Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of the node-wise and structure-wise affinity across graphs and the resulting objective, to guide the matching procedure effectively finding the true matching against noises. To this end, this paper devises an end-to-end differentiable deep network pipeline to learn the affinity for graph matching. It involves a supervised permutation loss regarding with node correspondence to capture the combinatorial nature for graph matching. Meanwhile deep graph embedding models are adopted to parameterize both intra-graph and cross-graph affinity functions, instead of the traditional shallow and simple parametric forms e.g. a Gaussian kernel. The embedding can also effectively capture the higher-order structure beyond second-order edges. The permutation loss model is agnostic to the number of nodes, and the embedding model is shared among nodes such that the network allows for varying numbers of nodes in graphs for training and inference. Moreover, our network is class-agnostic with some generalization capability across different categories. All these features are welcomed for real-world applications. Experiments show its superiority against state-of-the-art graph matching learning methods.
Graph matching bears the combinatorial nature. There is an emerging thread using learning to seek efficient solution, especially with deep networks. In @cite_41 , the well known NP-hard problem for coloring very large graphs is addressed using deep reinforcement learning. The resulting algorithm can learn new state of the art heuristics for graph coloring. While the Travelling Salesman Problem (TSP) is studied in @cite_29 and the authors propose a graph attention network based method which learns a heuristic algorithm that employs neural network policy to find a tour. Deep learning for node set is also explored in @cite_25 which seeks permutation invariant objective functions to a set of nodes.
@cite_41 @cite_29 @cite_25
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We show that recent innovations in deep reinforcement learning can effectively color very large graphs -- a well-known NP-hard problem with clear commercial applications. Because the Monte Carlo Tree Search with Upper Confidence Bound algorithm used in AlphaGoZero can improve the performance of a given heuristic, our approach allows deep neural networks trained using high performance computing (HPC) technologies to transform computation into improved heuristics with zero prior knowledge. Key to our approach is the introduction of a novel deep neural network architecture (FastColorNet) that has access to the full graph context and requires @math time and space to color a graph with @math vertices, which enables scaling to very large graphs that arise in real applications like parallel computing, compilers, numerical solvers, and design automation, among others. As a result, we are able to learn new state of the art heuristics for graph coloring. In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection. As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm. As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the 'labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm.