TY - JOUR
AU - Celeux, Gilles
AB -  Abstract Friedman proposed a regularization technique (RDA) of discriminant analysis in the Gaussian framework. RDA uses two regularization parameters to design an intermediate classifier between the linear, the quadratic the nearest-means classifiers. In this article we propose an alternative approach, called EDDA, that is based on the reparameterization of the covariance matrix [Σ k ] of a group Gk in terms of its eigenvalue decomposition Σ k = λ k D k A k D k ′, where λk specifies the volume of density contours of Gk, the diagonal matrix of eigenvalues specifies its shape the eigenvectors specify its orientation. Variations on constraints concerning volumes, shapes orientations λ k , A k , and D k lead to 14 discrimination models of interest. For each model, we derived the normal theory maximum likelihood parameter estimates. Our approach consists of selecting a model by minimizing the sample-based estimate of future misclassification risk by cross-validation. Numerical experiments on simulated and real data show favorable behavior of this approach compared to RDA. 
TI - Regularized Gaussian Discriminant Analysis through Eigenvalue Decomposition
JF - Journal of the American Statistical Association
DO - 10.1080/01621459.1996.10476746
DA - 1996-12-01
UR - https://www.deepdyve.com/lp/taylor-francis/regularized-gaussian-discriminant-analysis-through-eigenvalue-x00nviTpD0
SP - 1743
EP - 1748
VL - 91
IS - 436
DP - DeepDyve
ER -