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Abstract:
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Depression is clinical syndrome which is heterogeneous in its symptoms. While the heterogeneity in clinical symptoms of depression are well understood, the underlying neurobiological substrates that contribute to this heterogeneity have gained recent attention. Recently, resting state functional magnetic resonance imaging (fMRI) of a large number of depressed participants were used to discover four neurophysiological subtypes. In this article, we approach this multiclass classification problem with multiclass linear and quadratic discriminant analysis. The number of features, p, (regions of interest in the brain) are substantially larger than the number of patients, n. In such scenarios, the usual estimator of the p x p covariance matrix, which is needed in discriminant analysis, is a poor estimator of the true covariance matrix. We build on our previous work of estimating eigenvalues in such high-dimensional settings to provide an improved classification method based on linear and quadratic discriminant analysis. We present simulations to validate the method and apply our method on a real data example.
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