Visual Classification by ℓ1-Hypergraph Modeling

Visual classification has attracted considerable research interests in the past decades. In this paper, a novel $\ell _1$ -hypergraph model for visual classification is proposed. Hypergraph learning, as a natural extension of graph model, has been widely used in many machine learning tasks. In previous work, hypergraph is usually constructed by attribute-based or neighborhood-based methods. That is, a hyperedge is generated by connecting a set of samples sharing a same feature attribute or in a neighborhood. However, these methods are unable to explore feature space globally or sensitive to noises. To address these problems, we propose a novel hypergraph construction approach that leverages sparse representation to generate hyperedges and learns the relationship among hyperedges and their vertices. First, for each sample, a hyperedge is generated by regarding it as the centroid and linking it as well as its nearest neighbors. Then, the sparse representation method is applied to represent the centroid vertex by other vertices within the same hyperedge. The vertices with zero coefficients are removed from the hyperedge. Finally, the representation coefficients are used to define the incidence relation between the hyperedge and the vertices. In our approach, we also optimize the hyperedge weights to modulate the effects of different hyperedges. We leverage the prior knowledge on the hyperedges so that the hyperedges sharing more vertices can have closer weights, where a graph Laplacian is used to regularize the optimization of the weights. Our approach is named $\ell _1$ -hypergraph since the $\ell _1$ sparse representation is employed in the hypergraph construction process. The method is evaluated on various visual classification tasks, and it demonstrates promising performance.