Two-way multidimensional scaling: A review

IEEE Transactions on Systems, Man and Cybernetics Part C: Applications and Reviews

Volumn 41, Issue 5, 2011, Pages 644-661

  France, Stephen L ^a   Carroll, J Douglas ^b  

^a UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

Computational intelligence; data mining; multidimensional scaling (MDS); pattern analysis; visualization

Indexed keywords

COMBINATORIAL TECHNIQUES; CONTINUOUS OPTIMIZATION; DATA PREPROCESSING; DISTANCE-BASED; ENERGY FUNCTIONS; INDEPENDENT VARIABLES; INPUT DATAS; MOLECULAR CHEMISTRY; MULTI-DIMENSIONAL SCALING; NEIGHBORHOOD INFORMATION; NETWORK LOCALIZATION; NONLINEAR DATA; OPTIMIZATION METHOD; PATTERN ANALYSIS; POSSIBLE FUTURES; PROXIMITY MATRIX; SCALE DEVELOPMENT; SPRING SYSTEM;

AIR TRAFFIC CONTROL; ARTIFICIAL INTELLIGENCE; OPTIMIZATION; PATTERN RECOGNITION; ROBOTICS; SURVEYS; TERRORISM; VISUALIZATION;

DATA VISUALIZATION;

EID: 80052069040     PISSN: 10946977     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCC.2010.2078502     Document Type: Review

References (167)

1. S. Agarwal, J. Wills, L. Cayton, G. Lanckriet, D. Kriegman, and S. Belongie, "Generalized non-metric multidimensional scaling, " in Proc. AISTATS, 2007, pp. 1-8.
2. C. C. Aggarwal, A. Hinneburg, and D. A. Keim, "On the suprising behavior of distance metrics in high dimensional space, " in Proc. Database Theory (ICDT 2001), pp. 420-434.
3. D. K. Agrafiotis, D. N. Rassokhin, and V. S. Lobanov, "Multidimensional scaling and visualization of large molecular similarity tables, " J. Comp. Chem., vol. 22, no. 5, pp. 488-500, 2001. (Pubitemid 32291685)
4. U. Akkucuk, "Nonlinear mapping: Approaches based on optimizing an index of continuity and applying classical metric MDS on revised distances, " Ph. D. dissertation, Rutgers Univ., Newark, NJ, 2004.
5. U. Akkucuk and J. D. Carroll, "PARAMAP vs. isomap: A comparison of two nonlinear mapping algorithms, " J. Classif., vol. 23, no. 2, pp. 221-254, 2006. (Pubitemid 44704842)
6. U. Akkucuk and J. D. Carroll, "Nonlinear mapping using a hybrid of PARAMAP and isomap approaches, " in Proc. IFCS 2009, 2010, pp. 371-380.
7. P. Arabie, "Was euclid an unnecessarily sophisticated psychologist?" Psychometrika, vol. 56, no. 4, pp. 567-587, 1991.
8. P. Arabie, J. D. Carroll, and W. S. DeSarbo, Three-way Scaling and Clustering. Newbury Park, CA: Sage, 1987.
9. W. Basilaj, "Incremental multidimensional scaling method for database visualization, " in Proc. SPIE 1999, pp. 149-158.
10. M. Belkin and P. Niyogi, "Laplacian eigenmaps for dimensionality reduction and data representation, " Neural Comput., vol. 15, no. 6, pp. 1373-1396, 2003. (Pubitemid 37049796)
11. K. Beyer, J. Goldstein, R. Ramakrishnan, and U. Shaft, "When is "nearest neighbor" meaningful?" Lecture Notes in Computer Science: Database Theory - ICDT 1999, C. Beeri and P. Bunemanpp, Eds. Heidelberg, Germany: Springer, pp. 217-235, 1999.
12. I. Borg and P. J. F. Groenen, Modern Multidimensional Scaling: Theory and Applications. New York: Springer, 2005.
13. I. Borg and D. Leutner, "Measuring the similarity between MDS configurations, " Multivariate Behav. Res., vol. 20, no. 3, pp. 325-334, 1985.
14. U. Brandes and C. Pich, "Eigensolver methods for progressive multidimensional scaling of large data, " in Proc. 14th Int. Symp Graph Drawing (GD 2006), Lecture Notes in Computer Science, M. Kaufmann and W. Dorothea, Eds. Heidelberg, Germany: Springer, 2007, pp. 42-53.
15. D. L. Brodbeck and D. L. Girardin, "Combining topological clustering and multidimensional scaling for visualising large data sets, " unpublished.
16. M. M. Bronstein, A. M. Bronstein, R. Kimmel, and I. Yavneh, "Multigrid multidimensional scaling, " Numer. Linear Algebr., vol. 13, no. 2-3, pp. 149-171, 2006. (Pubitemid 43479876)
17. M. Brusco and D. Steinley, "A binary integer program to maximize the agreement between partitions, " J. Classif., vol. 25, no. 2, pp. 185-193, 2008.
18. M. J. Brusco, "A simulated annealing heuristic for unidimensional and multidimensional (city-block) scaling of symmetric proximity matrices, " J. Classif., vol. 18, no. 1, pp. 3-33, 2001. (Pubitemid 33397664)
19. M. J. Brusco and S. Stahl, "Using quadratic assignment methods to generate initial permutations for least-squares unidimensional scaling of symmetric proximity matrices, " J. Classif., vol. 17, no. 2, pp. 197-223, 2000.
20. M. J. Brusco and S. Stahl, "Optimal least-square unidimensional scaling: Improved branch-and-bound procedures and comparison to dynamic programming, " Psychometrika, vol. 70, no. 2, pp. 253-270, 2005. (Pubitemid 41251211)
21. A. Buja and D. F. Swayne, "Visualization methodology for multidimensional scaling, " J. Classif., vol. 19, no. 1, pp. 7-43, 2002. (Pubitemid 36161347)
22. A. Buja, D. F. Swayne, M. L. Littman, N. Dean, and H. Hofmann, "Data visualization with multidimensional scaling, " J. Comput. Graph. Stat., vol. 17, no. 2, pp. 444-472, 2008.
23. F. M. T. A. Busing, J. J. F. Commandeur, and W. J. Heiser, "PROXSCAL: A multidimensional scaling programfor individual differences scaling with constraints, " in Softstat'97: Advances in Statistical Software, W. Bandilla and F. Faulbaum, Eds. Stuttgart, Germany: Lucius & Lucius, 1997, pp. 67-74.
24. G. S. Carpenter, L. G. Cooper, D. M. Hanssens, and D. F. Midgley, "Modeling asymmetric competition, " Mark. Sci., vol. 7, no. 4, pp. 393-412, 1988.
25. J. D. Carroll, "Models and methods for multidimensional analysis of preferential choice (or other dominance) data, " Similarity and Choice, E. D. Lantermann and H. Feger, Eds., Bern, Switzerland: Hans Huber, pp. 234-289, 1980.
26. J. D. Carroll and P. Arabie, "Multidimensional scaling, " Handbook of Perception and Cognition. Volume 3: Measurement, Judgment and Decision Making, M. H. Birnbaum, Ed., San Diego, CA: Academic, pp. 179-250, 1998.
27. J. D. Carroll and J.-J. Chang, "Analysis of individual differences in multidimensional scaling via an N-way generalization of "Eckart- Young" decomposition, " Psychometrika, vol. 35, no. 3, pp. 283-319, 1970.
28. M. Chalmers, "A linear iteration time layout algorithm for visualizing high-dimensional data, " in Proc. 7th Conf. Vis. Los Alamitos, CA: IEEE Computer Society Press, 1996, pp. 127-132.
29. L. Chen, "Local multidimensional scaling for nonlinear dimension reduction, graph layout and proximity analysis, " Ph. D. dissertation, Univ. Pennsylvania, Philadelphia, PA, 2006.
30. L. Chen and A. Buja, "Energy/Stress functions for dimension reduction and graph drawing: Power laws and their clustering properties, Working Paper, Unpublished.
31. L. Chen and A. Buja, "Local multidimensional scaling for nonlinear dimension reduction, graph drawing, and proximity analysis, " J. Amer. Stat. Assoc., vol. 104, no. 486, pp. 209-219, 2009.
32. H. Choi and S. Choi, "Robust kernel isomap, " Pattern Recogn., vol. 40, no. 3, pp. 853-862, 2007. (Pubitemid 44667746)
33. C. H. Coombs, A Theory of Data. New York: Wiley, 1964.
34. R. Davidson and D. Harel, "Drawing graphs nicely using simulated annealing, " ACM Trans. Graph., vol. 15, no. 4, pp. 301-331, 1996. (Pubitemid 126418648)
35. J. de Leeuw, "Applications of convex analysis to multidimensional scaling, " in Recent Developments in Statistics, J. Barra, F. Brodeau, G. Romier, and B. Van Cutsem, Eds. Amsterdam, The Netherlands: North Holland, 1977, pp. 133-145.
36. J. de Leeuw, "Convergence of the majorization method for multidimensional scaling, " J. Classif., vol. 5, no. 2, pp. 163-180, 1998.
37. J. de Leeuw and W. J. Heiser, "Convergence of correction-matrix algorithms for multidimensional scaling, " Geometric Representations of Relational Data: Readings in Multidimensional Scaling, J. C. Lingoes, Ed., Ann Arbor, MI: Mathesis Press, pp. 735-752, 1977.
38. J. de Leeuw and W. J. Heiser, "Multidimensional scaling with restrictions on the configuration, " Multivariate Analysis, P. R. Krishnaiah, Ed., Amsterdam, The Netherlands: North-Holland, pp. 501-522, 1980.
39. J. de Leeuw and P. Mair, "Multidimensional scaling using majorization: SMACOF in R, " J. Stat. Soft., vol. 31, no. 3, pp. 1-30, 2009.
40. V. de Silva and J. B. Tenenbaum, "Sparse multidimensional scaling using landmark points, " Stanford Mathematics Technical Report. Unpublished (still under review).
41. D. Defays, "A short note on a method of seriation, " Brit. J. Math. Stat. Psy., vol. 31, pp. 49-53, 1978. (Pubitemid 9030853)
42. P. Demartines and J. Herault, "Curvilinear component analysis: A self-organizing neural network for nonlinear mapping of data sets, " IEEE. Trans. Neural Netw., vol. 8, no. 1, pp. 148-154, Jan. 1997. (Pubitemid 127767788)
43. W. S. DeSarbo and A. K. Manrai, "A new multidimensional scaling methodology for the analysis of asymmetric proximity data in marketing research, " Mark. Sci., vol. 11, no. 1, pp. 1-20, 1992.
44. P. Eades, "A heuristic for graph drawing, " in Proc. 13th Manitobia Conf. Num. Math. Comput., 1984, pp. 149-160.
45. C. Faloutos and K.-I. Lin, "FastMap: A fast algorithm for indexing, data-mining and visualization of traditional and multimedia datasets, " in Proc. SIGMOD 1995, pp. 163-174.
46. M. Fanty and R. Cole, "Spoken letter recognition, " in Proc. NIPS 1990, San Mateo, CA: Morgan Kaufmann, pp. 220-226.
47. S. L. France and J. D. Carroll, "Development of an agreement metric based upon the Rand index for the evaluation of dimensionality reduction techniques, with applications to mapping customer data, " in Proc. MLDM 2007, Lecture Notes in Computer Science, P. Perner, Ed. Heidelberg, Germany: Springer, pp. 499-517.
48. S. L. France and J. D. Carroll, "DEMScale: Large scale MDS accounting for a ridge operator and demographic variables, " in Proc. IDA 2009, Lecture Notes in Computer Science, N. M. Adams, C. Robardet, A. Siebes, and J. Boulicaut, Eds. Heidelberg, Germany: Springer, pp. 47-58.
49. S. L. France and J. D. Carroll, "Is the distance compression effect overstated? Some theory and experimentation, " in Proc. MLDM 2009, Lecture Notes in Computer Science, P. Perner, Ed. Heidelberg, Germany: Springer, pp. 280-294.
50. T. M. J. Fruchterman and E. M. Reingold, "Graph drawing by force-directed placement, " Softw. Pract. Exper., vol. 21, no. 1, pp. 1129-1164, 1991.
51. X. Geng, D.-C. Zhan, and Z.-H. Zhou, "Supervised nonlinear dimensionality reduction for visualization and classification, " IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 35, no. 6, pp. 1098-1107, Dec. 2005. (Pubitemid 41800411)
52. M. Greenacre, Correspondence Analysis in Practice. Boca Raton, FL: Chapman & Hall, 2007.
53. P. J. F. Groenen, J. de Leeuw, and R. Mathar, "Least squares multidimensional scaling with transformed distances, " in From Data to Knowledge: Theoretical and Practical Aspects of Classification, Data Analysis, W. Gaul and D. Pfeifer, Eds. Heidelberg, Germany: Springer, 1996, pp. 177-185.
54. P. J. K. Groenen and W. J. Heiser, "The tunneling method for global optimization in multidimensional scaling, " Psychometrika, vol. 61, no. 3, pp. 529-550, 1996.
55. P. J. K. Groenen, W. J. Heiser, and J. J. Meulman, "City-block scaling smoothing strategies for avoiding local minima, " in Classification, Data Analysis, and Data Highways, I. Balderjahn, R. Mathur, and M. Schader, Eds. Heidelberg, Germany: Springer, 1998, pp. 46-53.
56. P. J. K. Groenen, W. J. Heiser, and J. J. Meulman, "Global optimization in least-squares multidimensional scaling, " J. Classif., vol. 16, no. 2, pp. 225-254, 1999.
57. P. J. K. Groenen, R. Mathar, and W. J. Heiser, "The majorization approach to multidimensional scaling for Minkowski distances, " J. Classif., vol. 12, no. 1, pp. 3-19, 1995.
58. L. Guttman, "An approach for quantifying paired comparisons and rank order, " Ann. Math. Stat., vol. 17, no. 2, pp. 144-163, 1946.
59. L. Guttman, "A general nonmetric technique for finding the smallest coordinate space for a configuration of points, " Psychometrika, vol. 33, no. 4, pp. 469-506, 1968.
60. W. J. Heiser and J. de Leeuw, "SMACOF-I. Technical report ug-86-02, " Dept. Data Theory, Univ. Leiden, The Netherlands, Unpublished (still under review).
61. W. J. Heiser and J. J. Meulman, "Constrained multidimensional scaling including confirmation, " Appl. Psych. Meas., vol. 7, no. 4, pp. 381-404, 1983.
62. C. Ho, K. F. MacDorman, and Z. A. Dwi Pramono, "Human emotion and the uncanny valley: A GLM, MDS, and isomap analysis of robot video ratings, " in Proc. 3rd ACM/IEEE Int. Conf. Human Robot Interact., 2008, pp. 169-176.
63. E. W. Holman, "Completely nonmetric multidimensional scaling, " J. Math. Psychol., vol. 18, no. 1, pp. 39-51, 1978.
64. L. J. Hubert and P. Arabie, "Comparing partitions, " J. Classif., vol. 2, no. 1, pp. 193-218, 1985.
65. L. J. Hubert and P. Arabie, "Unidimensional scaling and combinatorial optimization, " Multidimensional Data Analysis, J. de Leeuw, J. J. Meulman, W. J. Heiser, and F. Critchley, Eds. Leiden, The Netherlands: DSWO Press, pp. 181-196, 1986.
66. L. J. Hubert and P. Arabie, "Relying on necessary conditions for optimization: Unidimensional scaling and some extensions, " Classification and Related Methods of Data Analysis, H. H. Bock, Ed., Amsterdam, The Netherlands: Elesevier, pp. 463-472, 1988.
67. L. J. Hubert, P. Arabie, and J. J. Meulman, "Linear and circular unidimensional scaling for symmetric proximity matrices, " Brit. J. Math. Stat. Psy., vol. 50, no. 2, pp. 253-284, 1997. (Pubitemid 127447208)
68. L. J. Hubert, P. Arabie, and J. J. Meulman, Combinatorial Data Analysis: Optimization by Dynamic Programming. Philadelphia, PA: SIAM, 2001.
69. H. Hwang, M. A. Tomiuk, and Y. Takane, "Correspondence analysis, multiple correspondence analysis and recent developments, " Handbook of Quantitative Methods in Psychology, R. E. Millsap and A. Maydeu-Olivares, Eds., London, U. K.: Sage Publications, pp. 243-263, 2009.
70. S. Ingram, T. Munzner, and M. Olano, "Glimmer: Multilevel MDS on the GPU, " IEEE Trans. Vis. Comput. Graphics, vol. 15, no. 2, pp. 249-261, Mar./Apr. 2008.
71. K. Iswandy and A. König, "Soft computing techniques to advance non-linear mappings for multivariate data visualization and wireless sensor localization, " Syst., Man Cybern. Soc. eNewsletter, no. 29, 2009. http://www.my-smc.org/back-issues.html and http://www.mysmc.org/news/back/2009- 12/main-article4.html.
72. H. Je and D. Kim, "Bayesian multidimensional scaling for multi-robot localization, " in Proc. ICNSC 2008, pp. 926-931.
73. O. C. Jenkins and M. J. Matarić, "A spatio-temporal extension to Isomap nonlinear dimension reduction, " in Proc. ICML 2004, pp. 441-448. (Pubitemid 40290839)
74. F. Jourdan and G. Melancon, "Multiscale hybrid MDS, " in Proc. IV 2004. Washington, DC: IEEE Computer Society, 2004, pp. 388-393.
75. T. Kamada and S. Kawai, "An algorithm for drawing general undirected graphs, " Inform. Process. Lett., vol. 31, no. 1, pp. 7-15, 1989.
76. S. Kaski, J. Nikkila, M. Oja, J. Venna, P. Törönen, and E. Castrén, "Trustworthiness and metrics in visualizing similarity of gene expression, " BMC Bioinf., vol. 4, no. 1, pp. 1-13, 2003.
77. A. Kearsley, R. Tapia, and M. W. Trosset, "An approach to parallelizing isotonic regression, " Working Paper, Rice University, Unpublished (still under review).
78. K. I. Kim, K. Jung, and H. J. Kim, "Face recognition using kernel principal component analysis, " IEEE Signal Process. Lett., vol. 9, no. 2, pp. 40-42, Feb. 2002. (Pubitemid 34490978)
79. T. Kohonen, Self-organizing Maps. Heidelberg, Germany: Springer, 2000.
80. P. M. Kroonenberg, Applied Multiway Data Analysis. Hoboken, NJ: Wiley, 2008.
81. C. L. Krumhansl, "Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density, " Psychol. Rev., vol. 85, no. 5, pp. 445-463, 1978.
82. J. B. Kruskal, "Multidimensional scaling for optimizing a goodness of fit metric to a nonmetric hypothesis, " Psychometrika, vol. 29, no. 1, pp. 1-27, 1964.
83. J. B. Kruskal, "Nonmetric multidimensional scaling: A numerical method, " Psychometrika, vol. 29, no. 2, pp. 115-129, 1964.
84. J. B. Kruskal, "Comments on "a nonlinear mapping for data structure analysis", " IEEE Trans. Comput., vol. 20, no. 12, pp. 1614-1614, Dec. 1971.
85. J. B. Kruskal and M. Wish, Multidimensional Scaling. Newbury Park, CA: Sage, 1978.
86. J. B. Kruskal, F. W. Young, and J. B. Seery, "How to use KYST a very flexible program to do multidimensional scaling and unfolding, " AT&T Bell Labs, Unpublished (still under review).
87. K. Lau, P. L. Leung, and K. Tse, "A nonlinear programming approach to metric unidimensional scaling, " J. Classif., vol. 15, no. 1, pp. 3-14, 1998.
88. M. H. C. Law and A. K. Jain, "Incremental nonlinear dimensionality reduction by manifold learning, " IEEE Trans. Pattern Anal. Mach. Intell., vol. 28, no. 3, pp. 377-391, Mar. 2006. (Pubitemid 43159634)
89. J. A. Lee, A. Lendasse, N. Donckers, and M. Verleysen, "A robust nonlinear projection method, " in Proc. ESANN 2000, pp. 13-20.
90. J. A. Lee, A. Lendasse, and M. Verleysen, "Nonlinear projection with curvilinear distances: Isomap versus curvilinear distance analysis, " Neurocomputing, vol. 57, pp. 49-76, 2004. (Pubitemid 38351861)
91. S. Lespinats, B. Fertil, P. Villemain, and J. Hérault, "RankVisu: Mapping from the neighborhood network, " Neurocomputing, vol. 72, no. 13-15, pp. 2964-2978, 2009.
92. S. Lespinats, M. Verleysen, A. Giron, and B. Fertil, "DD-HDS: A method for visualization and exploration of high-dimensional data, " IEEE Trans. Neural Netw., vol. 18, no. 5, pp. 1265-1279, Sep. 2007. (Pubitemid 47408531)
93. B. Li, D.-S. Huang, and C. Wang, "Improving the robustness of Isomap by de-noising, " in Proc. IJCNN 2008, pp. 266-270.
94. I. Liiv, "Pattern discovery using seriation and matrix reordering: A unified view, extensions and an application to inventory management, " Ph. D. thesis, Tallinn Univ. Tech., Tallinn, Estonia, 2008.
95. A. Lima, H. Zen, Y. Nankaku, C. Miyajima, K. Tokuda, and T. Kitamura, "On the use of kernel PCA for feature extraction in speech recognition, " IEICE Trans. Inf. Syst., vol. E87-D, no. 12, pp. 2802-2811, 2004. (Pubitemid 40021352)
96. D. C. Liu and J. Nocedal, "On the limited memory BFGS method for large scale optimization, " Math. Program., vol. 45, no. 1, pp. 503-528, 1989. (Pubitemid 20660315)
97. V. McGee, "The multidimensional analysis of elastic distances, " Brit. J. Math. Stat. Psy., vol. 19, no. 2, pp. 181-196, 1966.
98. G. Michailidis and J. de Leeuw, "The Gifi system of descriptive multivariate analysis, " Stat. Sci., vol. 13, no. 4, pp. 307-336, 1998. (Pubitemid 128465328)
99. G. A. Miller and P. E. Nicely, "An analysis of perceptual confusions among some English consonants, " J. Acoust. Soc. Am., vol. 27, no. 2, pp. 338-352, 1955.
100. A. Morrison and M. Chalmers, "A hybrid layout algorithm for sub-quadratic multidimensional scaling, " in Proc. InfoVis 2002, Los Alamitos, CA: IEEE, 2002, pp. 152-158.
101. A. Morrison, G. Ross, and M. Chalmers, "Fast multidimensional scaling through sampling, springs, and interpolation, " Inf. Vis., vol. 2, no. 1, pp. 68-77, 2003.
102. 2 unidimensional scaling, " J. Classif., vol. 22, no. 1, pp. 119-138, 2005. (Pubitemid 41060087)
103. F. Murtagh, Correspondence Analysis and Data Coding with Java and R. Boca Raton, FL: Chapman & Hall, 2005.
104. A. Naud, "Visualization of high-dimensional data using an association of multidimensional scaling to clustering, " in Proc. IEEE Conf. Cybern. Intell. Syst., 2004, pp. 252-255. (Pubitemid 40068618)
105. A. Naud, "An accurate MDS-based algorithm for the visualization of large multidimensional datasets, " in Proc. ICAISC 2006. Heidelberg, Germany: Springer, pp. 643-652.
106. S. Nishisato, "Optimal scaling of paired comparison and rank order data: An alternative to Guttman's formulation, " Psychometrika, vol. 43, no. 4, pp. 587-587, 1978.
107. S. Nishisato, Multidimensional Nonlinear Descriptive Analysis. Boca Raton, FL: Chapman & Hall, 2006.
108. A. Noack, "An energy model for visual graph clustering, " in Proc. GD 2003. Heidelberg, Germany: Springer, 2004, pp. 425-436. (Pubitemid 39744206)
109. A. Okada and T. Imaizumi, "Nonmetric multidimensional scaling of asymmetric proximities, " Behaviormetrika, vol. 14, no. 21, pp. 81-98, 1987.
110. J. C. Platt, "FastMap, MetricMap, and Landmark MDS are all Nyström algorithms, " in Proc. AISTATS, 2005, pp. 261-268.
111. V. Pliner, "A class of metric scaling models, " Automat. Rem. Contr., vol. 45, pp. 789-794, 1984.
112. V. Pliner, "Metric unidimensional scaling and global optimization, " J. Classif., vol. 13, no. 1, pp. 3-18, 1996. (Pubitemid 126331459)
113. M. Quist and G. Yona, "Distributional scaling. An algorithm for structure preserving embedding of metric and nonmetric spaces, " J. Mach. Learn. Res., vol. 5, pp. 399-430, 2004.
114. J. O. Ramsay, "Some statistical approaches to multidimensional scaling data, " J. Roy. Stat. Soc. A Sta., vol. 145, no. 3, pp. 285-312, 1982.
115. W. M. Rand, "Objective criteria for the evaluation of clustering methods, " J. Am. Stat. Assoc., vol. 66, no. 336, pp. 846-850, 1971.
116. F. Rehm, F. Klawonn, and R. Kruse, "MDS polar: A new approach for dimension reduction to visualize high dimensional data, " in Proc. IDA 2005, pp. 316-327.
117. v. F. Rehm, "Visual data analysis in air traffic management, " Ph. D. dissertation, Otto-von-Guericke Univ., Magdeburg, Germany, 2007.
118. R. Rocci and G. Bove, "Rotation techniques in asymmetric multidimensional scaling, " J Comput. Graph. Stat., vol. 11, no. 2, pp. 405-419, 2002.
119. R. Rosipal, M. Girolami, L. J. Trejo, and A. Cichocki, "Kernel PCA for feature extraction and de-noising in nonlinear regression, " Neural Comput. Appl., vol. 10, no. 3, pp. 231-243, 2001. (Pubitemid 33725829)
120. G. Rosman, A. M. Bronstein, M. M. Bronstein, A. Sidi, and R. Kimmel, "Fast multidimensional scaling using vector extrapolation, " Technicon University, CIS Working Paper CIS-2008-01, Unpublished.
121. S. T. Roweis and L. K. Saul, "Nonlinear dimensionality reduction by locally linear embedding, " Science, vol. 290, no. 5500, pp. 2323-2326, 2000. (Pubitemid 32041578)
122. S. Saburi and N. Chino, "A maximum likelihood method for an asymmetric MDS model, " Comput. Stat. Data An., vol. 52, no. 10, pp. 4673-4684, 2008.
123. T. Saito and S.-i. Takeda, "Multidimensional scaling of asymmetric proximity: Model and method, " Behaviormetrika, vol. 17, no. 28, pp. 49-80, 1990.
124. P. Salamon, P. Sibani, and R. Frost, Facts, Conjectures, and Improvements for Simulated Annealing. Philadelphia, PA: SIAM, 2002.
125. J. W. Sammon, "A nonlinear mapping for data structure analysis, " IEEE Trans. Comput., vol. 18, no. 5, pp. 401-409, May 1969.
126. J. W. Schneider and P. Borland, "Matrix comparison, part 1: Motivation and important issues for measuring the resemblance between proximity measures or ordination results, " J. Amer. Soc. Inf. Sci. Tec., vol. 58, no. 11, pp. 1586-1595, 2007. (Pubitemid 47397661)
127. J. W. Schneider and P. Borland, "Matrix comparison, part 2: Measuring the resemblance between proximity measures or ordination results by use of the mantel and procrustes statistics, " J. Amer. Soc. Inf. Sci. Tec., vol. 58, no. 11, pp. 1596-1609, 2007. (Pubitemid 47397662)
128. B. Schölkopf, "The kernel trick for distances, " in Proc. NIPS 2000, MA: MIT Press, 2001, pp. 301-307.
129. B. Schölkopf, A. Smola, and K.-R. Müller, "Kernel principal component analysis, " in Advances in Kernel Methods: Support Vector Learning, B. Schölkopf, C. J. C. Burges, and A. J. Smola, Eds. Cambridge, MA: MIT Press, 1999, pp. 583-588. (Pubitemid 127140297)
130. Y. Shang, W. Ruml, Y. Zhang, and M. Fromherz, "Localization from connectivity in sensor networks, " IEEE Trans. Parallel Distrib. Syst., vol. 15, no. 11, pp. 961-974, Nov. 2004.
131. R. N. Shepard, "Analysis of proximities: Multidimensional scaling with an unknown distance function. I, " Psychometrika, vol. 27, no. 2, pp. 125-140, 1962.
132. R. N. Shepard, "Analysis of proximities: Multidimensional scaling with an unknown distance function. II, " Psychometrika, vol. 27, no. 2, pp. 219-246, 1962.
133. R. N. Shepard and J. D. Carroll, "Parametric representation of nonlinear data structures, " Multivariate Analysis, P. R. Krishnaiah, Ed., New York, pp. 561-592, 1966.
134. V. D. Silva and J. B. Tenenbaum, "Global versus local methods in nonlinear dimensionality reduction, " in Proc. NIPS 2002, 2003, pp. 705-712.
135. E. Simantiraki, "Unidimensional scaling: A linear programming approach minimizing absolute deviations, " J. Classif., vol. 13, no. 1, pp. 19-25, 1996. (Pubitemid 126331460)
136. Á. Skupin, "From metaphor to method: Cartographic perspectives on information visualization, " in Proc. InfoVis 2000, pp. 91-97.
137. D. A. Smith, W. F. Ford, and A. Sidi, "Extrapolation methods for vector sequences, " SIAM Rev., vol. 29, no. 2, pp. 199-233, 1987.
138. J. P. Snyder, Flattening the Earth: Two Thousand Years of Map Projections. Chicago, IL: Univ. Chicago Press, 1997.
139. A. Strehl, J. Ghosh, and R. Mooney, "Impact of similarity measures on web-page clustering, " in Proc. AAAI 2000, Cambridge, MA, pp. 58-64.
140. M. Strickert, S. Teichmann, N. Sreenivasulu, and U. Seiffert, "High-throughput multi-dimensional scaling (HiT-MDS) for cDNA-array expression data, " in Proc. ICANN 2005, pp. 625-633.
141. Y. Takane, "Multidimensional successive categories scaling: A maximum likelihood method, " Psychometrika, vol. 46, no. 1, pp. 9-28, 1981.
142. Y. Takane, S. Jung, and Y. Oshima-Takane, "Multidimensional scaling, " in Handbook of Quantitative Methods in Psychology, R. E. Millsap and A. Maydeu-Olivares, Eds. London: Sage, 2009, pp. 219-242.
143. Y. Takane, F. W. Young, and J. de Leeuw, "Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features, " Psychometrika, vol. 42, no. 1, pp. 7-67, 1977.
144. J. B. Tenenbaum, V. de Silva, and J. C. Langford, "A global geometric framework for nonlinear dimensionality reduction, " Science, vol. 290, no. 5500, pp. 2319-2323, 2000. (Pubitemid 32041577)
145. W. S. Torgerson, "Multidimensional scaling I: Theory and method, " Psychometrika, vol. 17, no. 4, pp. 401-419, 1952.
146. W. S. Torgerson, Theory and Methods of Scaling. New York: Wiley, 1958.
147. M. W. Trosset, "A new formulation of the nonmetric Strain problem in multidimensional scaling, " J. Classif., vol. 15, no. 1, pp. 15-35, 1998. (Pubitemid 128365617)
148. M. W. Trosset and P. J. F. Groenen, "Multidimensional scaling algorithms for large data sets, " Comp. Sci. Stat., vol. 37, 2005.
149. A. Tversky, "Features of similarity, " Psychol. Rev., vol. 84, no. 4, pp. 327-352, 1977.
150. M. van de Velden, "Optimal scaling of paired comparison data, " J. Classif., vol. 21, no. 1, pp. 89-109, 2004. (Pubitemid 38835130)
151. J. Venna and S. Kaski, "Local multidimensional scaling, " Neural Netw., vol. 19, no. 6-7, pp. 889-899, Jul.-Aug. 2006. (Pubitemid 44148947)
152. J. F. Vera, W. J. Heiser, and A. Murillo, "Global optimization in any Minkowski metric: A premutation-translation simulated annealing algorithm for multidimensional scaling, " J. Classif., vol. 24, no. 2, pp. 277-301, 2007.
153. J. T. L. Wang, X. Wang, D. Shasta, and K. Zhang, "Metricmap: An embedding technique for processing distance-based queries in metric spaces, " IEEE Trans. Syst., Man, Cybern. B, Cybern., Part B, vol. 35, no. 5, Oct. 2005.
154. W. Wang and B. Bhargava, "Visualization of wormholes in sensor networks, " in Proc. WiSe 2004, pp. 51-60.
155. W. Wang and A. Lu, "Interactive wormhole detection and evaluation, " Inf. Vis., vol. 6, no. 1, pp. 3-17, 2007. (Pubitemid 46598304)
156. M. J. Watts, "A decade of Kasabov's evolving connectionist systems: A review, " IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 39, no. 3, pp. 253-269, May 2009.
157. A. Webb, "A kernel approach to metric multidimensional scaling, " in Proc. Joint IAPR International Workshops. Heidelberg, Germany: Springer, 2002, pp. 613-629.
158. M. Wedel, W. A. Kamakura, and W. S. DeSarbo, "Implications for asymmetry, nonproportionality, and heterogeneity in brand switching from piece-wise exponential mixture hazard models, " J. Mark. Res., vol. 32, no. 4, pp. 457-462, 1995.
159. P. Wesseling, An Introduction to Multigrid Methods. Flourtown, PA: R. T. Edwards, 2004.
160. C. K. I. Williams, "On a connection between kernel PCA and metric multidimensional scaling, " Machine Learn., vol. 46, no. 1, pp. 11-19, 2002. (Pubitemid 34129961)
161. M. Williams and T. Munzner, "Steerable, progressive multidimensional scaling, " in Proc. InfoVis 2004. Washington, DC: IEEE Computer Society, pp. 57-64.
162. J. Woelfel and G. A. Barnett, "Multidimensional scaling in Riemann space, " Qual. Quant., vol. 16, no. 6, pp. 469-491, 1982.
163. T. Yang, J. Liu, L. McMillan, and W. Wang, "A fast approximation to multidimensional scaling, " in Proc. CIMCV 2006, pp. 1-8.
164. H. Yin, "VISOM - a novel method for multivariate data projection and structure visualization, " IEEE Trans. Neural Netw., vol. 13, no. 1, pp. 237-243, Jan. 2002. (Pubitemid 34236851)
165. H. Yin, "On multidimensional scaling and the embedding of self-organising maps, " Neural Netw., vol. 21, no. 2-3, pp. 160-169, 2008.
166. G. Young and A. S. Householder, "Discussion of a set of points in terms of their mutual distances, " Psychometrika, vol. 3, no. 1, pp. 19-22, 1938.
167. K. Zhang and J. T. Kwok, "Density-weighted Nyström method for computing large kernel eigensystems, " Neural Comput., vol. 21, no. 1, pp. 121-146, 2009.