EntroPath

EntroPath: Maximum entropy path ensemble method for manifold learning and geodesic geometry recovery

EntroPath is a new manifold learning method that uses maximum entropy random walks (MERW) to build free-energy dissimilarities that converge to squared geodesic distances, addressing concentration bias in locally-normalized random walks and sensitivity to shortcut edges in shortest-path methods. The method provides a diffusion depth parameter that interpolates between local and global geometry, admits an exact Gram factorization connecting it to kernel methods, and includes scalable landmark projection extensions. Evaluations on synthetic manifolds and single-cell genomics benchmarks show EntroPath matches or outperforms diffusion- and shortest-path-based methods, with strongest gains on non-uniformly sampled manifolds and branching trajectories.