RATS: Unsupervised manifold learning using low-distortion alignment of tangent spaces.

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.