166
Views
1
CrossRef citations to date
0
Altmetric
Articles

Fast deflation sparse principal component analysis via subspace projections

, &
Pages 1399-1412 | Received 05 Dec 2019, Accepted 09 Feb 2020, Published online: 16 Feb 2020

References

  • Bro R, Smilde AK. Principal component analysis. Anal Methods. 2014;6:2812–2831. doi: 10.1039/C3AY41907J
  • Jolliffe IT. Principal component analysis. New York: Springer-Verlag; 1986.
  • Preisendorfer RW, Mobley CD. Principal component analysis in meteorology and oceanography. Amsterdam: Elsevier; 1988.
  • Abraham G, Inouye M. Fast principal component analysis of large-scalegenome-wide data. PLoS ONE. 2014;9(4):1–5. doi: 10.1371/journal.pone.0093766
  • Aitsahalia Y, Xiu D. Principal component analysis of high frequency data. J Am Stat Assoc. 2019;114:287–303. doi: 10.1080/01621459.2017.1401542
  • Bouwmans T, Zahzah E. Robust PCA via principal component pursuit: a review for a comparative evaluation in video surveillance. Comput Vis Image Underst. 2014;122:22–34. doi: 10.1016/j.cviu.2013.11.009
  • Dhindsa IS, Agarwal R, Ryait HS. Principal component analysis-based muscle identification for myoelectric-controlled exoskeleton knee. J Appl Stat. 2017;44:1707–1720. doi: 10.1080/02664763.2016.1221907
  • Fukuda K. Principal-component-based generalized-least-squares approach for panel data. J Stat Comput Sim. 2016;86:874–890. doi: 10.1080/00949655.2015.1041954
  • Hannachi A, Jolliffe IT, Stephenson DB, et al. In search of simple structures in climate: simplifying EOFs. Int J Climatol. 2006;26:7–28. doi: 10.1002/joc.1243
  • Hron K, Menafoglio A, Templ M, et al. Simplicial principal component analysis for density functions in bayes spaces. Comput Statist Data Anal. 2016;94:330–350. doi: 10.1016/j.csda.2015.07.007
  • Saad Y. Projection and deflation method for partial pole assignment in linear state feedback. IEEE Trans Automat Contr. 1988;33:290–297. doi: 10.1109/9.406
  • Hu Z, Pan G, Wang Y, et al. Sparse principal component analysis via rotation and truncation. IEEE Trans Neur Net Lear. 2016;27:875–890. doi: 10.1109/TNNLS.2015.2427451
  • Jolliffe IT, Trendafilov NT, Uddin M. A modified principal component technique based on the LASSO. J Comput Graph Stat. 2003;12:531–547. doi: 10.1198/1061860032148
  • Kawano S, Fujisawa H, Takada T, et al. Sparse principal component regression with adaptive loading. Comput Statist Data Anal. 2015;89:192–203. doi: 10.1016/j.csda.2015.03.016
  • Kawano S, Fujisawa H, Takada T, et al. Sparse principal component regression for generalized linear models. Comput Statist Data Anal. 2018;124:180–196. doi: 10.1016/j.csda.2018.03.008
  • Ma Z. Sparse principal component analysis and iterative thresholding. Ann Stat. 2013;41:772–801. doi: 10.1214/13-AOS1097
  • Zou H, Hastie T, Tibshirani R. Sparse principal component analysis. J Comput Graph Stat. 2006;15:265–286. doi: 10.1198/106186006X113430
  • d'Aspremont A, El Ghaoui L, Jordan MI, et al. A direct formulation for sparse PCA using semidefinite programming. SIAM Rev. 2007;49:434–448. doi: 10.1137/050645506
  • d'Aspremont A, Bach F, El Ghaoui L. Full regularization path for sparse principal component analysis. Proceedings of the 24th International Conference on Machine Learning; 2007. p. 177–184.
  • Mackey L. Deflation methods for sparse PCA. Adv NIPS. 2009;21:1017–1024.
  • Shen H, Huang JZ. Sparse principal component analysis via regularized low rank matrix approximation. J Multivariate Anal. 2008;99:1015–1034. doi: 10.1016/j.jmva.2007.06.007
  • Journee M, Nesterov Y, Richtarik P, et al. Generalized power method for sparse principal component analysis. J Mach Learn Res. 2010;11:517–553.
  • Yuan X, Zhang T. Truncated power method for sparse eigenvalue problems. J Mach Learn Res. 2013;14:899–925.
  • Halko N, Martinsson PG, Shkolnisky Y, et al. An algorithm for the principal component analysis of large data sets. SIAM J Sci Comput. 2011;33:2580–2594. doi: 10.1137/100804139
  • Wright SJ. Coordinate descent algorithms. Math Program. 2015;151:3–34. doi: 10.1007/s10107-015-0892-3
  • Drineas P, Kannan R, Mahoney MW. Fast Monte Carlo algorithms for matrices II: computing a low-rank approximation to a matrix. SIAM J Comput. 2006;36:158–183. doi: 10.1137/S0097539704442696
  • Trefethen LN, Bau D. Numerical linear algebra. Philadelphia: SIAM; 1997.
  • Givens W. Computation of plane unitary rotations transforming a general matrix to triangular form. J Soc Indus Appl Math. 1958;6:26–50. doi: 10.1137/0106004
  • Householder S. Unitary triangularization of a nonsymmetric matrix. J Assoc Comput Mach. 1958;5:339–342. doi: 10.1145/320941.320947
  • Krahmer F, Ward R. New and improved Johnson-Lindenstrauss embeddings via the restricted isometry property. SIAM J Math Anal. 2011;43(3):1269–1281. doi: 10.1137/100810447
  • Jeffers JN. Two case studies in the application of principal component analysis. Appl Stat. 1967;16:225–236. doi: 10.2307/2985919
  • Golub TR, Slonim DK, Tamayo P. Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science. 1999;286:531–537. doi: 10.1126/science.286.5439.531
  • Halko N, Martinsson PG, Tropp JA. Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. SIAM Rev. 2011;53(2):217–288. doi: 10.1137/090771806
  • Voronin S, Martinsson PG. Efficient algorithms for CUR and interpolative matrix decompositions. Adv Comput Math. 2017;43:495–516. doi: 10.1007/s10444-016-9494-8

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.