entropy-maximization-manifold

name	entropy-maximization-manifold
description	Maximum entropy path ensemble embedding for manifold learning and dimensionality reduction
category	machine-learning
activation	manifold learning, entropy maximization, path ensemble, dimensionality reduction, intrinsic structure, EntroPath
arxiv_id	2607.06497

Entropy Maximization Manifold Learning

Overview

Maximum entropy path ensemble embedding for manifold learning — discovers intrinsic data structure through entropy maximization combined with path-based embeddings.

Core Methodology

1. Path Ensemble Construction: Build path ensembles on data graph representing possible trajectories
2. Entropy Maximization: Maximize Shannon entropy over path distributions to find unbiased embeddings
3. Geometric Embedding: Project high-dimensional paths into low-dimensional manifold preserving intrinsic geometry
4. Iterative Refinement: Alternate between path ensemble update and embedding optimization

Key Components

• Path Distribution: Probability distribution over data paths (random walks, geodesics)
• Entropy Objective: Maximize H(P) = -Σ p(γ) log p(γ) subject to constraints
• Manifold Coordinates: Low-dimensional embedding preserving path-based similarities
• Regularization: Balance entropy maximization with geometric fidelity

Applications

• Dimensionality reduction for high-dimensional biomedical data
• Intrinsic structure discovery in complex datasets
• Manifold learning for single-cell genomics
• Geometric representation learning

Implementation Notes

• Works with any similarity/distance metric
• Handles nonlinear manifolds without parametric assumptions
• Complements t-SNE, UMAP, PCA with entropy-based principled approach