Linear discriminant analysis (LDA) is commonly used for dimensionality reduction. In real-world applications where labeled data are scarce, LDA does not work very well. However, unlabeled data are often available in large quantities. We propose a novel semi-supervised discriminant analysis algorithm called SSDA _CCCP_{\mathit{CCCP}} . We utilize unlabeled data to maximize an optimality criterion of LDA and use the constrained concave-convex procedure to solve the optimization problem. The optimization procedure leads to estimation of the class labels for the unlabeled data. We propose a novel confidence measure for selecting those unlabeled data points with high confidence. The selected unlabeled data can then be used to augment the original labeled data set for performing LDA. We also propose a variant of SSDA _CCCP_{\mathit{CCCP}} , called M-SSDA _CCCP_{\mathit{CCCP}} , which adopts the manifold assumption to utilize the unlabeled data. Extensive experiments on many benchmark data sets demonstrate the effectiveness of our proposed methods.