Regularized mixture discriminant analysis

Abstract – In this paper we seek a Gaussian mixture model (GMM) of the classconditional densities for plug-in Bayes classification. We propose a method for setting the number of the components and the covariance matrices of the class-conditional GMMs. It compromises between simplicity of the model selection based on the Bayesian information criterion (BIC) and the high accuracy of the model selection based on the cross-validation (CV) estimate of the correct classification rate. We apply an idea of Friedman (1989) to shrink a predefined covariance matrix to a parameterization with substantially reduced degrees of freedom (reduced number of the adjustable parameters). Our method differs from the original Friedman’s method by the meaning of the shrinkage. We operate on matrices computed for a certain class while the Friedman’s method shrinks matrices from different classes. We compare our method with the conventional methods for setting the GMMs based on the BIC and CV. The experim...

• Type: Journal
• Year: 2007
• Where: PRL
• Authors: Zohar Halbe, Mayer Aladjem
• Keywords: Correct Classification Rates, Gaussian Mixture Models, Model Selection, PRL 2007