TopOMetry - Topologically Optimized geoMetry
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A global framework for dimensionality reduction: learning topologic metrics, orthogonal bases and graph layouts
TopOMetry is a high-level python library to explore data topology. It allows learning topological metrics, dimensionality reduced basis and graphs from data, as well to visualize them with different layout optimization algorithms. The main aim is to achieve sequential approximations of the Laplace-Beltrami Operator, a natural way to describe data geometry and its high-dimensional topology. For more information, see the manuscript.
TopOMetry is designed to handle large-scale data matrices containing extreme topological diversity, such as those generated from single-cell omics, and can be used to perform topology-preserving visualizations.
TopOMetry main class is the TopOGraph object. In a TopOGraph, topological metrics are recovered with diffusion
harmonics, fuzzy simplicial sets or Continuous-k-Nearest-Neighbors, and used to obtain orthogonal basis (multiscale Diffusion Maps and/or
fuzzy or continuous versions of Laplacian Eigenmaps) that emphasize topological features and are robust to noise. On top of these basis, new graphs can be learned using k-nearest-neighbors
graphs or with new topological metrics. The learned similarity metrics, basis and graphs are stored at the
TopOGraph object.
Finally, different graph layout optimization algorithms built-in TopOMetry can be used for visualization:
- MAP (Manifold Approximation and Projection) - a lighter UMAP with looser assumptions
- MDE (Minimum Distortion Embedding) - the ultimate swiss-army knife for graph layout optimization
- tSNE (t-Stochasthic Neighborhood Embedding) - a classic of visualization, with parallelization
- TriMAP - dimensionality reduction using triplets
- NCVis (Noise Contrastive Visualization) - for blazing fast performance
- PaCMAP (Pairwise-controlled Manifold Approximation and Projection) - for balanced visualizations
The following image summarizes the TopOMetry workflow:
Contributing
Contributions are very welcome! If you're interested in adding a new feature, just let me know in the Issues section.
License
Citation
@article {Sidarta-Oliveira2022.03.14.484134,
author = {Sidarta-Oliveira, Davi and Velloso, Licio A},
title = {A comprehensive dimensional reduction framework to learn single-cell phenotypic topology uncovers T cell diversity},
elocation-id = {2022.03.14.484134},
year = {2022},
doi = {10.1101/2022.03.14.484134},
publisher = {Cold Spring Harbor Laboratory},
URL = {https://www.biorxiv.org/content/early/2022/03/17/2022.03.14.484134},
eprint = {https://www.biorxiv.org/content/early/2022/03/17/2022.03.14.484134.full.pdf},
journal = {bioRxiv}
}