Alternating Binary Classifier and Graph Learning from Partial Labels

Semi-supervised binary classifier learning is a fundamental machine learning task where only partial binary labels are observed, and labels of the remaining data need to be interpolated. Leveraging on the advances of graph signal processing (GSP), recently binary classifier learning is posed as a signal restoration problem regularized using a graph smoothness prior, where the undirected graph consists of a set of vertices and a set of weighted edges connecting vertices with similar features. In this paper, we improve the performance of such a graph-based classifier by simultaneously optimizing the feature weights used in the construction of the similarity graph. Specifically, we start by interpolating missing labels by first formulating a boolean quadratic program with a graph signal smoothness objective, then relax it to a convex semi-definite program, solvable in polynomial time. Next, we optimize the feature weights used for construction of the similarity graph by reusing the smoothness objective but with a convex set constraint for the weight vector. The reposed convex but non-differentiable problem is solved via an iterative proximal gradient descent algorithm. The two steps are solved alternately until convergence. Experimental results show that our alternating classifier / graph learning algorithm outperforms existing graph-based methods and support vector machines with various kernels1The work is partly funded by the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 734331..