M3C: A Framework towards Convergent, Flexible, and Unsupervised Learning of Mixture Graph Matching and Clustering

Existing graph matching methods typically assume that there are similar structures between graphs and they are matchable. However, these assumptions do not align with real-world applications. This work addresses a more realistic scenario where graphs exhibit diverse modes, requiring graph grouping before or along with matching, a task termed mixture graph matching and clustering. We introduce Minorize-Maximization Matching and Clustering (M3C), a learning-free algorithm that guarantees theoretical convergence through the Minorize-Maximization framework and offers enhanced flexibility via relaxed clustering. Building on M3C, we develop UM3C, an unsupervised model that incorporates novel edge-wise affinity learning and pseudo label selection. Extensive experimental results on public benchmarks demonstrate that our method outperforms state-of-the-art graph matching and mixture graph matching and clustering approaches in both accuracy and efficiency. Source code will be made publicly available.

Learning Universe Model for Partial Matching Networks over Multiple Graphs

We consider the general setting for partial matching of two or multiple graphs, in the sense that not necessarily all the nodes in one graph can find their correspondences in another graph and vice versa. We take a universe matching perspective to this ubiquitous problem, whereby each node is either matched into an anchor in a virtual universe graph or regarded as an outlier. Such a universe matching scheme enjoys a few important merits, which have not been adopted in existing learning-based graph matching (GM) literature. First, the subtle logic for inlier matching and outlier detection can be clearly modeled, which is otherwise less convenient to handle in the pairwise matching scheme. Second, it enables end-to-end learning especially for universe level affinity metric learning for inliers matching, and loss design for gathering outliers together. Third, the resulting matching model can easily handle new arriving graphs under online matching, or even the graphs coming from different categories of the training set. To our best knowledge, this is the first deep learning network that can cope with two-graph matching, multiple-graph matching, online matching, and mixture graph matching simultaneously. Extensive experimental results show the state-of-the-art performance of our method in these settings.

Deep Reinforcement Learning of Graph Matching

Graph matching under node and pairwise constraints has been a building block in areas from combinatorial optimization, machine learning to computer vision, for effective structural representation and association. We present a reinforcement learning solver that seeks the node correspondence between two graphs, whereby the node embedding model on the association graph is learned to sequentially find the node-to-node matching. Our method differs from the previous deep graph matching model in the sense that they are focused on the front-end feature and affinity function learning while our method aims to learn the backend decision making given the affinity objective function whatever obtained by learning or not. Such an objective function maximization setting naturally fits with the reinforcement learning mechanism, of which the learning procedure is label-free. Besides, the model is not restricted to a fixed number of nodes for matching. These features make it more suitable for practical usage. Extensive experimental results on both synthetic datasets, natural images, and QAPLIB showcase the superior performance regarding both matching accuracy and efficiency. To our best knowledge, this is the first deep reinforcement learning solver for graph matching.

Rethinking Sampling in 3D Point Cloud Generative Adversarial Networks

In this paper, we examine the long-neglected yet important effects of point sampling patterns in point cloud GANs. Through extensive experiments, we show that sampling-insensitive discriminators (e.g.PointNet-Max) produce shape point clouds with point clustering artifacts while sampling-oversensitive discriminators (e.g.PointNet++, DGCNN) fail to guide valid shape generation. We propose the concept of sampling spectrum to depict the different sampling sensitivities of discriminators. We further study how different evaluation metrics weigh the sampling pattern against the geometry and propose several perceptual metrics forming a sampling spectrum of metrics. Guided by the proposed sampling spectrum, we discover a middle-point sampling-aware baseline discriminator, PointNet-Mix, which improves all existing point cloud generators by a large margin on sampling-related metrics. We point out that, though recent research has been focused on the generator design, the main bottleneck of point cloud GAN actually lies in the discriminator design. Our work provides both suggestions and tools for building future discriminators. We will release the code to facilitate future research.