EntroPath: Maximum Entropy Path Ensemble Embedding for Manifold Learning

2016-10-01 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

EntroPath is a novel manifold learning method that recovers geodesic geometry from data graphs using ensembles of diffusion paths based on the maximum entropy random walk (MERW). Unlike methods relying on locally normalized random walks or shortest-path distances, EntroPath builds its dissimilarities from MERW, aggregating the full ensemble of k-step paths. This free-energy dissimilarity converges to squared geodesic distance in the short-time limit via Varadhan's heat-kernel formula. The method offers scalable extensions through landmark projection and diffusion-potential pseudotime. Across synthetic manifolds and single-cell benchmarks, EntroPath consistently matches or outperforms diffusion- and shortest-path-based methods, demonstrating particular gains on manifolds with non-uniform sampling density and well-separated branching trajectories. It achieves a trustworthiness of 0.981 on the non-uniform Swiss roll and embeds 110,427 single cells in approximately 15 seconds.

Key takeaway

For AI Scientists and Machine Learning Engineers working with high-dimensional biological or complex manifold data, you should consider EntroPath when existing methods struggle with non-uniform sampling or noisy graph structures. Its MERW-based path ensemble approach provides superior geodesic preservation and robustness, particularly for single-cell trajectory inference, offering a scalable solution that maintains geometric fidelity even on large datasets like the 110,427-cell root atlas.

Key insights

EntroPath uses maximum entropy random walks to derive a free-energy dissimilarity that approximates geodesic distances.

Principles

• Aggregating path ensembles reduces sensitivity to spurious graph edges.
• MERW's global entropy maximization preserves separation in sparse regions.
• Diffusion depth "k" interpolates between local and global geometry.

Method

EntroPath constructs an adaptive-bandwidth affinity graph, computes MERW k-step path ensemble free-energy dissimilarities, and embeds them using metric MDS, with scalable landmark projection for large datasets.

In practice

• Apply to single-cell RNA-seq data for robust trajectory inference.
• Use for dimensionality reduction on manifolds with non-uniform sampling.
• Employ landmark approximation for large datasets to reduce computation.

Topics

• Manifold Learning
• Dimensionality Reduction
• Maximum Entropy Random Walk
• Geodesic Distance
• Single-Cell Trajectory Inference
• Graph Embeddings

Code references

• rpprzemek/entropath

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.