KLAP: Galerkin spectral decomposition

Topic

Fast Implementation of Galerkin eigenvectors and eigenvalues estimation with kernel methods developped in [PIL20], [CAB21], [PIL23], [CAB23].

Author

Vivien Cabannes

Nighly Version

0.0.3

Stable Version

0.0.2 of 2023/03/21

Installation

From wheel

You can download our package from its pypi repository.

$ pip install klap

From source

You can download source code at https://github.com/VivienCabannes/laplacian/archive/master.zip. Once download, our packages can be install through the following command.

$ cd <path to code folder>
$ pip install -e .

The -e option is notably useful to add kernel and modify the codebase.

Usage

See notebooks folder.

Package Requirements

Most of the code is based on the following python libraries:

• scipy
• numpy
• numba

Testing done with notebook are based on:

• jupyter-notebook
• matplotlib
• pandas

The code could easily be rewritten for pytorch (with jit support). For generalized eigenvalues decomposition, see torch.lobpcg.

References

CAB21

Overcoming the curse of dimensionality with Laplacian regularization in semi-supervised learning, Vivien Cabannes, Loucas Pillaud-Vivien, Francis Bach and Alessandro Rudi, NeurIPS, 2021.

CAB23

Going Deeper with Spectral Decomposition, Loucas Pillaud-Vivien and Francis Bach, ArXiv, 2023.

PIL20

Statistical estimation of the poincaré constant and application to sampling multimodal distributions, Loucas Pillaud-Vivien, Francis Bach, Tony Lelièvre, Alessandro Rudi, Gabriel Stoltz, AISTATS, 2020.

PIL23

Kernelized Diffusion maps, Loucas Pillaud-Vivien and Francis Bach, COLT, 2023.