The fast convergence of incremental PCA

Advances in Neural Information Processing Systems

Volumn , Issue , 2013, Pages

  Balsubramani, Akshay ^a   Dasgupta, Sanjoy ^a   Freund, Yoav ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE RATES; DATA POINTS; FAST CONVERGENCE; INCREMENTAL PCA;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 84898987559     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (17)

1. A. Agarwal, O. Chapelle, M. Dudík, and J. Langford. A reliable effective terascale linear learning system. CoRR, abs/1110.4198, 2011.
2. R. Arora, A. Cotter, K. Livescu, and N. Srebro. Stochastic optimization for PCA and PLS. In 50th Annual Allerton Conference on Communication, Control, and Computing, pages 861-868. 2012.
3. R. Arora, A. Cotter, and N. Srebro. Stochastic optimization of PCA with capped MSG. In Advances in Neural Information Processing Systems, 2013.
4. G. Blanchard, O. Bousquet, and L. Zwald. Statistical properties of kernel principal component analysis. Machine Learning, 66(2-3):259-294, 2007.
5. T. T. Cai, Z. Ma, and Y. Wu. Sparse PCA: Optimal rates and adaptive estimation. CoRR, abs/1211.1309, 2012.
6. R. Durrett. Probability: Theory and Examples. Duxbury, second edition, 1995.
7. T.P. Krasulina. A method of stochastic approximation for the determination of the least eigenvalue of a symmetrical matrix. USSR Computational Mathematics and Mathematical Physics, 9(6):189-195, 1969.
8. I. Mitliagkas, C. Caramanis, and P. Jain. Memory limited, streaming PCA. In Advances in Neural Information Processing Systems, 2013.
9. E. Oja. Subspace Methods of Pattern Recognition. Research Studies Press, 1983.
10. E. Oja and J. Karhunen. On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix. Journal of Math. Analysis and Applications, 106:69-84, 1985.
11. A. Rakhlin, O. Shamir, and K. Sridharan. Making gradient descent optimal for strongly convex stochastic optimization. In International Conference on Machine Learning, 2012.
12. S. Roweis. EM algorithms for PCA and SPCA. In Advances in Neural Information Processing Systems, 1997.
13. T. Sim, S. Baker, and M. Bsat. The CMU pose, illumination, and expression database. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(12):1615-1618, 2003.
14. V.Q. Vu and J. Lei. Minimax rates of estimation for sparse PCA in high dimensions. Journal of Machine Learning Research-Proceedings Track, 22:1278-1286, 2012.
15. M.K. Warmuth and D. Kuzmin. Randomized PCA algorithms with regret bounds that are logarithmic in the dimension. In Advances in Neural Information Processing Systems. 2007.
16. J. Weng, Y. Zhang, and W.-S. Hwang. Candid covariance-free incremental principal component analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(8):1034-1040, 2003.
17. L. Zwald and G. Blanchard. On the convergence of eigenspaces in kernel principal component analysis. In Advances in Neural Information Processing Systems, 2005.