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Ascribe points in a list {xl ∈ Rn, l=1 . . . N} to the columns of a matrix. X = [ x1 · · · xN ] ∈ Rn×N (79) where N is regarded as cardinality of list X . When matrix D=[dij] is an EDM, its entries must be related to those points constituting the list by the Euclidean distance-square: for i, j =1 . . .
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.
If the $v_i$ are mean-centered ($\sum_i v_i = 0$) then the Gramian matrix can be calculated from the Euclidean distance matrix by $G = -\frac{1}{2}CDC,$ where $C = I - \frac{1}{n}\bf{1}^T \bf{1}$ is the n-by-n centering matrix.
29 mar 2014 · If you are looking for the most efficient way of computation - use SciPy's cdist() (or pdist() if you need just vector of pairwise distances instead of full distance matrix) as suggested in Tweakimp's comment.
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...
How do we reconstruct the molecule? Density map and structure of a molecule [10.7554/elife.01345] Euclidean Distance Matrix. Consider a set of n points X 2 Rd n, edm(X) contains the squared distances between the points, Equivalently, edm(X) = 1 diag(XTX)T. 2XTX + diag(XTX)1T. EDM properties: rank and essential uniqueness.
Euclidean distance. The immediate consequence of this is that the squared length of a vector x = [ x1 x2 ] is the sum of the squares of its coordinates (see triangle OPA in Exhibit 4.2, or triangle OPB – . | denotes the squared length of x, that is the distance between point O and P); and the .
