The paper introduces a new slicing operator called Hierarchical Hybrid Radon Transform (HHRT) to handle heterogeneous joint distributions. HHRT first applies Partial Generalized Radon Transform (PGRT) on each marginal argument to capture the information within each marginal, and then applies Partial Radon Transform (PRT) on the joint transformed arguments from all marginals to gather information among the marginals.
The authors then define the Hierarchical Hybrid Sliced Wasserstein (H2SW) distance using the HHRT as the slicing operator. They analyze the topological, statistical, and computational properties of H2SW, showing that it is a valid metric, does not suffer from the curse of dimensionality, and enjoys the same computational scalability as the original Sliced Wasserstein (SW) distance.
The authors demonstrate the favorable performance of H2SW compared to SW and Generalized Sliced Wasserstein (GSW) in 3D mesh deformation, deep 3D mesh autoencoder training, and dataset comparison on the product of Hadamard manifolds.
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by Khai Nguyen,... at arxiv.org 04-25-2024
https://arxiv.org/pdf/2404.15378.pdfDeeper Inquiries