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In this paper we consider various methods for nonmetric multidimensional scaling. We focus on the nonmetric phase, for which we consider various alternatives: Kruskal's nonmetric phase, Guttman's nonmetric phase, monotone regression by monotone splines, and monotone regression by a monotone neural network. All methods are briefly described. We use sequential quadratic programming to estimate the weights of the neural network. An experimental comparison of the methods is given for various synthetic and real-life datasets. The monotone neural network performs comparable to the traditional methods.