Evaluating Discriminant Performance of a Semi-Supervised Linear Discriminant Analysis Against a Supervised One for Heteroscedastic Normal Populations

• Activity Number: 367
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Kenichi Hayashi*+
• Companies: Osaka University Graduate School of Medicine
• Keywords: Linear discriminant analysis ; Multivariate analysis ; Semi-supervised learning

Abstract

Semi-supervised learning enables the incorporation of unlabeled cases in the construction of discriminant functions. Most methods assume that the unlabeled cases are uniformly observed in the feature space or at least that the marginal distribution of the features is common to the labeled and unlabeled data. However, this assumption is often not satisfied in practice, because of constraints on data collection. We have previously shown that a semi-supervised linear discriminant analysis (LDA) is not always superior to a supervised LDA for two normal populations with the same covariance matrix when the labeling mechanism (the probability of observing an unlabeled case conditioned on the features) depends on the features. In the present study, we formulate the asymptotic relative efficiency of the semi-supervised LDA to the supervised LDA for heteroscedastic normal populations with arbitrary labeling mechanisms. The formulation is based on the fact that the discriminant rule derived from the LDA maximizes the area under the ROC curve under heteroscedasticity. Some numerical examples are presented to illustrate when and how unlabeled cases contribute to improving discriminant performan