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