Single-cell RNA-seq data highlight limitations of contemporary dimensionality reduction and manifold learning techniques. Using simple test cases, studies have shown that key features of the Riemannian metric and topological structure are sacrificed by commonly used dimensionality reduction methods, such as uniform manifold approximation and projection (UMAP), t-distributed stochastic neighborhood embedding (tSNE), and Isomap. To preserve more of the underlying structure, we developed an approach for constructing a finite atlas, a mathematical structure involving local neighborhood coordinate charts, which can encode any topological manifold with compact closure. We are testing the atlas construct in (non-biological) data settings with known Riemannian manifold structure and plan to then investigate differential-geometric features of scRNA-seq data that can be learned with this atlas-graph structure approach.

Who is involved: Ryan Robinett