Skip to main content

Geodesic Sinkhorn with Chebyshev approximation

Project description

GeoSinkhorn

Code for the paper Geodesic Sinkhorn for Fast and Accurate Optimal Transport on Manifolds.

Note: This repository is still in development.

Installation

Clone the repository and install the library by running:

pip install -e .

or if you want to use the pre existing graph tools, run:

pip install -e .['graph']

To run the tests, you will need additional packages. Install them by running:

pip install -e .['dev']

Minimal Example

Building a graph between two Gaussian distributions and computing the distance between two signals on the graph.

import numpy as np
from geosink.sinkhorn import GeoSinkhorn 
from geosink.heat_kernel import laplacian_from_data

# Generate data and build graph.
data0 = np.random.normal(0, 1, (100, 5))
data1 = np.random.normal(5, 1, (100, 5))
data = np.concatenate([data0, data1], axis=0)
lap = laplacian_from_data(data, sigma=1.0)

# instantiate the GeoSinkhorn class
conv_sinkhorn = GeoSinkhorn(tau=1.0, order=10, method="cheb", lap=lap)

# create two signals
m_0 = np.zeros(200,)
m_0[:100] = 1
m_0 = m_0 / np.sum(m_0)
m_1 = np.zeros(200,)
m_1[100:] = 1
m_1 = m_1 / np.sum(m_1)

# compute the distance between the two signals
dist_w = conv_sinkhorn(m_0, m_1, max_iter=500)
print(dist_w)

Note that it is also possible to provide a graph instance directly to the GeoSinkhorn class with GeoSinkhorn(tau=1.0, order=10, method="cheb", graph=graph). The graph must have a Laplacian attribute graph.L. We suggest using a sparse Laplacian (e.g. in COO format) for better performance.

How to Cite

If you find this code useful in your research, please cite the following paper (expand for BibTeX):

Huguet, G., Tong, A., Zapatero, M. R., Tape, C. J., Wolf, G., & Krishnaswamy, S. (2023). Geodesic Sinkhorn for fast and accurate optimal transport on manifolds. In 2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing (MLSP).
@inproceedings{huguet2023geodesic,
  title={Geodesic Sinkhorn for fast and accurate optimal transport on manifolds},
  author={Huguet, Guillaume and Tong, Alexander and Zapatero, Mar{\'\i}a Ramos and Tape, Christopher J and Wolf, Guy and Krishnaswamy, Smita},
  booktitle={2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing (MLSP)},
  pages={1--6},
  year={2023},
  organization={IEEE}
}

Project details


Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

geosink-0.1.0.tar.gz (7.6 kB view hashes)

Uploaded Source

Built Distribution

geosink-0.1.0-py3-none-any.whl (6.7 kB view hashes)

Uploaded Python 3

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page