Random projections for κ-means clustering

Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010

Volumn , Issue , 2010, Pages

  Boutsidis, Christos ^a   Zouzias, Anastasios ^b   Drineas, Petros ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

D DIMENSIONS; DIMENSIONALITY REDUCTION; EQUAL PROBABILITY; MATRIX; MATRIX R; MEANS CLUSTERING; NUMERICAL IMPLEMENTATION; POINT SET; RANDOM MATRIX; RANDOM PROJECTIONS;

EID: 85162070280     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (23)

1. D. Achlioptas. Database-friendly random projections: Johnson- Lindenstrauss with binary coins. Journal of Computer and System Science, 66(4):671-687, 2003.
2. N. Ailon and B. Chazelle. Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform. In ACM Symposium on Theory of Computing (STOC), pages 557-563, 2006.
3. D. Aloise, A. Deshpande, P. Hansen, and P. Popat. NP-hardness of Euclidean sum-of-squares clustering. Machine Learning, 75(2):245-248, 2009.
4. E. Bingham and H. Mannila. Random projection in dimensionality reduction: applications to image and text data. In ACM SIGKDD international conference on Knowledge discovery and data mining (KDD), pages 245-250, 2001.
5. C. Boutsidis,M.W.Mahoney, and P. Drineas. Unsupervised feature selection for the k-means clustering problem. In Advances in Neural Information Processing Systems (NIPS), 2009.
6. P. Drineas, A. Frieze, R. Kannan, S. Vempala, and V. Vinay. Clustering in large graphs and matrices. In ACMSIAM Symposium on Discrete Algorithms (SODA), pages 291-299, 1999.
7. D. Foley and J. Sammon. An optimal set of discriminant vectors. IEEE Transactions on Computers, C-24(3):281-289, March 1975.
8. I. Guyon and A. Elisseeff. An introduction to variable and feature selection. Journal of Machine Learning Research, 3:1157-1182, 2003.
9. I. Guyon, S. Gunn, A. Ben-Hur, and G. Dror. Result analysis of the NIPS 2003 feature selection challenge. In Advances in Neural Information Processing Systems (NIPS), pages 545-552. 2005.
10. X. He, D. Cai, and P. Niyogi. Laplacian score for feature selection. In Advances in Neural Information Processing Systems (NIPS) 18, pages 507-514. 2006.
11. P. Indyk and R. Motwani Approximate nearest neighbors: towards removing the curse of dimensionality. In ACM Symposium on Theory of Computing (STOC), pages 604-613, 1998.
12. W. Johnson and J. Lindenstrauss. Extensions of Lipschitz mappings into a Hilbert space. Contemporary mathematics, 26(189-206):1-1, 1984.
13. E. Kokiopoulou, J. Chen and Y. Saad. Trace optimization and eigenproblems in dimension reduction methods. Numerical Linear Algebra with Applications, to appear.
14. A. Kumar, Y. Sabharwal, and S. Sen. A simple linear time (1+ε)-approximation algorithmfor k-means clustering in any dimensions. In IEEE Symposium on Foundations of Computer Science (FOCS), pages 454-462, 2004.
15. E. Liberty and S. Zucker. TheMailman algorithm: A note on matrix-vector multiplication. Information Processing Letters, 109(3):179-182, 2009.
16. S. Lloyd. Least squares quantization in PCM. IEEE Transactions on Information Theory, 28(2):129-137, 1982.
17. R. Ostrovsky, Y. Rabani, L. J. Schulman, and C. Swamy. The effectiveness of Lloyd-type methods for the κ-means problem. In IEEE Symposium on Foundations of Computer Science (FOCS), pages 165-176, 2006.
18. S. Roweis, and L. Saul. Nonlinear dimensionality reduction by locally linear embedding. Science, 290:5500, pages 2323-2326, 2000.
19. T. Sarlos. Improved approximation algorithms for large matrices via random projections. In IEEE Symposium on Foundations of Computer Science (FOCS), pages 329-337, 2006.
20. X. Wu et al. Top 10 algorithms in data mining. Knowledge and Information Systems, 14(1):1-37, 2008.
21. http://www.cs.uiuc.edu/~dengcai2/Data/FaceData.html
22. http://www.cs.uiuc.edu/~dengcai2/Data/data.html
23. http://www.cs.nyu.edu/~roweis/lle/