Toward Reliable Graph Matching: from Deterministic Optimization to Combinatorial Learning

Graph matching is a fundamental but notoriously difficult problem due to its NP-hard nature, and serves as a cornerstone for a series of applications in machine learning and computer vision, such as image matching, dynamic routing, drug design, to name a few. Although there has been massive previous investigation on high-performance graph matching solvers, it still remains a challenging task to tackle the matching problem under real-world scenarios with severe graph uncertainty (e.g., noise, outlier, misleading or ambiguous link).In this dissertation, a main focus is to investigate the essence and propose solutions to graph matching with higher reliability under such uncertainty. To this end, the proposed research was conducted taking into account three perspectives related to reliable graph matching: modeling, optimization and learning. For modeling, graph matching is extended from typical quadratic assignment problem to a more generic mathematical model by introducing a specific family of separable function, achieving higher capacity and reliability. In terms of optimization, a novel high gradient-efficient determinant-based regularization technique is proposed in this research, showing high robustness against outliers. Then learning paradigm for graph matching under intrinsic combinatorial characteristics is explored. First, a study is conducted on the way of filling the gap between discrete problem and its continuous approximation under a deep learning framework. Then this dissertation continues to investigate the necessity of more reliable latent topology of graphs for matching, and propose an effective and flexible framework to obtain it. Coherent findings in this dissertation include theoretical study and several novel algorithms, with rich experiments demonstrating the effectiveness.