Branch and bound algorithm for multidimensional scaling with city-block metric |
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Authors: | Antanas ?ilinskas Julius ?ilinskas |
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Institution: | 1. Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, 03225, Vilnius, Lithuania 2. Vilnius Gediminas Technical University, Saul?tekio 11, 10223, Vilnius, Lithuania
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Abstract: | A two level global optimization algorithm for multidimensional scaling (MDS) with city-block metric is proposed. The piecewise quadratic structure of the objective function is employed. At the upper level a combinatorial global optimization problem is solved by means of branch and bound method, where an objective function is defined as the minimum of a quadratic programming problem. The later is solved at the lower level by a standard quadratic programming algorithm. The proposed algorithm has been applied for auxiliary and practical problems whose global optimization counterpart was of dimensionality up to 24. |
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