Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning Article Swipe

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Keaton Hamm , Nick Henscheid , Shujie Kang ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.1137/22m1490053

.In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlinear dimensionality reduction algorithms in imaging applications. Wassmap represents images via probability measures in Wasserstein space, then uses pairwise Wasserstein distances between the associated measures to produce a low-dimensional, approximately isometric embedding. We show that the algorithm is able to exactly recover parameters of some image manifolds, including those generated by translations or dilations of a fixed generating measure. Additionally, we show that a discrete version of the algorithm retrieves parameters from manifolds generated from discrete measures by providing a theoretical bridge to transfer recovery results from functional data to discrete data. Testing of the proposed algorithms on various image data manifolds shows that Wassmap yields good embeddings compared with other global and local techniques.Keywordsmanifold learningnonlinear dimensionality reductionoptimal transportWasserstein spaceIsomapMSC codes68T1049Q22

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Nonlinear Dimensionality Reduction

Mathematics

Computer Science

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Physics

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Mechanical Engineering

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Nonlinear dimensionality reduction Dimensionality reduction Embedding Mathematics Manifold (fluid mechanics) Pairwise comparison Measure (data warehouse) Curse of dimensionality Image (mathematics) Nonlinear system Computer science Algorithm Artificial intelligence Data mining Physics Engineering Mechanical engineering Quantum mechanics

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Type: article
Language: en
Landing Page: https://doi.org/10.1137/22m1490053
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Cited By: 16
References: 46
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DOI: https://doi.org/10.1137/22m1490053

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Title: Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning

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Publication year: 2023

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Authors: Keaton Hamm, Nick Henscheid, Shujie Kang

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Concepts: Nonlinear dimensionality reduction, Dimensionality reduction, Embedding, Mathematics, Manifold (fluid mechanics), Pairwise comparison, Measure (data warehouse), Curse of dimensionality, Image (mathematics), Nonlinear system, Computer science, Algorithm, Artificial intelligence, Data mining, Physics, Engineering, Mechanical engineering, Quantum mechanics

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Cited by: 16

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