A regularized approach for unsupervised multi-view multi-manifold learning

In this paper, we focus on the fundamental problem of efficiently selecting uniform class-consistent neighbors from all available views for graph-based multi-view multi-manifold learning methods in an unsupervised manner. We define each class of objects with continuous varying of pose angle as a relatively independent object manifold. The ideal neighborhood set is unknown, and selecting an appropriate neighborhood is not an easy task if we have multiple manifolds that have some intersections. Our approach concentrated on choosing the comprehensive form of each object manifold. We propose a TV-regularized least square problem to represent each object in a weighted sum of its class-consistent neighbors under different views. The goal of the proposed method is to make a distinction between some class-consistent view-inconsistent objects and class-inconsistent view-consistent objects that may be very close and also select a significant subset of the class-consistent view-inconsistent neighbors. The results we achieve show the superiority of proposed neighborhood graph construction when applied to manifold learning methods. The proposed approach works as extensions for the current graph-based manifold learning methods, such as Isomap, LLE, and LE, to handle multiple manifolds. Neighborhood selection and recognition accuracy experiments on several benchmark multi-view data sets have verified the excellent performance of our novel approach.