Euclidean Distance Geometry

By John C. Gower. 1982

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Citations in the corpus

On the Schoenberg Transformations in Data Analysis: Theory and Illustrations (2010, background): “Other choices such as the circumcenter or the incenter are discussed in Gower (1982).”
Structured inverse eigenvalue problems (2002, unknown): “The molecular structure modelling for protein folding in R3 involves Euclidean distance matrices whose rank is no more than 5 (Glunt, Hayden, Hong and Wells 1990, Gower 1982).”
Hadamard inverses, square roots and products of almost semidefinite matrices (1999, background): “8 to give a simple proof of a well-known result for distance matrices (distance matrices are almost negative semidefinite matrices with positive offdiagonal entries, and zeroes on the diagonal [10],[19]).”
On Euclidean distance matrices (2007, methodology): “If D is a EDM, Gower [8] proved that 1 is in the column space of D and 1′D†1 0.”
From Classical to Canonical Ordination (2012, background): “A principal coordinate analysis of the distance matrices produced by these coefficients may generate negative eigenvalues; these eigenvalues indicate the non-Euclidean nature of the distance matrix (Gower 1982).”
A Generalized Kernel Approach to Dissimilarity-based Classification (2002, background): “The matrix B = − 1 2 J D (2) J is positive definite if and only if the distance matrix D ∈ R n×n is Euclidean (Borg and Groenen, 1997, Gower, 1986, 1982).”
Euclidean Distance Matrices: Essential theory, algorithms, and applications (2015, methodology): “A number of analytical results on EDMs were developed by Gower [16], [17].”
A distance-based framework for measuring functional diversity from multiple traits. (2010, background): “Indeed, some distance matrices will not allow the distance relationships among the objects to be fully represented in a Euclidean space (Gower 1982).”
The Proximity of an Individual to a Population with Applications in Discriminant Analysis (1997, unknown): “However, for any Euclideanrepresentation, (Gower 1982, Eq.”
Distributed Sensor Localization in Random Environments Using Minimal Number of Anchor Nodes (2008, background): “Completion of partially specified distance matrices is considered in [25] and [26].”
Generating valid Euclidean distance matrices (2019, background): “diagonal) symmetric matrix D~ and then weakly enforce D~ 2EDMnthrough a term in the loss. It can be shown that D~ 2EDMn, 1 2 JDJ~ positive semi-deﬁnite; (1) where J= I 1 n 11 >and 1 = (1;:::;1) 2Rn[33, 34]. However trying to use this relationship directly in the context of deep learning by parame”
Euclidean Distance Geometry and Applications (2012, background): “lidean distance matrix” to X 0, is derived by means of the statement that D is a Euclidean distance matrix if and only if D is negative semideﬁnite on the orthogonal complement of the all-one vector [81, 177] (see Sect. 3.4.4). In turn, this is related to Thm. 2.2. In [32, 60], interestingly, the co”
The communicability distance in graphs (2012, background): “Then, it is known from the theory of Euclidean distances [14–17] that ξpq has the following properties:”
Matching Node Embeddings for Graph Similarity (2017, background): “It would be very convenient if D was a Euclidean Distance Matrix (EDM) (Gower 1982; Gower and Legendre 1986).”