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Independent factor discriminant analysis

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  • Montanari, Angela
  • Calo, Daniela G.
  • Viroli, Cinzia

Abstract

In the general classification context the recourse to the so-called Bayes decision rule requires to estimate the class conditional probability density functions. A mixture model for the observed variables which is derived by assuming that the data have been generated by an independent factor model is proposed. Independent factor analysis is in fact a generative latent variable model whose structure closely resembles the one of the ordinary factor model, but it assumes that the latent variables are mutually independent and not necessarily Gaussian. The method therefore provides a dimension reduction together with a semiparametric estimate of the class conditional probability density functions. This density approximation is plugged into the classic Bayes rule and its performance is evaluated both on real and simulated data.

Suggested Citation

  • Montanari, Angela & Calo, Daniela G. & Viroli, Cinzia, 2008. "Independent factor discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3246-3254, February.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:6:p:3246-3254
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    References listed on IDEAS

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    1. Calo, Daniela G., 2007. "Gaussian mixture model classification: A projection pursuit approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 471-482, September.
    2. Polzehl, Jorg, 1995. "Projection pursuit discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 20(2), pages 141-157, August.
    3. McLachlan, G. J. & Peel, D. & Bean, R. W., 2003. "Modelling high-dimensional data by mixtures of factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 379-388, January.
    4. McLachlan, G.J. & Bean, R.W. & Ben-Tovim Jones, L., 2007. "Extension of the mixture of factor analyzers model to incorporate the multivariate t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5327-5338, July.
    5. Bohning, Dankmar & Seidel, Wilfried, 2003. "Editorial: recent developments in mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 349-357, January.
    6. Bohning, Dankmar & Seidel, Wilfried & Alfo, Macro & Garel, Bernard & Patilea, Valentin & Walther, Gunther, 2007. "Advances in Mixture Models," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5205-5210, July.
    7. Fraley C. & Raftery A.E., 2002. "Model-Based Clustering, Discriminant Analysis, and Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 611-631, June.
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    1. Colubi, Ana & González-Rodri­guez, Gil & Domi­nguez-Cuesta, Mari­a José & Jiménez-Sánchez, Montserrat, 2008. "Favorability functions based on kernel density estimation for logistic models: A case study," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4533-4543, May.

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