Semi-Supervised Graph Based Embedding With Non-Convex Sparse Coding Techniques

Abstract

We consider the problem of semi-supervised graph-based learning upon multimodal and mixmodal data. Since in semi-supervised settings, the labeled information is very limited, we first propose a non-convex sparse-coding based label propagation ( $\alpha$ α -SLP) method to estimate the soft labels, and thereby to enrich the supervised information. By considering the structural properties of multimodal and mixmodal data, we present a semi-supervised graph-based embedding (SGE) approach that incorporates the soft label information with the hierarchical local geometric information of within-class, between-class, and overall-class data. Based on this, subspaces characterizing the multimodal and mixmodal data structure can be derived by maximizing the weighted between-class separability and minimizing the locality-preserved within-class as well as overall-class distances of the training samples. We further extend SGE into semi-supervised sparse subspace learning scenarios and present an $\alpha$ α -structural-regularization-induced SGE ( $\alpha$ α -SSGE) model, which can give better results in extracting discriminative groups of features by utilizing the non-convex structural regularization techniques. Experiments for multimodal and mixmodal digit as well as face recognition verify the validity and effectiveness of the proposed models.