TY - GEN
T1 - Analysis of a privacy-preserving PCA algorithm using random matrix theory
AU - Wei, Lu
AU - Sarwate, Anand D.
AU - Corander, Jukka
AU - Hero, Alfred
AU - Tarokh, Vahid
N1 - Funding Information:
L. Wei, A. Hero, and V. Tarokh's work was partially supported by ARO grant W911NF-15-1-0479. A. Sarwate's work was partially supported by NSF grant CCF-1453432, NIH grant 1R01DA040487-01A1, and DARPA and the US Navy under contract N66001-15-C-4070.
Publisher Copyright:
© 2016 IEEE.
PY - 2017/4/19
Y1 - 2017/4/19
N2 - To generate useful summarization of data while maintaining privacy of sensitive information is a challenging task, especially in the big data era. The privacy-preserving principal component algorithm proposed in [1] is a promising approach when a low rank data summarization is desired. However, the analysis in [1] is limited to the case of a single principal component, which makes use of bounds on the vector-valued Bingham distribution in the unit sphere. By exploring the non-commutative structure of data matrices in the full Stiefel manifold, we extend the analysis to an arbitrary number of principal components. Our results are obtained by analyzing the asymptotic behavior of the matrix-variate Bingham distribution using tools from random matrix theory.
AB - To generate useful summarization of data while maintaining privacy of sensitive information is a challenging task, especially in the big data era. The privacy-preserving principal component algorithm proposed in [1] is a promising approach when a low rank data summarization is desired. However, the analysis in [1] is limited to the case of a single principal component, which makes use of bounds on the vector-valued Bingham distribution in the unit sphere. By exploring the non-commutative structure of data matrices in the full Stiefel manifold, we extend the analysis to an arbitrary number of principal components. Our results are obtained by analyzing the asymptotic behavior of the matrix-variate Bingham distribution using tools from random matrix theory.
UR - http://www.scopus.com/inward/record.url?scp=85019230748&partnerID=8YFLogxK
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U2 - 10.1109/GlobalSIP.2016.7906058
DO - 10.1109/GlobalSIP.2016.7906058
M3 - Conference contribution
AN - SCOPUS:85019230748
T3 - 2016 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2016 - Proceedings
SP - 1335
EP - 1339
BT - 2016 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2016 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2016 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2016
Y2 - 7 December 2016 through 9 December 2016
ER -