Principal component analysis and higher correlations for distributed data

Journal of Machine Learning Research

Volumn 35, Issue , 2014, Pages 1040-1057

  Kannan, Ravindran ^a   Vempala, Santosh S ^b   Woodruff, David P ^c  

^a MICROSOFT RESEARCH INDIA   (India)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^c IBM ALMADEN RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION ALGORITHMS; APPROXIMATION THEORY; COMPUTATION THEORY; PRINCIPAL COMPONENT ANALYSIS;

ALGORITHMIC PROBLEMS; DISTRIBUTED DATA; HIGHER ORDER CORRELATION; INPUT DATAS; LOW RANK APPROXIMATIONS; MASSIVE DATA SETS; OPTIMAL COMMUNICATION; SUBGRAPHS;

MATRIX ALGEBRA;

EID: 84915816508     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (25)

1. Dimitris Achlioptas. Database-friendly random projections: Johnson-lindenstrauss with binary coins. J. Comput. Syst. Sci., 66(4):671-687, 2003.
2. Nir Ailon and Bernard Chazelle. The fast johnson-lindenstrauss transform and approximate nearest neighbors. SIAM J. Comput., 39(1):302-322, 2009.
3. Noga Alon, Yossi Matias, and Mario Szegedy. The space complexity of approximating the frequency moments. J. Comput. Syst. Sci., 58(1):137-147, 1999.
4. Sanjeev Arora, Elad Hazan, and Satyen Kale. A fast random sampling algorithm for sparsifying matrices. In APPROX-RANDOM, pages 272-279, 2006.
5. Rosa I. Arriaga and Santosh Vempala. An algorithmic theory of learning: Robust concepts and random projection. In FOCS, pages 616-623, 1999.
6. Rosa I. Arriaga and Santosh Vempala. An algorithmic theory of learning: Robust concepts and random projection. Machine Learning, 63(2):161-182, 2006.
7. Haim Avron, Huy L. Nguyen, and David P. Woodruff. Subspace embeddings for the polynomial kernel, 2014.
8. Maria-Florina Balcan, Vandana Kanchanapally, Yingyu Liang, and David P. Woodruff. Fast and communication efficient algorithms for distributed pca. Manuscript, 2014.
9. Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. An information statistics approach to data stream and communication complexity. J. Comput. Syst. Sci., 68(4):702-732, 2004.
10. Christos Boutsidis and David P. Woodruff. Optimal cur matrix factorizations. In STOC, 2014.
11. Mark Braverman, Faith Ellen, Rotem Oshman, Toniann Pitassi, and Vinod Vaikuntanathan. Tight bounds for set disjointness in the message passing model. CoRR, abs/1305.4696, 2013.
12. Amit Chakrabarti, Subhash Khot, and Xiaodong Sun. Near-optimal lower bounds on the multiparty communication complexity of set disjointness. In IEEE Conference on Computational Complexity, pages 107-117, 2003.
13. Kenneth L. Clarkson and David P. Woodruff. Numerical linear algebra in the streaming model. In STOC, pages 205-214, 2009.
14. Kenneth L. Clarkson and David P. Woodruff. Low rank approximation and regression in input sparsity time. STOC, 2013.
15. Uriel Feige and Eran Ofek. Spectral techniques applied to sparse random graphs. Random Struct. Algorithms, 27(2):251-275, 2005.
16. Dan Feldman, Melanie Schmidt, and Christian Sohler. Turning big data into tiny data: Constant-size coresets for k-means, pca and projective clustering. In SODA, pages 1434-1453, 2013.
17. Mina Ghashami and Jeff M. Phillips. Relative errors for deterministic low-rank matrix approximations. CoRR, abs/1307.7454, 2013.
18. Andre Gronemeier. Asymptotically optimal lower bounds on the nih-multi-party information complexity of the and-function and disjointness. In STACS, pages 505-516, 2009.
19. T. S. Jayram. Hellinger strikes back: A note on the multi-party information complexity of and. In APPROX-RANDOM, pages 562-573, 2009.
20. Daniel M. Kane, Raghu Meka, and Jelani Nelson. Almost optimal explicit johnson-lindenstrauss families. In APPROX-RANDOM, pages 628-639, 2011.
21. Yingyu Liang, Maria-Florina Balcan, and Vandana Kanchanapally. Distributed pca and k-means clustering. In The Big Learning Workshop at NIPS, 2013.
22. Xiangrui Meng and Michael W. Mahoney. Low-distortion subspace embeddings in input-sparsity time and applications to robust linear regression. In STOC, pages 91-100, 2013.
23. Jelani Nelson and Huy L. Nguyen. Osnap: Faster numerical linear algebra algorithms via sparser subspace embeddings. CoRR, abs/1211.1002, 2012.
24. Jeff M. Phillips, Elad Verbin, and Qin Zhang. Lower bounds for number-in-hand multiparty communication complexity, made easy. In SODA, pages 486-501, 2012.
25. David P. Woodruff and Qin Zhang. Tight bounds for distributed functional monitoring. In STOC, pages 941-960, 2012.