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Books and survey papers containing a treatment of Euclidean distance matrices in-clude, for example, [31, 44, 87], and most recently [3]. The topic of rank mini-mization for Euclidean distance matrix problems is discussed in, for example, [34, 35, 55, 56, 99, 100].
The issue stems from the element-wise square rooting operation. Since d( x) = p 1 dx, 2 x any zero values in the distance matrix will produce infinite gradients. This is encountered, for example, when implementing a contrastive loss [3] (see [4] for details).
1 sty 2011 · 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 an EDM.We...
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.
The nearest (or approximate) Euclidean distance matrix problem is to find a Euclidean distance matrix, EDM, that is nearest in the Frobenius norm to the matrix A, when the free variables are discounted. In this paper we introduce two algorithms: one for the exact completion problem and one for the approximate completion problem.
3.1] A Euclidean distance matrix, an EDM in RN×N +, is an exhaustive table of distance-square dij between points taken by pair from a list of N points {xℓ, ℓ=1...N} in Rn; the squared metric, the measure of distance-square: dij = kxi − xjk 2 2, hxi − xj, xi − xji (1037)
For examples of applications requiring solutions of EDM problems with different complications, see Figure 1. There are two fundamental problems associated with distance geometry [10]: 1) given a matrix, determine whether it is an EDM and 2) given a possibly incomplete set of distances, determine
