topometry 0.1.0.0

A comprehensive dimensional reduction framework to recover latent information from data.

https://img.shields.io/github/stars/davisidarta/topometry?style=social

TopOMetry - Topologically Optimized geoMetry

Documentation available at Read The Docs.

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.

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 topological basis (multiscale Diffusion Maps and/or fuzzy or continuous versions of Laplacian Eigenmaps). On top of these basis, new graphs can be learned using k-nearest-neighbors graphs or with new topological metrics. The learned metrics, basis and graphs are stored as different attributes of 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

MIT License