Semi-supervised discriminant analysis via spectral transduction

Linear Discriminant Analysis (LDA) is a popular method for dimensionality reduction and classification. In real-world applications when there is no sufficient labeled data, LDA suffers from serious performance drop or even fails to work. In this paper, we propose a novel method called Spectral Transduction Semi-Supervised Discriminant Analysis (STSDA), which can alleviate such problem by utilizing both labeled and unla-beled data. Our method takes into consideration both label augmenting and local structure preserving. First, we formulate label transduction with labeled and unlabeled data as a constrained convex optimization problem and solve it efficiently with a closed-form solution by using orthogonal projector matrices. Then, unlabeled data with reliable class estimations are selected with a balanced strategy to augment the original labeled data set. At last, LDA with manifold regularization is performed. Experimental results on face recognition demonstrate the effectiveness of our proposed method.