论文标题
在等距到符号设置中表面上距离的距离和最小歧管学习的最小值估计
Minimax Estimation of Distances on a Surface and Minimax Manifold Learning in the Isometric-to-Convex Setting
论文作者
论文摘要
我们首先考虑在平滑的子手机上估算固有距离的问题。我们表明，为此目的，可以通过对表面的重构进行重建，并讨论特定网格结构（切向Delaunay复合物）的使用。然后，我们转向多种学习，并认为ISOMAP的变体在重建的表面上计算距离是最小值，对于问题的等值变体而言是最佳的。
We start by considering the problem of estimating intrinsic distances on a smooth submanifold. We show that minimax optimality can be obtained via a reconstruction of the surface, and discuss the use of a particular mesh construction -- the tangential Delaunay complex -- for that purpose. We then turn to manifold learning and argue that a variant of Isomap where the distances are instead computed on a reconstructed surface is minimax optimal for the isometric variant of the problem.
