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RATS: Unsupervised manifold learning using low-distortion alignment of tangent spaces
Biorxiv : the Preprint Server for Biology
|November 18, 2024
Summary
This study introduces Riemannian Alignment of Tangent Spaces (RATS), a new manifold learning method. RATS reduces distortion in high-dimensional data, improving the visualization of latent variables in biological datasets.
Area of Science:
- Computational Biology
- Data Science
- Topology
Background:
- High-dimensional biological datasets are common.
- Identifying underlying manifold structures is key to understanding latent variables.
- Existing manifold learning methods often introduce distortion and lack robust evaluation metrics.
Purpose of the Study:
- To develop a novel distortion measure for evaluating manifold learning techniques.
- To introduce a new bottom-up manifold learning method, Riemannian Alignment of Tangent Spaces (RATS).
- To enable the embedding of closed manifolds into their intrinsic dimension.
Main Methods:
- Development of a novel distortion metric for assessing low-dimensional embeddings.
- Introduction of the Riemannian Alignment of Tangent Spaces (RATS) algorithm.
- Application of RATS to idealized, biological, and surrogate datasets.
Main Results:
- RATS demonstrates lower distortion compared to existing manifold learning techniques.
- The proposed distortion measure effectively evaluates the quality of recovered manifolds.
- RATS facilitates superior visualization and deciphering of latent variables.
Conclusions:
- RATS is an effective manifold learning technique for high-dimensional data.
- The new distortion measure aids in selecting appropriate manifold learning methods.
- Accurate manifold recovery is crucial for biological data analysis and latent variable discovery.
