论文标题
WASSMAP：图像歧管学习的Wasserstein等距映射
Wassmap: Wasserstein Isometric Mapping for Image Manifold Learning
论文作者
论文摘要
在本文中，我们提出了WasSerstein等距映射（WassMap），这是一种非线性降低降低技术，可为成像应用中现有的全球非线性降低算法中的某些缺点提供解决方案。 WASSMAP通过Wasserstein空间中的概率度量表示图像，然后在相关措施之间使用成对的Wasserstein距离来产生低维，近似等距的嵌入。我们表明，该算法能够精确恢复某些图像歧管的参数，包括通过固定生成度量的翻译或扩张产生的参数。此外，我们表明，该算法的离散版本从离散度量产生的流形中检索参数，通过提供从功能数据传输恢复的理论桥梁到离散数据。在各种图像数据歧管上对所提出的算法进行测试表明，与其他全球和本地技术相比，wassmap可以产生良好的嵌入。
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 show that Wassmap yields good embeddings compared with other global and local techniques.
