Semi-supervised dimensionality reduction using estimated class membership probabilities

Abstract. In solving pattern-recognition tasks with partially labeled training data, the semi-supervised dimensionality reduction method, which considers both labeled and unlabeled data, is preferable for improving the classification and generalization capability of the testing data. Among such techniques, graph-based semi-supervised learning methods have attracted a lot of attention due to their appealing properties in discovering discriminative structure and geometric structure of data points. Although they have achieved remarkable success, they cannot promise good performance when the size of the labeled data set is small, as a result of inaccurate class matrix variance approximated by insufficient labeled training data. In this paper, we tackle this problem by combining class membership probabilities estimated from unlabeled data and ground-truth class information associated with labeled data to more precisely characterize the class distribution. Therefore, it is expected to enhance performance in classification tasks. We refer to this approach as probabilistic semi-supervised discriminant analysis (PSDA). The proposed PSDA is applied to face and facial expression recognition tasks and is evaluated using the ORL, Extended Yale B, and CMU PIE face databases and the Cohn–Kanade facial expression database. The promising experimental results demonstrate the effectiveness of our proposed method.