Robust graph learning via constrained elastic-net regularization

Abstract

Graph has been widely researched for characterizing data structure and successfully applied in many fields. To date, one popular kind of graph constructing methods is based on linear reconstruction coefficients. However, it is still a challenge to make the graph maintain the intra-class relations and diminish the inter-class relations. In this paper, we propose a robust graph learning method via a constrained elastic-net regularization (CEN). In CEN, the representation coefficients are imposed by a combination of Frobenius norm and weighted ℓ1-norm. Among them, the weighted ℓ1-norm benefits from our proposed shape interaction weighting (SIW) scheme to strengthen the intra-subspace compactness and enhance the inter-subspace separability. Moreover, the CEN model is extended with non-negative constraints for wild applications. We carry out experiments on real-world datasets to evaluate the effectiveness of the proposed framework.