DeepAtlas: a tool for effective manifold learning
This addresses the challenge of validating and applying manifold learning for researchers in fields like bioinformatics, though it appears incremental as it builds on existing concepts with new algorithmic tools.
The authors tackled the problem of assessing whether data conforms to the manifold hypothesis and generating local manifold representations, resulting in DeepAtlas, which successfully learns manifold structures and identifies that many real datasets, like single-cell RNA-sequencing, do not follow the hypothesis.
Manifold learning builds on the "manifold hypothesis," which posits that data in high-dimensional datasets are drawn from lower-dimensional manifolds. Current tools generate global embeddings of data, rather than the local maps used to define manifolds mathematically. These tools also cannot assess whether the manifold hypothesis holds true for a dataset. Here, we describe DeepAtlas, an algorithm that generates lower-dimensional representations of the data's local neighborhoods, then trains deep neural networks that map between these local embeddings and the original data. Topological distortion is used to determine whether a dataset is drawn from a manifold and, if so, its dimensionality. Application to test datasets indicates that DeepAtlas can successfully learn manifold structures. Interestingly, many real datasets, including single-cell RNA-sequencing, do not conform to the manifold hypothesis. In cases where data is drawn from a manifold, DeepAtlas builds a model that can be used generatively and promises to allow the application of powerful tools from differential geometry to a variety of datasets.