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Explore a 37-minute lecture from the ESI's Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications" that delves into the Gromov-Wasserstein (GW) distance and its applications in data science and machine learning. Learn about the collaborative work between Martin Bauer, Facundo Mémoli, Mao Nishino, and the speaker in developing Z-Gromov-Wasserstein (Z-GW) distance, a generalization that introduces Z-networks as measure spaces with Z-valued kernels. Discover the geometric and topological properties of Z-GW distances and their practical applications in shape analysis, particularly focusing on shape graphs - graph structures with shape-endowed edges used in analyzing filamentary structures like arterial and road networks.
