  Stochastic kernel based dimensionality reduction approaches have become
popular in the last decade. The central component of many of these methods is a
symmetric kernel that quantifies the vicinity between pairs of data points and
a kernel-induced Markov chain on the data. Typically, the Markov chain is fully
specified by the kernel through row normalization. However, in many cases, it
is desirable to impose user-specified stationary-state and dynamical
constraints on the Markov chain. Unfortunately, no systematic framework exists
to impose such user-defined constraints. Here, we introduce a path entropy
maximization based approach to derive the transition probabilities of Markov
chains using a kernel and additional user-specified constraints. We illustrate
the usefulness of these Markov chains with examples.
