Random projections decrease the dimensionality of a finite set of vectors while ensuring approx- imate congruence, up to a multiplicative constant. Based on the theory of random projections in conic programming we derive an application of random projections to a nonconvex mathematical programming problem in distance geometry, namely that of finding the positions of the vertices of a graph in a vector space of given dimension, while ensuring that every pair of adjacent vertices is placed at a Euclidean distance equal to the corresponding edge weight.
Random projections for the distance geometry problem
Benedetto Manca;
2022-01-01
Abstract
Random projections decrease the dimensionality of a finite set of vectors while ensuring approx- imate congruence, up to a multiplicative constant. Based on the theory of random projections in conic programming we derive an application of random projections to a nonconvex mathematical programming problem in distance geometry, namely that of finding the positions of the vertices of a graph in a vector space of given dimension, while ensuring that every pair of adjacent vertices is placed at a Euclidean distance equal to the corresponding edge weight.
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