A hybrid global optimization algorithm for multidimensional scaling

Authors

R. Mathar,

Abstract

        Local search algorithms in Multidimensional Scaling (MDS), based on gradients or subgradients, often get stuck at local minima of STRESS, particularly if the underlying dissimilarity matrix is far from being Euclidean. However, in order to remove ambiguity from the model building process, it is of paramount interest to fit a suggested model best to a given data set. Hence, finding the global minimum of STRESS is very important for applications of MDS.

In this paper a hybrid iteration scheme is suggested consisting of a local optimization phase and a genetic type global optimization step. Local search is based on the simple and fast majorization approach. Extensive numerical testing shows that the presented method has a high success probability and clearly outperforms simple random multistart.

BibTEX Reference Entry 

@inbook{Ma97b,
	author = {Rudolf Mathar},
	title = "A hybrid global optimization algorithm for {M}ultidimensional {S}caling",
	pages = "63-71",
	publisher = "Springer-Verlag",
	series = "Classification and Knowledge Organization",
	editor = "R. Klar, O.Opitz",
	address = "Heidelberg",
	year = 1997,
	hsb = RWTH-CONV-223635,
	}

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