Collaborative Representation Based Neighborhood Preserving Projection for Dimensionality Reduction

Collaborative graph-based discriminant analysis (CGDA) has been recently proposed for dimensionality reduction and classification. It uses available samples to construct sample collaboration via L2 norm minimization-based representation, thus showing great computational efficiency. However, CGDA only constructs the intra-class graph, so it only takes into account local geometry and ignores the separability for samples in different classes. In this paper, we propose a novel method termed as collaborative representation based neighborhood preserving projection (CRNPP) for dimensionality reduction. By incorporating the intra-class and inter-class discriminant information into the graph construction of collaborative representation coefficients, CRNPP not only maintains the same level of time cost as CGDA, but also preserves both global and local geometry of the data simultaneously. In this way, the collaborative relationship of the data from the same class is strengthened while the collaborative relationship of the data from different classes is inhibited in the projection subspace. Experiments on benchmark face databases validate the effectiveness and efficiency of the proposed method.