# Introducing user-prescribed constraints in Markov chains for nonlinear dimensionality reduction

arXiv: https://arxiv.org/abs/1806.05096 · HTML: https://mlsanity.com/paper/1806.05096/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2018.

## Built on by (most cited first, 1 of 1)

- [Reweighted Manifold Learning of Collective Variables from Enhanced Sampling Simulations](https://mlsanity.com/paper/2207.14554/) (2022)

## Abstract (arXiv)

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.