Principal axes analysis of symbolic histogram variables

Statistical Analysis and Data Mining

Volumn 9, Issue 3, 2016, Pages 188-200

  Makosso Kallyth, Sun ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

Principal Component Analysis (PCA); Quantiles; Symbolic histogram variable; Symbolic interval variables

Indexed keywords

GRAPHIC METHODS;

ANALYSIS FRAMEWORKS; INTERVAL VARIABLE; PRINCIPAL AXIS ANALYSIS; PRINCIPAL COMPONENT ANALYSE; PRINCIPAL-COMPONENT ANALYSIS; QUANTILE; SYMBOLIC DATA ANALYSIS; SYMBOLIC HISTOGRAM VARIABLE; SYMBOLIC INTERVAL VARIABLE; WASSERSTEIN DISTANCE;

PRINCIPAL COMPONENT ANALYSIS;

EID: 84969837153     PISSN: 19321864     EISSN: 19321872     Source Type: Journal    
DOI: 10.1002/sam.11270     Document Type: Article

References (30)

1. E. Diday, F. Afonso, and R. Haddad, The symbolic data analysis paradigm, discriminant discretization and financial application. Revue des Nouvelles Technologies de l'Information Advances in Theory and Applications of High Dimensional and Symbolic Data Analysis, RNTI-E-25. (2013), 1-14.
2. H.-H. Bock and E. Diday, Analysis of Symbolic Data, Exploratory Methods for Extracting Statistical Informations from Complex Data, Berlin, Springer, 2000.
3. L. Billard and E. Diday, Symbolic Data Analysis: Conceptual Statistics and Data Mining, Berlin, Wiley Series in Computational Statistics, 2006.
4. E. Diday and M. Noirhomme-Fraiture, Symbolic Data Analysis and the SODAS Software, Chichester, UK, Wiley Interscience, 2008.
5. O. Rodriguez, E. Diday, and S. Winberg, Generalization of the principal components analysis to histogram data. 4th European Conference on Principles and Practice of Knowledge Discovery in Data Bases, Lyon, France. 2000.
6. P. Nagabhushan and R. P. Kumar, Histogram PCA, ISNN vol. 2, 1012-1021, 2007.
7. M. Ichino, The quantile method for symbolic principal component analysis, Stat Anal Data Min 4(2) (2011), 225-233.
8. E. Diday, Principal component analysis for bar charts and metabins tables, Stat Anal Data Min 6(5) (2013), 403-430.
9. S. Makosso-Kallyth and E. Diday . Adaptation of interval pca to symbolic histogram variables, Adv Data Anal Classif 6 (2012), 147-159.
10. M. Chen, H. Wang, and Z. Qin, Principal component analysis for probabilistic symbolic data: a more generic and accurate algorithm, Adv Data Anal Classif 9 (2014), 59-79.
11. R. Verde, A. Irpino, and A. Balzanella, Dimension reduction techniques for distributional symbolic data, IEEE Trans Cybern 99 (2015), 1.
12. M. Noirhomme-Fraiture and P. Brito, Far beyond the classical data models: symbolic data analysis, Stat Anal Data Min 4(2) (2011), 157-170.
13. A. Irpino, R. Verde, and F. A. T. de Carvalho, Dynamic clustering of histogram data based on adaptive squared Wasserstein distances, Expert Syst Appl 41(7) (2014), 3351-3366.
14. P. Cazes, Analyse factorielle d'un tableau de lois de probabilités, Revue de Statistique appliquée 50(3) (2002), 5-24.
15. P. Bertrand and F. Goupil, Descriptive statistics for symbolic data, Analysis of Symbolic Data: Exploratory Methods for Extracting Statistical Information from Complex Data, H.-H. Bock and E. Diday, eds., Berlin, Springer, 2000, 103-124.
16. L. Billard . Some analyses of interval data, J Comp Inform Technol 16(4) (2008), 225-233.
17. A. Irpino and R. Verde, Basic statistics for distributional symbolic variables: a new metric-based approach, Adv Data Anal Classif 9 (2014), 143-175.
18. A. L. Gibbs and F. E. Su . On choosing and bounding probability metrics, Int Stat Rev 70(3) (2002), 419-435.
19. R. A. Fisher, On the probable error of a coefficient of correlation deduced from a small sample, Metron 1 (1921), 3-32.
20. K. S. Law, The use of Fisher's z in Schmidt-Hunter type meta-analyses, J. Educ Behav Stat 20(3), 1995, 287-306.
21. N. C. Silver and W. P. Dunlap, Averaging correlation coefficients: should Fisher's z transformation be used?, J Appl Psychol 72 (1987), 146-148.
22. I. Olkin and J. W. Pratt, Unbiased estimation of certain correlation coefficients, Ann Math Stat 29(1) (1958), 201-211.
23. M. Viana, Combined estimators for the equicorrelation coefficient, Comm Stat Theory Meth 11(11) (1982), 1483-1504.
24. A. Irpino, C. Lauro, and R. Verde, Visualizing symbolic data by closed shapes, Between Data Science and Applied Data Analysis, Berlin and Heidelberg, Springer, 2003, 244-251.
25. S. Lê, J. Josse and F. Husson, Factominer: an r package for multivariate analysis, J Stat Softw 25(1) (2008), 1-18.
26. P. Cazes, A. Chouakria, E. Diday and Y. Schektman, Extension de l'analyse en composantes principales á des donnés intervalles, Revue de Statistique appliquée 45(3) (1997), 5-24.
27. J. Murillo and O. Rodriguez, Rsda: an r package for symbolic data analysis. Workshop in Symbolic Data Analysis. 2011. Namur, Belgium.
28. E. Diday, L. Billard and A. Douzal-Chouakria, Principal component analysis for interval-valued observations, Stat Anal Data Min 4 (2011), 229-246.
29. J. Brahim Brahim and S. Makosso-Kallyth, Gpciv and graphpca: two r packages for PCA of complex data. JSM, 2014, Boston, MA.
30. J. Le-Rademacher and L. Billard, Symbolic covariance principal component analysis and visualization for interval-valued data, J Comput Graph Stat 21(2) (2012), 413-432.