***************************** Tam Le RIKEN AIP October 24th, 2019 tam.le@riken.jp ***************************** NOTE: A valid positive definite Wasserstein kernel for persistence diagrams: exp(-TW/t) or exp(-TSW/t) Matlab code for tree-Wasserstein distance in the paper: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Tree-Sliced Variants of Wasserstein Distances Neural Information Processing Systems (NeurIPS/NIPS), 2019. Tam Le, Makoto Yamada, Kenji Fukumizu, Marco Cuturi ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Link https://arxiv.org/pdf/1902.00342.pdf @ Third party toolbox for the farthest-point clustering + figtreeKCenterClustering.m And mex-File for MAC and LINUX @ Illustrated data: + Subset_200.mat: containing 200 empirical measures + Subset_1000.mat: containing 1000 empirical measures @ Main functions for computing tree-Wasserstein distance + BuildTreeMetric_HighDim_V2.m: build tree metric from input empirical measures by using the farthest-point clustering approach + TreeMapping.m: tree representation vectors for new input empirical measure data. @ Examples: + testTreeWasserstein1.m: using empirical measures from Subset_1000.mat to construct tree metric, then compute tree-Wasserstein distance matrix for the same empirical measures from Subset_1000.mat. + testTreeWasserstein2.m: using empirical measures from Subset_200.mat to construct tree metric, then compute tree-Wasserstein distance matrix for new input empirical measure data from Subset_1000.mat