论文标题
用于高维（健壮）WasSerstein对齐的数据依赖性方法
A Data-dependent Approach for High Dimensional (Robust) Wasserstein Alignment
论文作者
论文摘要
许多实际问题可以作为两种几何模式之间的对齐方式提出。以前，大量的研究集中在计算机视觉领域中2D或3D模式的对齐方式。最近，高维度中的一致性问题在实践中发现了一些新的应用。但是，该研究在算法方面仍然相当有限。据我们所知，大多数现有的方法只是对2D和3D案例的简单扩展，并且经常遭受诸如高计算复杂性之类的问题。在本文中，我们提出了一个有效的框架来压缩高维几何模式。任何现有的比对方法都可以应用于压缩的几何模式，并且可以大大降低时间复杂性。我们的想法的灵感来自观察到高维数据通常具有较低的内在维度。我们的框架是一种``数据依赖性''方法，它具有复杂性，具体取决于输入数据的内在维度。我们的实验结果表明，与原始模式的结果相比，在压缩模式上运行对齐算法可以达到相似的质量，但是运行时间（包括压缩的时间成本）大大降低。
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.
