Beyond the graphs: Semi-parametric semi-supervised discriminant analysis

Linear discriminant analysis (LDA) is a popular feature extraction method that has aroused considerable interests in computer vision and pattern recognition fields. The projection vectors of LDA is usually achieved by maximizing the between-class scatter and simultaneously minimizing the within-class scatter of the data set. However, in practice, there is usually a lack of sufficient labeled data, which makes the estimated projection direction inaccurate. To address the above limitations, in this paper, we propose a novel semi-supervised discriminant analysis approach. Unlike traditional graph based methods, our algorithm incorporates the geometric information revealed by both labeled and unlabeled data points in a semi-parametric way. Specifically, the final projections of the data points will contain two parts: a discriminant part learned by traditional LDA (or KDA) on the labeled points and a geometrical part learned by kernel PCA on the whole data set. Therefore we call our algorithm semi-parametric semi-supervised discriminant analysis (SSDA). Experimental results on face recognition and image retrieval tasks are presented to show the effectiveness of our method.