Title. An Overview of Mixture Discriminant Analysis
Authors. John A. Ramey
- Abstract. Hastie and Tibshirani (1996) proposed a discriminant analysis model based on a mixture of Gaussians, each of which share a common covariance matrix. The mixture discriminant analysis (MDA) model provides a natural extension of the standard Gaussian assumptions underlying the well-known linear and quadratic discriminant analysis methods. However, because the estimators for the model have no closed-form, an EM algorithm was used. In this document, we provide a verbose construction of the model along with a thorough derivation of the parameter estimators as some of the details from Hastie and Tibshirani (1996) were indeed sparse. Using a simple two-dimensional simulated data set, we demonstrate that the MDA classifier identifies three classes, each of which has non-adjacent subclasses, whereas standard Gaussian assumption employed in linear and quadratic discriminant analysis is clearly inadequate and produces poor decision boundaries.
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