In Discrete Discriminant Analysis one often has to deal with dimensionality problems. In fact, even a moderate number of explanatory variables leads to an enormous number of possible states (outcomes) when compared to the number of objects under study, as occurs particularly in the social sciences, humanities and health-related elds. As a consequence, classi cation or discriminant models may exhibit poor performance due to the large number of parameters to be estimated. In the present paper, we discuss variable selection techniques which aim to address the issue of dimensionality. We speci cally perform classi cation using a combined model approach. In this setting, variable selection is particularly pertinent, enabling the handling of degrees of freedom and reducing computational cost.
@article{bwmeta1.element.doi-10_2478_bile-2013-0013,
author = {Anabela Marques and Ana Sousa Ferreira and Margarida G.M.S. Cardoso},
title = {Selection of variables in Discrete Discriminant Analysis},
journal = {Biometrical Letters},
volume = {50},
year = {2013},
pages = {1-14},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_bile-2013-0013}
}
Anabela Marques; Ana Sousa Ferreira; Margarida G.M.S. Cardoso. Selection of variables in Discrete Discriminant Analysis. Biometrical Letters, Tome 50 (2013) pp. 1-14. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_bile-2013-0013/
Benjamini Y., Hochberg Y.(1995): Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society. Series B (Methodological) 57 289-300. | Zbl 0809.62014
Bishop C.M.(1995): Neural Networks for Pattern Recognition. Oxford University Press. | Zbl 0868.68096
Brito I., Celeux C., Ferreira A.S.(2006): Combining Methods in Supervised Classication: a Comparative Study on Discrete and Continuous Problems. Revstat-Statistical Journal: 4(3): 201-225. | Zbl 1125.62059
Celeux G., Mkhadri A.(1992): Discrete regularized discriminant analysis. Statistics and Computing 2(3): 143-151.[Crossref]
Celeux G., Nakache J.P.(1994): Analyse Discriminante sur Variables Qualitatives. G. Celeux et J. P. Nakache diteurs, Polytechnica.
Ferreira A.S.(2000): Combinação de Modelos em Análise Discriminante sobre Variáveis Qualitativas. PhD thesis (in portuguese), Universidade Nova de Lisboa.
Ferreira A.S.(2010): A Comparative Study on Discrete Discriminant Analysis through a Hierarchical Coupling Approach. In Classication as a Tool for Research, Studies in Classication, Data Analysis, and Knowledge Organization; Hermann Locarek-Junge, Claus Weihs (Eds.), Springer-Verlag, Heidelberg- Berlin: 137-145.
Ferreira A.S.(2004): Combining models approach in Discrete Discriminant Analysis through a committee of methods. In Classication, Clustering, and Data Mining Applications; D. Banks, L. House, F. R. McMorris, P. Arabie, W. Gaul (Eds.), Springer: 151-156.
Ferreira A.S., Cardoso M.(2010): Evaluation of Results in Discrete Discriminant Analysis. Book of Abstracts of Stochastic Modeling Techniques and Data Analysis International Conference, Skiadas, C. H. (Eds.), Chania, Creta, Grécia, Junho: 94-95.
Ferreira A.S., Celeux G., Bacelar-Nicolau H.(1999): Combining models in discrete discriminant analysis by an hierarchical coupling approach. Proceedings of the IX International Symposium of ASMDA: 159-164.
Ferreira A.S., Celeux G., Bacelar-Nicolau H.(2000): Discrete Discriminant Analysis: The performance of Combining Models by an Hierarchical Coupling Approach. In Kiers, Rasson, Groenen and Shader, editors, Data Analysis, Classication and Related Methods, Springer: 181{186. | Zbl 1028.62050
Ferreira A.S., Celeux G., Bacelar-Nicolau H.(2001): New developments on combining models in Discrete Discriminant Analysis by a Hierarchical Coupling approach. Applied Stochastic Models and Data Analysis- ASMDA; G. Govaert, J. Janssen, N. Limnios (Eds.), UTC: 430-435.
Goldstein M., Dillon W.R.(1978): Discrete Discriminant Analysis. New York: Wiley. | Zbl 0396.62042
Holm S.(1979): A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6(2): 65-70. | Zbl 0402.62058
Marques A., Ferreira A.S., Cardoso M. (2008): Uma proposta de combinação de modelos em Análise Discriminante. Estatística - Arte de Explicar o Acaso, in Oliveira I. et al. Editores, Ci^encia Estatística, Edições S.P.E.: 393{403.
Matusita K. (1955): Decision rules based on distance for problems of fit, two samples and estimation. In Ann. Inst. Stat. Math. 26(4): 631-640.[Crossref] | Zbl 0065.12101
Pawlak Z.(1982): Rough sets. International Journal of Computer and Information Sci. 11: 341{356. | Zbl 0501.68053
Pearl J.(1988): Probabilistic reasoning in intelligent systems: Networks of plausible inference. Los Altos: Morgan Kaufmann. | Zbl 0746.68089
Prazeres N.L.(1996): Ensaio de um Estudo sobre Alexitimia com o Rorschach e a Escala de Alexitimia de Toronto (TAS-20). Master Thesis, Univ. Lisbon.
Saraiva F.(2010): Satisfaçao Conjugal e relaçao coparental ao longo do ciclo vital da familia. Master Thesis, Univ. Lisbon.
Silva A.P.D.(2010): Classicaçao supervisionada para dados de elevada dimensăo. Livro de resumos das XVII Jornadas de Classicaçao e Anlise de Dados (JOCLAD 2010), ISCTE Eds. pp. 17.