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Regularized Gaussian discriminant analysis through eigenvalue decomposition
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DOI：10.2307/2291604.png)
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摘要
En 中文
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, and the nearest-means classifiers. In this article we propose an alternative approach, called EDDA, that is based on the reparameterization of the covariance matrix [Sigma(k)] of a group G(k) in terms of its eigenvalue decomposition Sigma(k) = lambda(k)D(k)A(k)D(k)', where lambda(k) specifies the volume of density contours of G(k), the diagonal matrix of eigenvalues specifies its shape, and the eigenvectors specify its orientation. Variations on constraints concerning volumes, shapes, and orientations lambda(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.
Keyword:
covariance matrix
maximum likelihood
normal-based classification
spectral decomposition
