DeepAtlas: a tool for effective manifold learning

Area of Science:

• Computational biology
• Machine learning
• Data science

Background:

• Manifold learning assumes high-dimensional data lies on lower-dimensional manifolds.
• Current methods produce global embeddings, not local maps needed for manifold definition.
• Existing tools cannot validate the manifold hypothesis for a given dataset.

Purpose of the Study:

• Introduce DeepAtlas, an algorithm for learning local data structures.
• Enable assessment of the manifold hypothesis's validity in datasets.
• Facilitate generative modeling and differential geometry applications on manifold data.

Main Methods:

• DeepAtlas creates low-dimensional local neighborhood embeddings.
• Deep neural networks map between local embeddings and original data.
• Topological distortion quantifies manifold adherence and dimensionality.

Main Results:

• DeepAtlas successfully learns manifold structures in test datasets.
• Many real-world datasets, including single-cell RNA-sequencing, do not conform to the manifold hypothesis.
• The algorithm identifies datasets suitable for manifold-based analysis.

Conclusions:

• DeepAtlas provides a robust method for manifold learning and hypothesis testing.
• The findings highlight the limitations of the manifold hypothesis in complex biological data.
• DeepAtlas opens avenues for advanced data analysis using differential geometry.