Computing the nearest Euclidean distance matrix with low embedding dimensions

Computing the nearest Euclidean distance matrix with low embedding dimensions

Euclidean distance embedding appears in many high-profile applications including wireless sensor network localization, where not all pairwise distances among sensors are known or accurate. The classical Multi-Dimensional Scaling (cMDS) generally works well when the partial or contaminated Euclidean Distance Matrix (EDM) is close to the true EDM, but otherwise performs poorly. A natural step pre...

Structure method for solving the nearest Euclidean distance matrix problem

*Correspondence: [email protected] Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia Abstract A matrix with zero diagonal is called a Euclidean distance matrix when the matrix values are measurements of distances between points in a Euclidean space. Because of data errors such a matrix may not be exactly Euclidean and it is desira...

Computing the Nearest Correlation Matrix

A Semismooth Newton Method for the Nearest Euclidean Distance Matrix Problem

The Nearest Euclidean distance matrix problem (NEDM) is a fundamental computational problem in applications such as multidimensional scaling and molecular conformation from nuclear magnetic resonance data in computational chemistry. Especially in the latter application, the problem is often large scale with the number of atoms ranging from a few hundreds to a few thousands. In this paper, we in...

Euclidean distance matrix completion problems

A Euclidean distance matrix is one in which the (i, j) entry specifies the squared distance between particle i and particle j. Given a partially-specified symmetric matrix A with zero diagonal, the Euclidean distance matrix completion problem (EDMCP) is to determine the unspecified entries to make A a Euclidean distance matrix. We survey three different approaches to solving the EDMCP.We advoca...