- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 890589, 15 pages
An Improved Exact Algorithm for Least-Squares Unidimensional Scaling
Faculty of Informatics, Kaunas University of Technology, Studentu 50-408, 51368 Kaunas, Lithuania
Received 16 October 2012; Accepted 31 March 2013
Academic Editor: Frank Werner
Copyright © 2013 Gintaras Palubeckis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- I. Borg and P. J. F. Groenen, Modern Multidimensional Scaling: Theory and Appplications, Springer, New York, NY, USA, 2nd edition, 2005.
- L. Hubert, P. Arabie, and J. Meulman, The Structural Representation of Proximity Matrices with MATLAB, vol. 19, SIAM, Philadelphia, Pa, USA, 2006.
- S. Meisel and D. Mattfeld, “Synergies of Operations Research and Data Mining,” European Journal of Operational Research, vol. 206, no. 1, pp. 1–10, 2010.
- G. Caraux and S. Pinloche, “PermutMatrix: a graphical environment to arrange gene expression profiles in optimal linear order,” Bioinformatics, vol. 21, no. 7, pp. 1280–1281, 2005.
- M. K. Ng, E. S. Fung, and H.-Y. Liao, “Linkage disequilibrium map by unidimensional nonnegative scaling,” in Proceedings of the 1st International Symposium on Optimization and Systems Biology (OSB '07), pp. 302–308, Beijing, China, 2007.
- P. I. Armstrong, N. A. Fouad, J. Rounds, and L. Hubert, “Quantifying and interpreting group differences in interest profiles,” Journal of Career Assessment, vol. 18, no. 2, pp. 115–132, 2010.
- L. Hubert and D. Steinley, “Agreement among supreme court justices: categorical versus continuous representation,” SIAM News, vol. 38, no. 7, 2005.
- A. Dahabiah, J. Puentes, and B. Solaiman, “Digestive casebase mining based on possibility theory and linear unidimensional scaling,” in Proceedings of the 8th WSEAS International Conference on Artificial Intelligence, Knowledge Engineering and Data Bases (AIKED '09), pp. 218–223, World Scientific and Engineering Academy and Society (WSEAS), Stevens Point, Wis, USA, 2009.
- A. Dahabiah, J. Puentes, and B. Solaiman, “Possibilistic pattern recognition in a digestive database for mining imperfect data,” WSEAS Transactions on Systems, vol. 8, no. 2, pp. 229–240, 2009.
- Y. Ge, Y. Leung, and J. Ma, “Unidimensional scaling classifier and its application to remotely sensed data,” in Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS '05), pp. 3841–3844, July 2005.
- J. H. Bihn, M. Verhaagh, M. Brändle, and R. Brandl, “Do secondary forests act as refuges for old growth forest animals? Recovery of ant diversity in the Atlantic forest of Brazil,” Biological Conservation, vol. 141, no. 3, pp. 733–743, 2008.
- D. Defays, “A short note on a method of seriation,” British Journal of Mathematical and Statistical Psychology, vol. 31, no. 1, pp. 49–53, 1978.
- M. J. Brusco and S. Stahl, “Optimal least-squares unidimensional scaling: improved branch-and-bound procedures and comparison to dynamic programming,” Psychometrika, vol. 70, no. 2, pp. 253–270, 2005.
- L. J. Hubert and P. Arabie, “Unidimensional scaling and combinatorial optimization,” in Multidimensional Data Analysis, J. de Leeuw, W. J. Heiser, J. Meulman, and F. Critchley, Eds., pp. 181–196, DSWO Press, Leiden, The Netherlands, 1986.
- L. J. Hubert, P. Arabie, and J. J. Meulman, “Linear unidimensional scaling in the -norm: basic optimization methods using MATLAB,” Journal of Classification, vol. 19, no. 2, pp. 303–328, 2002.
- M. J. Brusco and S. Stahl, Branch-and-Bound Applications in Combinatorial Data Analysis, Springer Science + Business Media, New York, NY, USA, 2005.
- V. Pliner, “Metric unidimensional scaling and global optimization,” Journal of Classification, vol. 13, no. 1, pp. 3–18, 1996.
- A. Murillo, J. F. Vera, and W. J. Heiser, “A permutation-translation simulated annealing algorithm for and unidimensional scaling,” Journal of Classification, vol. 22, no. 1, pp. 119–138, 2005.
- M. J. Brusco, “On the performance of simulated annealing for large-scale unidimensional scaling,” Journal of Classification, vol. 23, no. 2, pp. 255–268, 2006.
- M. J. Brusco, H. F. Köhn, and S. Stahl, “Heuristic implementation of dynamic programming for matrix permutation problems in combinatorial data analysis,” Psychometrika, vol. 73, no. 3, pp. 503–522, 2008.
- G. Palubeckis, “Iterated tabu search for the maximum diversity problem,” Applied Mathematics and Computation, vol. 189, no. 1, pp. 371–383, 2007.
- G. Palubeckis, “A new bounding procedure and an improved exact algorithm for the Max-2-SAT problem,” Applied Mathematics and Computation, vol. 215, no. 3, pp. 1106–1117, 2009.
- J. Kluabwang, D. Puangdownreong, and S. Sujitjorn, “Multipath adaptive tabu search for a vehicle control problem,” Journal of Applied Mathematics, vol. 2012, Article ID 731623, 20 pages, 2012.
- N. Sarasiri, K. Suthamno, and S. Sujitjorn, “Bacterial foraging-tabu search metaheuristics for identification of nonlinear friction model,” Journal of Applied Mathematics, vol. 2012, Article ID 238563, 23 pages, 2012.
- A. Jouglet and J. Carlier, “Dominance rules in combinatorial optimization problems,” European Journal of Operational Research, vol. 212, no. 3, pp. 433–444, 2011.
- E. Z. Rothkopf, “A measure of stimulus similarity and errors in some paired-associate learning tasks,” Journal of Experimental Psychology, vol. 53, no. 2, pp. 94–101, 1957.
- I. Düntsch and G. Gediga, “Modal-Style Operators in Qualitative Data Analysis,” Tech. Rep. CS-02-15, Department of Computer Science, Brock University, St. Catharines, Ontario, Canada, 2002.
- R. N. Shepard, “Analysis of proximities as a technique for the study of information processing in man,” Human factors, vol. 5, pp. 33–48, 1963.
- P. J. F. Groenen and W. J. Heiser, “The tunneling method for global optimization in multidimensional scaling,” Psychometrika, vol. 61, no. 3, pp. 529–550, 1996.
- L. Hubert, P. Arabie, and J. Meulman, Combinatorial Data Analysis: Optimization by Dynamic Programming, SIAM, Philadelphia, Pa, USA, 2001.
- B. H. Ross and G. L. Murphy, “Food for thought: cross-classification and category organization in a complex real-world domain,” Cognitive Psychology, vol. 38, no. 4, pp. 495–553, 1999.