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magnipy: Metric Space Magnitude Computations 🔍

This is a repository for computing the magnitude of a metric space, which encodes the effective size, diversity and geometry of a metric space. Given a dataset or distance matrix, magnitude measures the effective number of distinct points in the space at a scale of dissimilarity between observations.

Magnipy enables the computation of:

  • magnitude, magnitude weights and magnitude functions across varying resolutions
  • magnitude dimension profiles and the magnitude dimension to estimate intrinsic dimensionality
  • an automated scale-finding procedure to find suitable evaluation scales
  • MagArea the area under a magnitude function, a multi-scale measure of the intrinsic diversity of a space
  • MagDiff the area between two magnitude functions to measure the difference in diversity between two spaces

Diversipy enables the comparison of multiple spaces by:

  • computing the magnitude functions across a set of input datasets
  • automatically choosing shared evaluation scales
  • computing MagDiffs in comparison with a reference space or computing all pairwise MagDiffs
  • computing MagAreas across the same resolutions for all spaces

Dependencies

Dependencies are managed using poetry. To setup the environment, please run poetry install from the main directory.

Running magnipy

All main implementations for computing magnitude are collected in the Magnipy class. tutorial_magnipy.ipynb demonstrates how to set up and use this class to compute magnitude functions and magnitude dimension profiles.

Citation

Please consider citing our work!

@misc{limbeck2023metric,
  title         = {Metric Space Magnitude for Evaluating the Diversity of Latent Representations}, 
  author        = {Katharina Limbeck and Rayna Andreeva and Rik Sarkar and Bastian Rieck},
  year          = {2023},
  eprint        = {2311.16054},
  archivePrefix = {arXiv},
  primaryClass  = {cs.LG}
}

@inproceedings{andreeva2023metric,
  title         = {Metric Space Magnitude and Generalisation in Neural Networks},
  author        = {Andreeva, Rayna and Limbeck, Katharina and Rieck, Bastian and Sarkar, Rik},
  year          = {2023},
  booktitle     = {Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning~(TAG-ML)},
  volume        = {221},
  pages         = {242--253}
}