Universal multi-dimensional scaling

Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

Volumn , Issue , 2010, Pages 1149-1158

  Agarwal, Arvind ^a   Phillips, Jeff M ^a   Venkatasubramanian, Suresh ^a  

^a University of Utah   (United States)

Author keywords

Dimensionality reduction; Multi dimensional scaling

Indexed keywords

ALGORITHMIC FRAMEWORK; DIMENSIONALITY REDUCTION; EXISTING METHOD; GEODESIC DISTANCES; GUARANTEED CONVERGENCE; HIGH-DIMENSIONAL; ITERATIVE SCHEMES; JOHNSON-LINDENSTRAUSS LEMMATA; LARGE DATASETS; MULTI-DIMENSIONAL SCALING; SMALL MEMORY FOOTPRINT; TARGET SPACE;

ALGORITHMS; COST FUNCTIONS; GEODESY; SPHERES;

CONVERGENCE OF NUMERICAL METHODS;

EID: 77956220111     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1835804.1835948     Document Type: Conference Paper

References (39)

1. P. K. Agarwal, S. Har-Peled, and H. Yu. On embeddings of moving points in Euclidean space. In Proc. 23rd Symposium on Computational Geometry, 2007.
2. D. M. Blei, A. Y. Ng, and M. I. Jordan. Latent Dirichlet allocation. J. Mach. Learn. Res., 3:993-1022, 2003.
3. I. Borg and P. J. F. Groenen. Modern Multidimensional Scaling. Springer, 2005.
4. P. Bose, A. Maheshwari, and P. Morin. Fast approximations for sums of distances, clustering and the Fermat-Weber problem. Comput Geom. Theory Appl., 24(3):135-146, 2003.
5. U. Brandes and C. Pich. Eigensolver methods for progressive multidimensional scaling of large data. In Graph Drawing, pages 42-53. Springer, 2006.
6. p distances. Operations Research, 41(6):1153-1163, 1993.
7. A. M. Bronstein, M. M. Bronstein, and R. Kimmel. Numerical Geometry of Non-Rigid Shapes. Springer, 2008.
8. M. Bronstein. Accelerated MDS. http://tosca.cs.technion.ac.il/book/ resources-sw.html.
9. L. Cayton and S. Dasgupta. Robust Euclidean embedding. In Proc. 23rd International Conference on Machine Learning, pages 169-176, 2006.
10. L. Chen and A. Buja. Local multidimensional scaling for nonlinear dimension reduction, graph drawing, and proximity analysis. Journal of the Americal Statistical Association, 104:209-219, 2009.
11. T. F. Cox and M. A. A. Cox. Multidimensional Scaling, Second Edition. Chapman & Hall/CRC, September 2000.
12. N. Dalal and B. Triggs. Histograms of oriented gradients for human detection. In Proc. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 886-893, 2005.
13. J. de Leeuw. Applications of convex analysis to multidimensional scaling. In J. Barra, F. Brodeau, G. Romier, and B. Van Custem, editors, Recent Developments in Statistics, pages 133-146. North Holland Publishing Company, 1977.
14. J. de Leeuw and P. Mair. Multidimensional scaling using majorization: SMACOF in R. Technical Report 537, UCLA Statistics Preprints Series, 2009.
15. V de Silva and J. B. Tenenbaum. Global versus local methods in nonlinear dimensionality reduction. In S. Becker, S. Thrun, and K. Obermayer, editors, NIPS, pages 705-712. MIT Press, 2002.
16. A. E. Elad, Y. Keller, and R. Kimmel. Texture mapping via spherical multi-dimensional scaling. In R. Kimmel, N. A. Sochen, and J. Weickert, editors, Scale-Space, volume 3459 of Lecture Notes in Computer Science, pages 443-455. Springer, 2005.
17. C. Faloutsos and K.-I. Lin. Fastmap: a fast algorithm for indexing, data-mining and visualization of traditional and multimedia datasets. In Proc. SIGMOD, pages 163-174, NewYork, NY, USA, 1995. ACM.
18. P. T Fletcher, S. Venkatasubramanian, and S. Joshi. The Geometric Median on Riemannian Manifolds with Application to Robust Atlas Estimation. Neuroimage (invited to special issue), 45(1):S143-S152, March 2009.
19. R. Gray, A. Buzo, A. Gray Jr, and Y Matsuyama. Distortion measures for speech processing. Acoustics, Speech and Signal Processing, IEEE Transactions on, 28(4):367-376, Aug 1980.
20. P. Indyk and J. Matousek. Low-distortion embeddings of finite metric spaces. In Handbook of Discrete and Computational Geometry, pages 177-196. CRC Press, 2004.
21. T Joachims. Learning to Classify Text Using Support Vector Machines-Methods, Theory, and Algorithms. Kluwer/Springer, 2002.
22. W. B. Johnson and J. Lindenstrauss. Extensions of Lipschitz mappings into Hilbert space. Contemporary Mathematics, 26:189-206, 1984.
23. H. Karcher. Riemannian center of mass and mollifier smoothing. Comm. on Pure and Appl. Math., 30:509-541, 1977.
24. I. N. Katz. Local convergence in Fermat's problem. Mathematical Programming, 6:89-104, 1974.
25. J. B. Kruskal. Multidimensional scaling by optimizing goodness of fit to nonmetric hypothesis. Psychometrika, 29:1-27, 1964.
26. J. B. Kruskal and M. Wish. Multidimensional scaling. In E. M. Uslander, editor, Quantitative Applications in the Social Sciences, volume 11. Sage Publications, 1978.
27. H. W. Kuhn. A note on Fermat's problem. Mathematical Programming, 4:98-107, 1973.
28. D. G. Lowe. Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vision, 60(2), 2004.
29. A. Magen. Dimensionality reductions that preserve volumes and distance to affine spaces, and their algorithmic applications. In Proc. 6th International Workshop on Randomization and Approximation Techniques, Lecture Notes In Computer Science; Vol. 2483, 2002.
30. A. W. Marshall and I. Olkin. Inequalities: Theory of Majorization and Its Applications. Academic Press, 1979.
31. L. M. Ostresh. On the convergence of a class of iterative methods for solving the Weber location problem. Operations Research, 26:597-609, 1978.
32. F. Pereira, N. Tishby and L. Lee. Distributional clustering of English words. In Proc. 31st Annual Meeting of the Association for Computational Linguistics, pages 183-190, 1993.
33. R. Pietersz and P. J. F. Groenen. Rank reduction of correlation matrices by majorization. Technical Report 519086, SSRN, 2004.
34. R. Pless and I. Simon. Embedding images in non-flat spaces. In Proc. of the International Conference on Imaging Science, Systems, and Technology, 2002.
35. T Sarlós. Improved approximation algorithms for large matrices via random projections. In Proc. 47th Annual IEEE Symp. Foundations of Computer Science, 2006.
36. W S. Torgerson. Multidimensional scaling: I. theory and method. Psychometrika, 17:401-419, 1952.
37. J. T.-L Wang, X. Wang, K.-I. Lin, D. Shasha, B. A. Shapiro, and K. Zhang. Evaluating a class of distance-mapping algorithms for data mining and clustering. In Proc. 5th ACM SIGKDD international conference on Knowledge discovery and data mining, pages 307-311, New York, NY, USA, 1999. ACM.
38. E. Weiszfeld. Sur le point pour lequel la somme des distances de n points donnés est minimum. Tohoku Math. J., 43:355-386, 1937.
39. G. Young and A. S. Householder. Discussion of a set of points in terms of their mutual distances. Psychometrika, 3:19-22, 1938.