Multidimensional Unfolding in a Case of Extremely Low Number of Targets
УДК 519.6 + 519.25
Abstract
Let the set of objects under study be divided into two parts — the set of observers and the set of targets. There is a problem of multidimensional unfolding when visualizing this set using incomplete data of pairwise distances or differences between them and only the distances between each observer and each of the targets are known. Typically, the known methods to solve such problem involve filling the missing positions in the matrix of pairwise differences using one way or another. Also, it is considered that the two sets (both observers and targets) of objects contain at least two or three elements. In this paper, an algorithm to solve the multidimensional unfolding problem for a single element set of targets is considered. Traditional approaches are not applicable to this practically important case. Therefore, the maximization of the minimum of distances between observers is used to select the best solution from a sufficiently large class of possible ones. Practical aspects are discussed, and a simple non-iterative method to solve the multidimensional unfolding problem for the case of two targets is proposed.
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