing random walk based
network embedding methods to handle directed graphs and neighbors of different
degrees. Through optimization via gradient ascent, we embed the weighted graph
vertices into a low-dimensional vector space Rd while preserving the
neighborhood of each node. We then demonstrate the effectiveness of the method
on dimension reduction through several examples regarding identification of
transition states of chemical reactions, especially for entropic systems.
