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Linear discriminant analysis (LDA), which works by maximizing the within-class similarity and minimizing the between-class similarity simultaneously, is a popular dimensionality reduction technique in pattern recognition and machine learning. In real-world applications when labeled data are limited, LDA does not work well. Under many situations, however, it is easy to obtain unlabeled data in large quantities. In this paper, we propose a novel dimensionality reduction method, called semi-supervised discriminant analysis (SSDA), which can utilize both labeled and unlabeled data to perform dimensionality reduction in the semi-supervised setting. Our method uses a robust path-based similarity measure to capture the manifold structure of the data and then uses the obtained similarity to maximize the separability between different classes. A kernel extension of the proposed method for nonlinear dimensionality reduction in the semi-supervised setting is also presented. Experiments on face recognition demonstrate the effectiveness of the proposed method.