Robust graph-based image classifier learning with negative edge weights

Abstract

We study semi-supervised learning for image classifiers from a graph signal processing (GSP) perspective. Specifically, by viewing a binary classifier as a graph-signal in a high-dimensional feature space, we cast classifier learning as a signal restoration problem via a classical maximum a posteriori (MAP) formulation. Unlike previous graph-signal restoration works, we consider in addition edges with negative weights expressing dissimilarity between samples. We make two key contributions by interpreting a graph as an electrical circuit. First, for graph construction we show how 'effective resistance' can guide node pair selection for negative edge insertions. Second, for classification that tolerates a small rejection rate, we define generalized smoothness on graphs that promotes ambiguity in the classifier signal, so that unsure estimated samples can be rejected. We show that generalized graph-signal smoothness is equivalent to satisfying Kirchhoff's current law (KCL) at a given node - this explains why negative edges should not be used to compute generalized smoothness on graphs. Finally, we propose an algorithm based on iterative reweighted least squares (IRLS) that solves the posed MAP problem efficiently. Simulation results show that our algorithm outperforms both SVM variants and graph-based classifiers using positive-edge graphs noticeably.