E. Cazelles, V. Seguy, J. Bigot, M. Cuturi, N. Papadakis, 'Geodesic PCA versus Log-PCA of histograms in the Wasserstein space', https://arxiv.org/abs/1708.08143
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toolbox
README.md
algo_GPCA_1D_iter.m
algo_GPCA_1D_surface.m
test_GPCA_vs_logPCA.m

README.md

2017-GPCA-vs-LogPCA-Wasserstein

Matlab code to reproduce the results of the paper 'Geodesic PCA versus Log-PCA of histograms in the Wasserstein space', E. Cazelles, V. Seguy, J. Bigot, M. Cuturi, N. Papadakis

Arxiv: https://arxiv.org/abs/1708.08143

Content :

test_GPCA_vs_logPCA.m : main script to launch the computation for Gaussian data. Display the figures :

 1- Gaussian data    
 2- True Wasserstein barycenter of the data
 3- Data projection along principal component in Euclidean PCA     
 4- Reprensentation of the 1st and 2nd components of the Euclidean PCA    
 5- Smooth barycenter of the data     
 6- Log-maps of the data at the barycenter     
 7- Exponential map of the data at the barycenter     
 8- Data projection along principal component in log-PCA    
 9- Representation of the 1st and 2nd components of log-PCA    
 10- Representation of the 1st and 2nd components and the principal geodesic surface of the iterative geodesic approach    
 11- Representation of the 1st and 2nd components and the principal geodesic surface of the geodesic surface approach   
 12- Comparison between projections of the data onto iterative PG and log-PC

algo_GPCA_1D_surface.m : Compute principal geodesics via Geodesic surface approach

algo_GPCA_1D_iter.m : Compute principal geodesics via Iterative Geodesic approach

toolbox/ : various helper functions