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Description:

heatgeo 0.0.1

Start with HeatGeo

The Heat-Geodesic embedding preserves the heat-geodesic dissimilarity
defined as
d_t(x_i,x_j) = \bigg[ -4t \log (\mathbf{H}_t)_{ij} - \sigma 4 t \log(\mathbf{V})_{ij} \bigg] ^{1/2},

where Ht is a heat kernel on a graph, and V is
a volume regularization term. This dissimilarity is inspired by
Varadhan’s formula which relates the heat kernel to the geodesic
distance on a manifold. For more details on the heat-geodesic
dissimilarity read our preprint A Heat Diffusion Perspective on
Geodesic Preserving Dimensionality
Reduction.

Note
We are currently updating this repository to provide examples and
improve the documentation.

Install
The package is not yet available with pip or conda. To install it, you
can clone this repo and install from setup.py.
git clone https://github.com/KrishnaswamyLab/HeatGeo.git
cd HeatGeo
pip install -e .

To reproduce the results in experiments/ or try the embeddings with
different graph constructions, you need additional packages that can be
installed via the development version. In this case run
cd HeatGeo
pip install -e '.[dev]'

We provide an example below.
How to use
Google colab example on the swiss roll
The directory experiments contains code to reproduce our main results.
We used hydra, the parameters can be changed in config or directly
in the CLI. In notebooks, we provide examples on toy datasets.
Contributing
We are using nbdev for this package and the documentation. See this
introduction to start
using nbdev. The code and documentation should be modified in the
notebooks nbs/, then run nbdev_prepare before a commit. This command
will export the notebooks to .py files in heatgeo, it will also
clean the metadata, and run some test. The page will then automatically
be deployed through GitHub actions.
Acknowledgements
This repository is a simplified version of a larger codebase used for
development. It loses the original commit history which contains
contributions from other authors of the paper. This repository uses or
modify code from the PHATE
implementation, and the
Chebychev polynomials
implementation
of the paper Fast Multiscale Diffusion on
Graphs.