ON THE EXISTENCE OF A SOLUTION IN METRIC MULTIDIMENSIONAL SCALING

Abstract

A minimization problem in metric multidimensional scaling is discussed. Each object is embeded as a point in t-dimensional Euclidean space such that the points minimize the sum of Euclidean norm between the mean of dissimilarity value and Euclidean distance of two points. The existence of a solution which attains the minimum value of the least squares criterion is shown.