Semi-supervised Discriminant Analysis Based on Sparse-coding Theory

We consider the problem of semi-supervised graphbased learning. Since in semi-supervised settings, the labeled information is limited, we first propose la-norm-based label propagation (a-SLP) model to estimate the soft labels by using small set of labeled and large amount of unlabeled training data, and thereby enrich the supervised information. Based on the a-SLP results, we conduct semi-supervised discriminant analysis and present graph-based embedding (SGE) approach by incorporating the estimated soft labels with the local geometric information of both the within-class and between-class training data. Within-class affinity matrices and between-class weight matrix are introduced to preserve the propagated label information and local geometric information of data. This gets rid of the problem that merely concerning about the soft labels may lead to errors. By minimizing the locality-preserved within-class distances and maximizing the weighted betweenclass separability, subspaces that characterize the intrinsic data structure can be well captured. Experiments in face recognition verify the validity and effectiveness of the proposed methods.