Self-Supervised Bidirectional Learning for Graph Matching

Abstract Deep learning methods have demonstrated promising performance on the NP-hard Graph Matching (GM) problems. However, the state-of-the-art methods usually require the ground-truth labels, which may take extensive human efforts or be impractical to collect. In this paper, we present a robust self-supervised bidirectional learning method (IA-SSGM) to tackle GM in an unsupervised manner. It involves an affinity learning component and a classic GM solver. Specifically, we adopt the Hungarian solver to generate pseudo correspondence labels for the simple probabilistic relaxation of the affinity matrix. In addition, a bidirectional recycling consistency module is proposed to generate pseudo samples by recycling the pseudo correspondence back to permute the input. It imposes a consistency constraint between the pseudo affinity and the original one, which is theoretically supported to help reduce the matching error. Our method further develops a graph contrastive learning jointly with the affinity learning to enhance its robustness against the noise and outliers in real applications. Experiments deliver superior performance over the previous state-of-the-arts on five real-world benchmarks, especially under the more difficult outlier scenarios, demon- strating the effectiveness of our method.