Riemannian Optimization for Euclidean Distance Geometry

Chandler Mack Smith, Samuel P. Lichtenberg, HanQin Cai, Abiy Tasissa

Keywords: Euclidean Distance Geometry, Matrix Completion, Riemannian Optimization

TL;DR: In this paper we define a novel Euclidean Distance Geometry algorithm fusing a dual-basis approach with Riemannian matrix completion techniques.

Abstract:

The Euclidean distance geometry (EDG) problem is a crucial machine learning task that appears in many applications. Utilizing the pairwise Euclidean distance information of a given point set, EDG reconstructs the configuration of the point system. When only partial distance information is available, matrix completion techniques can be incorporated to fill in the missing pairwise distances. In this paper, we propose a novel dual basis Riemannian gradient descent algorithm, coined RieEDG, for the EDG completion problem. The numerical experiments verify the effectiveness of the proposed algorithm. In particular, we show that RieEDG can precisely reconstruct various datasets consisting of 2- and 3-dimensional points by accessing a small fraction of pairwise distance information.

Submission Number: 67