高维(鲁棒)Wasserstein对准的数据依赖方法

Q2 Mathematics
Hu Ding, Wenjie Liu, Mingquan Ye
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引用次数: 0

摘要

许多现实世界中的问题可以公式化为两个几何图案之间的对齐。以前,在计算机视觉领域,大量的研究集中在2D或3D图案的对齐上。最近,高维对准问题在实践中发现了一些新的应用。然而,在算法方面的研究仍然相当有限。据我们所知,大多数现有的方法只是对2D和3D情况下的对应方法的简单扩展,并且经常存在计算复杂度高等问题。在本文中,我们提出了一个有效的框架来压缩高维几何图案。任何现有的对准方法都可以应用于压缩的几何图案,并且可以显著降低时间复杂性。我们的想法受到了高维数据通常具有低内在维度的观察的启发。我们的框架是一种“依赖数据”的方法,其复杂性取决于输入数据的内在维度。我们的实验结果表明,与在原始模式上的结果相比,在压缩模式上运行对齐算法可以获得类似的质量,但运行时间(包括压缩的时间成本)要低得多。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Data-dependent Approach for High Dimensional (Robust) Wasserstein Alignment
Many real-world problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns in the field of computer vision. Recently, the alignment problem in high dimensions finds several novel applications in practice. However, the research is still rather limited in the algorithmic aspect. To the best of our knowledge, most existing approaches are just simple extensions of their counterparts for 2D and 3D cases, and often suffer from the issues such as high computational complexities. In this paper, we propose an effective framework to compress the high dimensional geometric patterns. Any existing alignment method can be applied to the compressed geometric patterns and the time complexity can be significantly reduced. Our idea is inspired by the observation that high dimensional data often has a low intrinsic dimension. Our framework is a “data-dependent” approach that has the complexity depending on the intrinsic dimension of the input data. Our experimental results reveal that running the alignment algorithm on compressed patterns can achieve similar qualities, comparing with the results on the original patterns, but the runtimes (including the times cost for compression) are substantially lower.
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来源期刊
Journal of Experimental Algorithmics
Journal of Experimental Algorithmics Mathematics-Theoretical Computer Science
CiteScore
3.10
自引率
0.00%
发文量
29
期刊介绍: The ACM JEA is a high-quality, refereed, archival journal devoted to the study of discrete algorithms and data structures through a combination of experimentation and classical analysis and design techniques. It focuses on the following areas in algorithms and data structures: ■combinatorial optimization ■computational biology ■computational geometry ■graph manipulation ■graphics ■heuristics ■network design ■parallel processing ■routing and scheduling ■searching and sorting ■VLSI design
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