Distance-preserving dimensionality reduction

Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery

Volumn 1, Issue 5, 2011, Pages 369-380

  Yang, Li ^a  

^a Parkview Campus   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTERING ALGORITHMS; ITERATIVE METHODS; MATRIX ALGEBRA;

COMMON FEATURES; GEODESIC DISTANCES; HIGH DIMENSIONAL DATA; ITERATIVE OPTIMIZATION; LOW-DIMENSIONAL SPACES; MATRIX COMPUTATION; TECHNICAL BACKGROUND; TECHNICAL INFORMATION;

DIMENSIONALITY REDUCTION;

EID: 84866454507     PISSN: 19424787     EISSN: 19424795     Source Type: Journal    
DOI: 10.1002/widm.39     Document Type: Article

References (23)

1. Jolliffe I. Principal Component Analysis. 2nd ed. New York: Springer; 2002.
2. Cox T, Cox M. Multidimensional Scaling. 2nd ed. London: Chapman and Hall/CRC; 2000.
3. Stone JV. Independent Component Analysis: A Tutorial Introduction. Cambridge: The MIT Press; 2004.
4. Hyv̈arinen A, Karhunen J, Oja E. Independent Component Analysis. New York: Wiley-Interscience; 2001.
5. Bingham E, Mannila H. Random projection in dimensionality reduction: applications to image and text data. In: Proceedings of the 7thACMSIGKDD international conference on Knowledge discovery and data mining (KDD '01). New York: ACM Press; 2001, 245-250.
6. Schölkopf B, Smola A, Müller K-R. Nonlinear component analysis as a kernel eigenvalue problem. 1998, 10:1299-1319.
7. Kruskal JB, Wish M. Multidimensional Scaling. Beverly Hills, CA: Sage Publications; 1978.
8. Sammon JJ. A nonlinear mapping for data structure analysis. IEEE Trans Comput 1969, C-18:401-409.
9. Demartines P, Herault J. Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets. IEEE Trans Neural Netw 1997, 8:148-154.
10. Niemann H, Weiss J. A fast converging algorithm for nonlinear mapping of high-dimensional data onto a plane. IEEE Trans Comput 1979, C-28:142-147.
11. Lee RC, Slagle JR, Blum H. A triangulation method for the sequential mapping of points from N-space to two-space. IEEE Trans Comput 1977, 26:288-292.
12. Yang L. Distance-preserving projection of highdimensional data for nonlinear dimensionality reduction. IEEE Trans Pattern Anal Machine Intell 2004, 26: 1243-1246.
13. Tenenbaum JB, Silva Vd, Langford JC. A global geometric framework for nonlinear dimensionality reduction. Science 2000, 290:2319-2323.
14. Yang L. Sammon's nonlinear mapping using geodesic distances. In: Proceedings of the 17th International Conference on Pattern Recognition (ICPR'04). Vol. 2. IEEE Computer Society, Cambridge; 2004.
15. Lee JA, Lendasse A, Donckers N, Verleysen M. A robust nonlinear projection method. In: Proceedings of the 8th European Symposium on Artificial Neural Networks (ESANN2000) Bruges; 2000, 13-20.
16. Roweis ST, Saul LK. Nonlineaar dimensionality reduction by locally linear embedding. Science 2000, 290: 2323-2326.
17. Belkin M, Niyogi P. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput 2003, 15:1373-1396.
18. Donoho DL, Grimes C. Hessian eigenmaps: locally linear embedding techniques for high-dimensional data. Proc Natl Acad Sci 2003, 100:5591-5596.
19. Zhang Z, Zha H. Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM J Sci Comput 2005, 26:313-338.
20. Yang L. Alignment of overlapping locally scaled patches for multidimensional scaling and dimensionality reduction. IEEE Tran Pattern Anal Machine Intell 2008, 30: 438-450.
21. Weinberger KQ, Sha F, Saul LK. Learning a kernel matrix for nonlinear dimensionality reduction. In: Proceedings of the 21st International Conference on Machine Learning (ICML-04). Banff: ACM Press; 2004, 839-846.
22. Yang L. Building connected neighborhood graphs for isometric data embedding. In: Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD'2005). ACM Press, Chicago, IL; 2005.
23. Law MH, Jain AK. Incremental nonlinear dimensionality reduction by manifold learning. IEEE Trans Pattern Anal Machine Intell 2006, 28:377-391. FURTHER