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Non-Metric Multidimensional Scaling using Simulated Annealing  

Lee, Chang-Yong (공주대학교 산업시스템공학과)
Lee, Dong-Ju (공주대학교 산업시스템공학과)
Publication Information
Journal of KIISE:Computing Practices and Letters / v.16, no.6, 2010 , pp. 648-653 More about this Journal
Abstract
The non-metric multidimensional scaling (nMDS) is a method for analyzing the relation among objects by mapping them onto the Euclidean space. The nMDS is useful when it is difficult to use the concept of distance between pairs of objects due to non-metric dissimilarities between objects. The nMDS can be regarded as an optimization problem in which there are many local optima. Since the conventional nMDS algorithm utilizes the steepest descent method, it has a drawback in that the method can hardly find a better solution once it falls into a local optimum. To remedy this problem, in this paper, we applied the simulated annealing to the nMDS and proposed a new optimization algorithm which could search for a global optimum more effectively. We examined the algorithm using benchmarking problems and found that improvement rate of the proposed algorithm against the conventional algorithm ranged from 0.7% to 3.2%. In addition, the statistical hypothesis test also showed that the proposed algorithm outperformed the conventional one.
Keywords
Non-metric multidimensional scaling; simulated annealing; pure nMDS; global optimum; random network;
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