GW-MDS reformulates multidimensional scaling as a Gromov-Wasserstein minimization problem and shows embeddings whose pairwise distances correlate with the original ones comparably to MDS and Isomap.
Recent Advances in Optimal Transport for Machine Learning
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abstract
Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to different problems in machine learning, such as generative modeling and transfer learning. In this survey we explore contributions of Optimal Transport for Machine Learning over the period 2012 -- 2023, focusing on four sub-fields of Machine Learning: supervised, unsupervised, transfer and reinforcement learning. We further highlight the recent development in computational Optimal Transport and its extensions, such as partial, unbalanced, Gromov and Neural Optimal Transport, and its interplay with Machine Learning practice.
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A dimensionality reduction technique based on the Gromov-Wasserstein distance
GW-MDS reformulates multidimensional scaling as a Gromov-Wasserstein minimization problem and shows embeddings whose pairwise distances correlate with the original ones comparably to MDS and Isomap.