2017/11/16 by Nilson Moreira, Moreira, Nilson, Leonardo Tomazeli Duarte +5
Computer Science · Engineering · #FOS: Mathematics #Face and Expression Recognition #Indoor and Outdoor Localization Technologies #Optical measurement and interference techniques #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1711.06182
openalex publication_date 2017/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Euclidean Distance Matrix (EDM) is a table of distance-square between\npoints on a k- dimensional Euclidean space, with applications in many fields\n(e.g. engineering, geodesy, economics, genetics, biochemistry, psychology). A\nproblem that often arises is the absence (or uncertainty) of some EDM elements.\nIn many situations, only a subset of all pairwise distances is available and it\nis desired to have some procedure to estimate the missing distances. In this\npaper, we address the problem of missing data in EDM through low-rank matrix\ncompletion techniques. We exploit the fact that the rank of a EDM is at most\nk+2 and does not depend on the number of points, which is, in general, much\nbigger then k. We use a Singular Value Decomposition approach that considers\nthe rank of the matrix to be completed and computes, in each iteration, a\nparameter that controls the convergence of the method. After performing a\nnumber of computational experiments, we could observe that our proposal was\nable to recover, with high precision, random EDMs with more than one thousand\npoints and up to 98 percent of missing data in few minutes. Additionally, our\nmethod required a smaller number of iterations when compared to other\ncompetitive state-of-art technique.\n