L1-norm projection pursuit principal component analysis

Computational Statistics and Data Analysis

Volumn 50, Issue 6, 2006, Pages 1441-1451

  Choulakian, V ^a  

^a UNIVERSITÉ DE MONCTON   (Canada)

Author keywords

Ascent algorithm; Benzcri's measure of influence; Centroid decomposition; Contraction mapping; Duality; Matrix norms; Outlier identification

Indexed keywords

ALGORITHMS; CONFORMAL MAPPING; ITERATIVE METHODS; MATHEMATICAL MODELS; MATRIX ALGEBRA;

ASCENT ALGORITHMS; CENTROID DECOMPOSITION; DUALITY; MATRIX NORMS;

PRINCIPAL COMPONENT ANALYSIS;

EID: 27744568756     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2005.01.009     Document Type: Article

References (27)

1. A.C. Atkinson Fast very robust methods for the detection of multiple outliers J. Amer. Statist. Assoc. 89 1994 1329 1339
2. A. Baccini, Ph. Besse, and A. de Falguerolles A L 1 -norm PCA and a heuristic approach E. Diday Y. Lechevalier O. Opitz Ordinal and Symbolic Data Analysis 1996 Springer Berlin 359 368
3. M. Benayade, and B. Fichet Algorithms for a geometrical PCA in L 1 -norm E. Diday Y. Lechevallier M. Schader P. Bertrand B. Burtschy New Approaches in Classification and Data Analysis 1994 Springer Berlin 75 84
4. J.P. Benzecri Analyse Des Données II. L'Analyse des Correspondences 1973 Dunod Paris
5. C. Burt The Distribution and Relations of Educational Abilities 1917 P.S. King & Son London, UK
6. V. Choulakian Robust Q-mode principal component analysis in L 1 Comput. Statist. Data Anal. 37 2001 135 150
7. V. Choulakian The centroid method revisited Psychometrika 68 2003 473 475
8. V. Choulakian A comparison of two methods of principal component analysis Y. Antoch COMPSTAT 2004 2004 Springer Berlin 769 774
9. V. Choulakian Transposition invariant principal component analysis in L 1 for long tailed data Statist. Probab. Lett. 71 2005 23 31
10. V. Choulakian, and J. Almhana An algorithm for nonmetric discriminant analysis Comput. Statist. Data Anal. 35 2001 253 264
11. M.T. Chu, and R.E. Funderlic The centroid decomposition relationships between discrete variational decompositions and SVDs Siam J. Matrix Anal. Appl. 23 2002 1025 1044
12. J.J. Daudin, C. Duby, and P. Trecourt Stability of principal component analysis studied by the bootstrap method Statistics 19 1988 241 258
13. K.R. Gabriel, and S. Zamir Lower rank approximation of matrices by least squares with any choice of weights Technometrics 21 1979 489 498
14. J.S. Galpin, and D.M. Hawkins L 1 estimation of a covariance matrix Comput. Statist. Data Anal. 5 1987 305 319
15. H.H. Harman Modern Factor Analysis 1967 The University of Chicago Press Chicago, IL
16. D.M. Hawkins, D. Bradu, and G.V. Kass Location of several outliers in multiple regression data using elemental sets Technometrics 26 1984 197 208
17. W.J. Heiser Correspondence analysis with least absolute residuals Comput. Statist. Data Anal. 5 1987 337 356
18. P. Horst Factor Analysis of Data Matrices 1965 Rinehart and Winston Holt, NY
19. J.E. Jackson A User's Guide To Principal Components 1991 Wiley New York
20. I.T. Jolliffe Principal Component Analysis second ed 2002 Springer New York
21. Li, B., 2005. Sign eigenanalysis and its applications to optimization problems and robust statistics. Comput. Statist. Data Anal., in press.
22. G. Li, and Z. Chen Projection-pursuit approach to robust dispersion matrices and principal components primary theory and Monte Carlo J. Amer. Statist. Assoc. 80 1985 759 766
23. G. Michailidis, and J. De Leeue Homogeneity analysis using absolute deviations Comput. Statist. Data Anal. 48 2004 587 603
24. D.M. Rocke, and D. Woodruff Identification of outliers in multivariate data J. Amer. Statist. Assoc. 91 1996 1047 1061
25. L.L. Thurstone Multiple factor analysis Psychol. Rev. 38 1931 406 427
26. L.L. Thurstone Multiple-Factor Analysis 1947 The University of Chicago Press Chicago
27. H. Wold Estimation of principal components and related models by iterative least squares P.R. Krishnaiah Multivariate Analysis 1966 Academic Press New York 391 420