Global Optimization Methods for Multidimensional Scaling Applied to Mobile Communications

The purpose of this paper is to present a short overview of recent developments of global optimization in least squares multidimensional scaling. Three promising candidates —the genetic algorithm, simulated annealing, and distance smoothing— are discussed in more detail and compared on a data set arising in mobile communication.

[1]  J. Kruskal.  Nonmetric multidimensional scaling: A numerical method , 1964 .

[2]  D. Defays.  A short note on a method of seriation , 1978 .

[3]  Leen Stougie,et al.  Global optimization : a stochastic approach , 1980 .

[4]  I. Borg,et al.  Geometric Representations of Relational Data , 1981 .

[5]  J. Meulman.  A Distance Approach to Nonlinear Multivariate Analysis , 1986 .

[6]  G. T. Timmer,et al.  Stochastic global optimization methods part I: Clustering methods , 1987, Math. Program..

[7]  G. T. Timmer,et al.  Stochastic global optimization methods part II: Multi level methods , 1987, Math. Program..

[8]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[9]  J. Leeuw.  Convergence of the majorization method for multidimensional scaling , 1988 .

[10]  J. Leeuw,et al.  Multidimensional Data Analysis , 1989 .

[11]  D. E. Goldberg,et al.  Genetic Algorithms in Search, Optimization & Machine Learning , 1989 .

[12]  Timothy F. Havel.  An evaluation of computational strategies for use in the determination of protein structure from distance constraints obtained by nuclear magnetic resonance. , 1991, Progress in biophysics and molecular biology.

[13]  J. Meulman.  The integration of multidimensional scaling and multivariate analysis with optimal transformations , 1992 .

[14]  Mouzid Machmouchi.  Contributions à la mise en oeuvre des méthodes d'analyse des données de dissimilarité , 1992 .

[15]  Patrick J. F. Groenen,et al.  The majorization approach to multidimensional scaling : some problems and extensions , 1993 .

[16]  Marcos Raydan,et al.  Molecular conformations from distance matrices , 1993, J. Comput. Chem..

[17]  Patrick J. F. Groenen,et al.  A Comparison of Two Methods for Global Optimization in Multidimensional Scaling , 1993 .

[18]  Rudolf Mathar,et al.  A class of test functions for global optimization , 1994, J. Glob. Optim..

[19]  Michael P. Windham,et al.  Information and classification: Concepts, methods and applications , 1995 .

[20]  V. Pliner.  Metric unidimensional scaling and global optimization , 1996 .

[21]  P. Groenen,et al.  The tunneling method for global optimization in multidimensional scaling , 1996 .

[22]  R. Mathar.  A Hybrid Global Optimization Algorithm for Multidimensional Scaling , 1997 .

[23]  Otto Opitz,et al.  Classification and Knowledge Organization , 1997 .

[24]  P. Groenen,et al.  Global Optimization in Least-Squares Multidimensional Scaling by Distance Smoothing , 1999 .

[25]  P. Groenen,et al.  Modern Multidimensional Scaling: Theory and Applications , 1999 .