  A Euclidean Distance Matrix (EDM) is a table of distance-square between
points on a k- dimensional Euclidean space, with applications in many fields
(e.g. engineering, geodesy, economics, genetics, biochemistry, psychology). A
problem that often arises is the absence (or uncertainty) of some EDM elements.
In many situations, only a subset of all pairwise distances is available and it
is desired to have some procedure to estimate the missing distances. In this
paper, we address the problem of missing data in EDM through low-rank matrix
completion techniques. We exploit the fact that the rank of a EDM is at most
k+2 and does not depend on the number of points, which is, in general, much
bigger then k. We use a Singular Value Decomposition approach that considers
the rank of the matrix to be completed and computes, in each iteration, a
parameter that controls the convergence of the method. After performing a
number of computational experiments, we could observe that our proposal was
able to recover, with high precision, random EDMs with more than one thousand
points and up to 98 percent of missing data in few minutes. Additionally, our
method required a smaller number of iterations when compared to other
competitive state-of-art technique.
