Principal component analysis: A review and recent developments

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 374, Issue 2065, 2016, Pages

  Jollife, Ian T ^a   Cadima, Jorge ^b,c  

^a UNIVERSITY OF EXETER   (United Kingdom)

^b INSTITUTO SUPERIOR DE AGRONOMIA   (Portugal)

^c Center of Statistics Applications of Lisbon University CEAUL   (Portugal)

Author keywords

Dimension reduction; Eigenvectors; Multivariate analysis; Palaeontology

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MULTIVARIANT ANALYSIS;

DATA ANALYSIS TECHNIQUES; DATA TYPES AND STRUCTURES; DIMENSION REDUCTION; INFORMATION LOSS; INTERPRETABILITY; MULTI VARIATE ANALYSIS; PALAEONTOLOGY; PRINCIPAL COMPONENTS;

PRINCIPAL COMPONENT ANALYSIS;

EID: 84960361801     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2015.0202     Document Type: Review

References (51)

1. Pearson K. 1901 On lines and planes of closest fit to systems of points in space. Phil. Mag. 2, 559-572. (doi:10.1080/14786440109462720)
2. Hotelling H. 1933 Analysis of a complex of statistical variables into principal components. J. Educ. Psychol. 24, 417-441, 498-520. (doi:10.1037/h0071325)
3. Jackson JE. 1991 A user's guide to principal components. New York, NY: Wiley.
4. Jolliffe IT. 2002 Principal component analysis, 2nd edn. New York, NY: Springer-Verlag.
5. Diamantaras KI, Kung SY 1996 Principal component neural networks: theory and applications. New York, NY: Wiley.
6. Flury B. 1988 Common principal components and related models. New York, NY: Wiley.
7. Horn R, Johnson C. 1985 Matrix analysis. Cambridge, UK: Cambridge University Press.
8. Hudlet R, Johnson RA 1982 An extension of some optimal properties of principal components. Ann. Inst. Statist. Math. 34, 105-110. (doi:10.1007/BF02481011)
9. Okamoto M. 1969 Optimality of principal components. In Multivariate analysis II(ed. PR Krishnaiah), pp. 673-685. New York, NY: Academic Press.
10. McCabe GP. 1984 Principal variables. Technometrics 26, 137-144. (doi:10.1080/00401706.1984.10487939)
11. Cadima J, Cerdeira JO, Minhoto M. 2004 Computational aspects of algorithms for variable selection in the context of principal components. Comp. Stat. Data Anal. 47, 225-236. (doi:10.1016/j.csda.2003.11.001)
12. Gill PG, Purnell MA, Crumpton N, Brown K.R., Gostling NJ, Stampanoni M, Rayfield EJ. 2014 Dietary specializations and diversity in feeding ecology of the earliest stem mammals. Nature 512, 303-305. (doi:10.1038/nature13622)
13. R Development Core Team. 2015 R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. See http://www.R-project.org.
14. Gabriel KR. 1971 The biplot graphical display of matrices with application to principal component analysis. Biometrika 58, 453-467. (doi:10.1093/biomet/58.3.453)
15. Cadima J, Jolliffe IT 2009 On relationships between uncentred and column-centred principal component analysis. Pak. J. Stat. 25, 473-503.
16. Ringner M. 2008 What is principal component analysis? Nat. Biotechnol. 26, 303-304. (doi:10.1038/nbt0308-303)
17. Lee D, Lee W, Lee Y., Pawitan Y. 2010 Super-sparse principal component analyses for highthroughput genomic data. BMC Bioinform. 11, 296. (doi:10.1186/1471-2105-11-296)
18. Birnbaum A, Johnstone IM, Nadler B, Paul D. 2013 Minimax bounds for sparse PCA with noisy high-dimensional data. Ann. Stat. 41, 1055-1084. (doi:10.1214/12-AOS1014)
19. Johnstone IM, Lu AY 2009 On consistency and sparsity for principal components analysis in high dimensions. J. Am. Stat. Assoc. 104, 682-693. (doi:10.1198/jasa.2009.0121)
20. Ramsay JO, Silverman BW 2006 Functional data analysis, 2nd edn. Springer Series in Statistics. New York, NY: Springer.
21. Rao CR. 1958 Some statistical methods for comparison of growth curves. Biometrics 14, 1-17. (doi:10.2307/2527726)
22. Li Y, Wang N, Carroll RJ 2013 Selecting the number of principal components in functional data. J. Am. Stat. Assoc. 108, 1284-1294. (doi:10.1080/01621459.2013.788980)
23. Boente G, Silibian-Barrera M. 2015 S-estimators for functional principal components. J. Am. Stat. Assoc. 110, 1100-1111. doi:10.1080/01621459.2014.946991)
24. Hörmann S., Kidziński L, Hallin M. 2015 Dynamic functional principal components. J. R. Stat. Soc. B 77, 319-348. (doi:10.1111/rssb.12076)
25. Brillinger DR. 1981 Time series: data analysis and theory, Expanded edn. San Francisco, CA: Holden-Day.
26. Cattell RB. 1978 The scientific use of factor analysis in behavioral and life sciences. New York, NY: Plenum Press.
27. Jolliffe IT, Trendafilov N, Uddin M. 2003 A modified principal component technique based on the LASSO. J. Comput. Graph. Stat. 12, 531-547. (doi:10.1198/1061860032148)
28. Hastie T, Tibshirani R, Wainwright M. 2015 Statistical learning with sparsity: the LASSO and generalizations. Boca Raton, FL: CRC Press.
29. Zou H, Hastie T, Tibshirani R. 2006 Sparse principal components. J. Comput. Graph. Stat. 15, 262-264. (doi:10.1198/jcgs.2006.s7)
30. Witten D, Tibshirani R, Hastie T. 2009 A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics 10, 515-534. (doi:10.1093/biostatistics/kxp008)
31. d'Aspremont A., El Ghaoui L, Jordan MI, Lanckriet GRG. 2007 A direct formulation for sparse PCA using semidefinite programming. SIAM Rev. 49, 434-448. (doi:10.1137/050645506)
32. Lei J, Vu VQ 2015 Sparsistency and agnostic inference in sparse PCA. Ann. Stat. 43, 299-322. (doi:10.1214/14-AOS1273)
33. Obukhov AM. 1947 Statistically homogeneous fields on a sphere. Usp. Mat. Navk. 2, 196-198.
34. Lorenz EN. 1956 Empirical orthogonal functions and statistical weather prediction. Technical report, Statistical Forecast Project Report 1, Dept. of Meteor. MIT: 49.
35. Preisendorfer RW, Mobley CD 1988 Principal component analysis in meteorology and oceanography. Amsterdam, The Netherlands: Elsevier.
36. Hannachi A, Jolliffe IT, Stephenson D.B., Trendafilov N. 2006 In search of simple structures in climate: simplifying EOFs. Int. J. Climatol. 26, 7-28. (doi:10.1002/joc.1243)
37. Huber PJ. 1977 Robust statistical procedures. Philadelphia, PA: Society for Industrial and Applied Mathematics.
38. Huber PJ. 1981 Robust statistics. New York, NY: Wiley.
39. Ruymagaart FH. 1981 A robust principal component analysis. J. Multivariate Anal. 11, 485-497. (doi:10.1016/0047-259X(81)90091-9)
40. Hallin M, Paindaveine D, Verdebout T. 2014 Efficient R-estimation of principal and common principal components. J. Am. Stat. Assoc. 109, 1071-1083. (doi:10.1080/01621459.2014.880057)
41. Huber PJ, Ronchetti EM 2009 Robust statistics, 2nd edn. Wiley Series in Probability and Statistics. New York, NY: Wiley.
42. De la Torre F, Black MJ. 2003 A framework for robust subspace learning. Int. J. Comput. Vis. 54, 117-142. (doi:10.1023/A:1023709501986)
43. Wright J, Peng Y, Ma Y., Ganesh A, Rao S. 2009 Robust principal component analysis: exact recovery of corrupted low-rank matrices by convex optimization. In Proc. of Neural Information Processing Systems 2009 (NIPS 2009), Vancouver, BC, Canada, 7-10 December 2009. See http://papers.nips.cc/paper/3704-robust-principal-component-analysis-exact-recovery-of-corrupted-low-rank-matrices-via-convex-optimization.pdf.
44. Candès E.J., Li X, Ma Y., Wright J. 2011 Robust principal component analysis? J. ACM 58, 11:1-11:37.
45. Zhao Q, Meng D, Xu Z., Zuo W, Zhang L. 2014 Robust principal component analysis with complex noise. In Proc. of the 31st Int. Conf. on Machine Learning, Beijing, China, 21-26 June 2014. See http://jmlr.org/proceedings/papers/v32/zhao14.pdf.
46. Bouwmans T, Zahzah E. 2014 Robust PCA via principal component pursuit: a review for a comparative evaluation in video surveillance. Comput. Vis. Image Underst. 122, 22-34. (doi:10.1016/j.cviu.2013.11.009)
47. Bock H-H, Diday E. 2000 Analysis of symbolic data. Berlin, Germany: Springer.
48. Brito P. 2014 Symbolic data analysis: another look at the interaction of data mining and statistics. WIREs Data Mining Knowl. Discov. 4, 281-295. (doi:10.1002/widm.1133)
49. Ichino M, Yaguchi H. 1994 Generalized Minkowski metrics for mixed feature type data analysis. IEEE Trans. Syst. Man Cybern. 24, 698-708. (doi:10.1109/21.286391)
50. Makosso-Kallyth S. In press. Principal axes analysis of symbolic histogram variables. Stat. Anal. Data Mining. (doi:10.1002/sam.11270)
51. Vichi M, Saporta G. 2009 Clustering and disjoint principal component analysis. Comp. Stat. Data Anal. 53, 3194-3208. (doi:10.1016/j.csda.2008.05.028)