Geometrical Optimization Toolbox
Switch branches/tags
Nothing to show
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Permalink
Type Name Latest commit message Commit time
Failed to load latest commit information.
Thirdparty
eg
kotz
manoptAuxiliary
means-medians
.gitignore
LICENSE.txt
README.md
generate_plots.m
install.m
install_eg.m
siam_plots.m

README.md

ABOUT

The GOPT toolbox contains functions for optimization over the manifold of PSD (HPD) matrices, as well as a collection of functions for computing maximum-likelihood estimates for Elliptical Gamma Distributions (EGDs) and calculating the KL-divergence between EGDs.

Please see the end of this README for a list of the algorithms available.

This toolbox is copyright (C) 2014 by Reshad Hosseini & Suvrit Sra and is distributed under the terms of the GNU General Public License (GPL) version 3 (or later).

Contact: Reshad Hosseini or Suvrit Sra

Quick installation guide

  • Unzip and copy the whole gopt directory you just downloaded in a location of your choice on disk, say, in /my/directory/.

  • Go to /my/directory/eg/ at the Matlab command prompt and execute 'install' (or 'install_eg'). You may save this path for your next Matlab sessions: follow the menu File . Set Path... and save.

##Directory structure##

./ The top directory with README.md
 |manoptAuxiliary   - Added solver and manifold (use with manopt)
   |--- lbfgsSolver/       - Manifold BFGS
   |--- pdManifold/        - psd and hpd classes 
   |--- wolfeLinesearch/   - Line search algorithm satisfy Wolfe conditions
 | means-medians/   - algos for means and medians of PSD matrices
 | examples/        - some examples showing how to use GOPT
 | eg/              - algorithms specific to EGDs
 | kotz/            - algorithms specific to Kotz type distributions
 | ThirdParty/      - Third party tools
   |--- randraw/          - m-function written by Alex Bar-Guy
   |--- manopt/           - the manopt toolbox
   |--- prettyPlot/       - our version of Mark Schmidt's plot tools

HOW TO CITE

If you find manifold LBFGS or the PSD (HPD) manifold useful in your work, please cite the following two papers:

@Article{gopt,
  title={Conic Geometric Optimization on the Manifold of Positive Definite Matrices},
  author={Sra, Suvrit and Hosseini, Reshad},
  journal={SIAM Journal on Optimization},
  volume={25},
  number={1},
  pages={713--739},
  year={2015},
  publisher={SIAM}
}

@Article{manopt,
  author  = {Nicolas Boumal and Bamdev Mishra and P.-A. Absil and Rodolphe Sepulchre},
  title   = {{M}anopt, a {M}atlab Toolbox for Optimization on Manifolds},
  journal = {Journal of Machine Learning Research},
  year    = {2014},
  volume  = {15},
  pages   = {1455--1459},
  url     = {http://www.manopt.org}
}

If you are using functions for estimating KL-divergence between EGDs or ML-estimation of parameters of EGD, please cite the following paper:

@Article{egd,
  author  = {Reshad Hosseini and Suvrit Sra and Lucas Theis and Matthias Bethge},
  title   = {Statistical Inference with the Elliptical Gamma Distribution},
  journal = {arXiv:1410.4812},
  year    = {2014},
}

ALGORITHMS

  • Fixed point iteration for S-Divergence means
  • Fixed point iteration for S-Divergence medians
  • Sampling based algorithm (of M. Bacak) for the Riemannian / Karcher Mean
  • Limited memory Riemannian BFGS algorithm for optimization over smooth manifolds using manopt
  • Fixed point iterations for ML estimation for EGDs
  • Numerical computation of KL-Divergence between EGDs
  • Fixed point iterations for ML estimation for Kotz type distributions

COMING UP

  • Manifold optimization algorithms for Riemannian Dictionary Learning (based on the paper: A. Cherian, S. Sra (Dictionary learning, sparse coding with PSD matrices)
  • Faster computation of matrix geometric means (S. Sra (2013))
  • Implementation of methods for computing matrix means and medians

Last updated Thu Jul 02 14:34:20 EST 2015