Path-entropy maximized Markov chains for dimensionality reduction

Stochastic kernel based dimensionality reduction methods have become popular in the last decade. The central component of these methods is a symmetric kernel that quantifies the vicinity of pairs of data points and a kernel-induced Markov chain. Typically, the Markov chain is fully specified by the kernel through row normalization. However, it may be desirable to impose user-specified stationary-state and dynamical constraints on the Markov chain. Notably, no systematic framework exists to prescribe user-defined constraints on Markov chains. Here, we use a path entropy maximization based approach to derive Markov chains on data using a kernel and additional user-defined constraints. We illustrate the usefulness of the path entropy normalization procedure with multiple real and artificial data sets. All scripts are available at: https://github.com/dixitpd/maxcaldiffmap