We approach the graph generation problem from a spectral perspective by first generating the dominant parts of the graph Laplacian spectrum and then building a graph matching these eigenvalues and eigenvectors. Spectral conditioning allows for direct modeling of the global and local graph structure and helps to overcome the expressivity and mode collapse issues of one-shot graph generators. Our novel GAN, called SPECTRE, enables the one-shot generation of much larger graphs than previously possible with one-shot models. SPECTRE outperforms state-of-the-art deep autoregressive generators in terms of modeling fidelity, while also avoiding expensive sequential generation and dependence on node ordering. A case in point, in sizable synthetic and real-world graphs SPECTRE achieves a 4-to-170 fold improvement over the best competitor that does not overfit and is 23-to-30 times faster than autoregressive generators.
We study the problem of multi-robot active mapping, which aims for complete scene map construction in minimum time steps. The key to this problem lies in the goal position estimation to enable more efficient robot movements. Previous approaches either choose the frontier as the goal position via a myopic solution that hinders the time efficiency, or maximize the long-term value via reinforcement learning to directly regress the goal position, but does not guarantee the complete map construction. In this paper, we propose a novel algorithm, namely NeuralCoMapping, which takes advantage of both approaches. We reduce the problem to bipartite graph matching, which establishes the node correspondences between two graphs, denoting robots and frontiers. We introduce a multiplex graph neural network (mGNN) that learns the neural distance to fill the affinity matrix for more effective graph matching. We optimize the mGNN with a differentiable linear assignment layer by maximizing the long-term values that favor time efficiency and map completeness via reinforcement learning. We compare our algorithm with several state-of-the-art multi-robot active mapping approaches and adapted reinforcement-learning baselines. Experimental results demonstrate the superior performance and exceptional generalization ability of our algorithm on various indoor scenes and unseen number of robots, when only trained with 9 indoor scenes.
We consider the problem of learning latent community structure from multiple correlated networks. We study edge-correlated stochastic block models with two balanced communities, focusing on the regime where the average degree is logarithmic in the number of vertices. Our main result derives the precise information-theoretic threshold for exact community recovery using multiple correlated graphs. This threshold captures the interplay between the community recovery and graph matching tasks. In particular, we uncover and characterize a region of the parameter space where exact community recovery is possible using multiple correlated graphs, even though (1) this is information-theoretically impossible using a single graph and (2) exact graph matching is also information-theoretically impossible. In this regime, we develop a novel algorithm that carefully synthesizes algorithms from the community recovery and graph matching literatures.
The similarity of graph structures, such as Meaning Representations (MRs), is often assessed via structural matching algorithms, such as Smatch (Cai and Knight, 2013). However, Smatch involves a combinatorial problem that suffers from NP-completeness, making large-scale applications, e.g., graph clustering or search, infeasible. To alleviate this issue, we learn SMARAGD: Semantic Match for Accurate and Rapid Approximate Graph Distance. We show the potential of neural networks to approximate Smatch scores, i) in linear time using a machine translation framework to predict alignments, or ii) in constant time using a Siamese CNN to directly predict Smatch scores. We show that the approximation error can be substantially reduced through data augmentation and graph anonymization.
We present a hybrid classical-quantum framework based on the Frank-Wolfe algorithm, Q-FW, for solving quadratic, linearly-constrained, binary optimization problems on quantum annealers (QA). The computational premise of quantum computers has cultivated the re-design of various existing vision problems into quantum-friendly forms. Experimental QA realizations can solve a particular non-convex problem known as the quadratic unconstrained binary optimization (QUBO). Yet a naive-QUBO cannot take into account the restrictions on the parameters. To introduce additional structure in the parameter space, researchers have crafted ad-hoc solutions incorporating (linear) constraints in the form of regularizers. However, this comes at the expense of a hyper-parameter, balancing the impact of regularization. To date, a true constrained solver of quadratic binary optimization (QBO) problems has lacked. Q-FW first reformulates constrained-QBO as a copositive program (CP), then employs Frank-Wolfe iterations to solve CP while satisfying linear (in)equality constraints. This procedure unrolls the original constrained-QBO into a set of unconstrained QUBOs all of which are solved, in a sequel, on a QA. We use D-Wave Advantage QA to conduct synthetic and real experiments on two important computer vision problems, graph matching and permutation synchronization, which demonstrate that our approach is effective in alleviating the need for an explicit regularization coefficient.
Domain Adaptive Object Detection (DAOD) leverages a labeled domain to learn an object detector generalizing to a novel domain free of annotations. Recent advances align class-conditional distributions by narrowing down cross-domain prototypes (class centers). Though great success,they ignore the significant within-class variance and the domain-mismatched semantics within the training batch, leading to a sub-optimal adaptation. To overcome these challenges, we propose a novel SemantIc-complete Graph MAtching (SIGMA) framework for DAOD, which completes mismatched semantics and reformulates the adaptation with graph matching. Specifically, we design a Graph-embedded Semantic Completion module (GSC) that completes mismatched semantics through generating hallucination graph nodes in missing categories. Then, we establish cross-image graphs to model class-conditional distributions and learn a graph-guided memory bank for better semantic completion in turn. After representing the source and target data as graphs, we reformulate the adaptation as a graph matching problem, i.e., finding well-matched node pairs across graphs to reduce the domain gap, which is solved with a novel Bipartite Graph Matching adaptor (BGM). In a nutshell, we utilize graph nodes to establish semantic-aware node affinity and leverage graph edges as quadratic constraints in a structure-aware matching loss, achieving fine-grained adaptation with a node-to-node graph matching. Extensive experiments verify that SIGMA outperforms existing works significantly. Our code is available at https://github.com/CityU-AIM-Group/SIGMA.
Recently, graph neural networks (GNNs) have been shown powerful capacity at modeling structural data. However, when adapted to downstream tasks, it usually requires abundant task-specific labeled data, which can be extremely scarce in practice. A promising solution to data scarcity is to pre-train a transferable and expressive GNN model on large amounts of unlabeled graphs or coarse-grained labeled graphs. Then the pre-trained GNN is fine-tuned on downstream datasets with task-specific fine-grained labels. In this paper, we present a novel Graph Matching based GNN Pre-Training framework, called GMPT. Focusing on a pair of graphs, we propose to learn structural correspondences between them via neural graph matching, consisting of both intra-graph message passing and inter-graph message passing. In this way, we can learn adaptive representations for a given graph when paired with different graphs, and both node- and graph-level characteristics are naturally considered in a single pre-training task. The proposed method can be applied to fully self-supervised pre-training and coarse-grained supervised pre-training. We further propose an approximate contrastive training strategy to significantly reduce time/memory consumption. Extensive experiments on multi-domain, out-of-distribution benchmarks have demonstrated the effectiveness of our approach. The code is available at: https://github.com/RUCAIBox/GMPT.
Registration of longitudinal optical coherence tomography (OCT) images assists disease monitoring and is essential in image fusion applications. Mouse retinal OCT images are often collected for longitudinal study of eye disease models such as uveitis, but their quality is often poor compared with human imaging. This paper presents a novel but efficient framework involving an optimal transport based graph matching (OT-GM) method for 3D mouse OCT image registration. We first perform registration of fundus-like images obtained by projecting all b-scans of a volume on a plane orthogonal to them, hereafter referred to as the x-y plane. We introduce Adaptive Weighted Vessel Graph Descriptors (AWVGD) and 3D Cube Descriptors (CD) to identify the correspondence between nodes of graphs extracted from segmented vessels within the OCT projection images. The AWVGD comprises scaling, translation and rotation, which are computationally efficient, whereas CD exploits 3D spatial and frequency domain information. The OT-GM method subsequently performs the correct alignment in the x-y plane. Finally, registration along the direction orthogonal to the x-y plane (the z-direction) is guided by the segmentation of two important anatomical features peculiar to mouse b-scans, the Internal Limiting Membrane (ILM) and the hyaloid remnant (HR). Both subjective and objective evaluation results demonstrate that our framework outperforms other well-established methods on mouse OCT images within a reasonable execution time.
This paper studies the problem of matching two complete graphs with edge weights correlated through latent geometries, extending a recent line of research on random graph matching with independent edge weights to geometric models. Specifically, given a random permutation $\pi^*$ on $[n]$ and $n$ iid pairs of correlated Gaussian vectors $\{X_{\pi^*(i)}, Y_i\}$ in $\mathbb{R}^d$ with noise parameter $\sigma$, the edge weights are given by $A_{ij}=\kappa(X_i,X_j)$ and $B_{ij}=\kappa(Y_i,Y_j)$ for some link function $\kappa$. The goal is to recover the hidden vertex correspondence $\pi^*$ based on the observation of $A$ and $B$. We focus on the dot-product model with $\kappa(x,y)=\langle x, y \rangle$ and Euclidean distance model with $\kappa(x,y)=\|x-y\|^2$, in the low-dimensional regime of $d=o(\log n)$ wherein the underlying geometric structures are most evident. We derive an approximate maximum likelihood estimator, which provably achieves, with high probability, perfect recovery of $\pi^*$ when $\sigma=o(n^{-2/d})$ and almost perfect recovery with a vanishing fraction of errors when $\sigma=o(n^{-1/d})$. Furthermore, these conditions are shown to be information-theoretically optimal even when the latent coordinates $\{X_i\}$ and $\{Y_i\}$ are observed, complementing the recent results of [DCK19] and [KNW22] in geometric models of the planted bipartite matching problem. As a side discovery, we show that the celebrated spectral algorithm of [Ume88] emerges as a further approximation to the maximum likelihood in the geometric model.
In this paper, based on the assumption that the object boundaries (e.g., buildings) from the over-view data should coincide with footprints of fa\c{c}ade 3D points generated from street-view photogrammetric images, we aim to address this problem by proposing a fully automated geo-registration method for cross-view data, which utilizes semantically segmented object boundaries as view-invariant features under a global optimization framework through graph-matching: taking the over-view point clouds generated from stereo/multi-stereo satellite images and the street-view point clouds generated from monocular video images as the inputs, the proposed method models segments of buildings as nodes of graphs, both detected from the satellite-based and street-view based point clouds, thus to form the registration as a graph-matching problem to allow non-rigid matches; to enable a robust solution and fully utilize the topological relations between these segments, we propose to address the graph-matching problem on its conjugate graph solved through a belief-propagation algorithm. The matched nodes will be subject to a further optimization to allow precise-registration, followed by a constrained bundle adjustment on the street-view image to keep 2D29 3D consistencies, which yields well-registered street-view images and point clouds to the satellite point clouds.
Graph matching finds the correspondence of nodes across two correlated graphs and lies at the core of many applications. When graph side information is not available, the node correspondence is estimated on the sole basis of network topologies. In this paper, we propose a novel criterion to measure the graph matching accuracy, structural inconsistency (SI), which is defined based on the network topological structure. Specifically, SI incorporates the heat diffusion wavelet to accommodate the multi-hop structure of the graphs. Based on SI, we propose a Structural Inconsistency reducing Graph Matching Algorithm (SIGMA), which improves the alignment scores of node pairs that have low SI values in each iteration. Under suitable assumptions, SIGMA can reduce SI values of true counterparts. Furthermore, we demonstrate that SIGMA can be derived by using a mirror descent method to solve the Gromov-Wasserstein distance with a novel K-hop-structure-based matching costs. Extensive experiments show that our method outperforms state-of-the-art methods.
Cross-camera image data association is essential for many multi-camera computer vision tasks, such as multi-camera pedestrian detection, multi-camera multi-target tracking, 3D pose estimation, etc. This association task is typically stated as a bipartite graph matching problem and often solved by applying minimum-cost flow techniques, which may be computationally inefficient with large data. Furthermore, cameras are usually treated by pairs, obtaining local solutions, rather than finding a global solution at once. Other key issue is that of the affinity measurement: the widespread usage of non-learnable pre-defined distances, such as the Euclidean and Cosine ones. This paper proposes an efficient approach for cross-cameras data-association focused on a global solution, instead of processing cameras by pairs. To avoid the usage of fixed distances, we leverage the connectivity of Graph Neural Networks, previously unused in this scope, using a Message Passing Network to jointly learn features and similarity. We validate the proposal for pedestrian multi-view association, showing results over the EPFL multi-camera pedestrian dataset. Our approach considerably outperforms the literature data association techniques, without requiring to be trained in the same scenario in which it is tested. Our code is available at \url{http://www-vpu.eps.uam.es/publications/gnn_cca}.
Mapping and localization are two essential tasks for mobile robots in real-world applications. However, largescale and dynamic scenes challenge the accuracy and robustness of most current mature solutions. This situation becomes even worse when computational resources are limited. In this paper, we present a novel lightweight object-level mapping and localization method with high accuracy and robustness. Different from previous methods, our method does not need a prior constructed precise geometric map, which greatly releases the storage burden, especially for large-scale navigation. We use object-level features with both semantic and geometric information to model landmarks in the environment. Particularly, a learning topological primitive is first proposed to efficiently obtain and organize the object-level landmarks. On the basis of this, we use a robot-centric mapping framework to represent the environment as a semantic topology graph and relax the burden of maintaining global consistency at the same time. Besides, a hierarchical memory management mechanism is introduced to improve the efficiency of online mapping with limited computational resources. Based on the proposed map, the robust localization is achieved by constructing a novel local semantic scene graph descriptor, and performing multi-constraint graph matching to compare scene similarity. Finally, we test our method on a low-cost embedded platform to demonstrate its advantages. Experimental results on a large scale and multi-session real-world environment show that the proposed method outperforms the state of arts in terms of lightweight and robustness.
We present a framework of Training Free Graph Matching (TFGM) to boost the performance of Graph Neural Networks (GNNs) based graph matching, providing a fast promising solution without training (training-free). TFGM provides four widely applicable principles for designing training-free GNNs and is generalizable to supervised, semi-supervised, and unsupervised graph matching. The keys are to handcraft the matching priors, which used to be learned by training, into GNN's architecture and discard the components inessential under the training-free setting. Further analysis shows that TFGM is a linear relaxation to the quadratic assignment formulation of graph matching and generalizes TFGM to a broad set of GNNs. Extensive experiments show that GNNs with TFGM achieve comparable (if not better) performances to their fully trained counterparts, and demonstrate TFGM's superiority in the unsupervised setting. Our code is available at https://github.com/acharkq/Training-Free-Graph-Matching.
Most previous learning-based graph matching algorithms solve the \textit{quadratic assignment problem} (QAP) by dropping one or more of the matching constraints and adopting a relaxed assignment solver to obtain sub-optimal correspondences. Such relaxation may actually weaken the original graph matching problem, and in turn hurt the matching performance. In this paper we propose a deep learning-based graph matching framework that works for the original QAP without compromising on the matching constraints. In particular, we design an affinity-assignment prediction network to jointly learn the pairwise affinity and estimate the node assignments, and we then develop a differentiable solver inspired by the probabilistic perspective of the pairwise affinities. Aiming to obtain better matching results, the probabilistic solver refines the estimated assignments in an iterative manner to impose both discrete and one-to-one matching constraints. The proposed method is evaluated on three popularly tested benchmarks (Pascal VOC, Willow Object and SPair-71k), and it outperforms all previous state-of-the-arts on all benchmarks.
Answering semantically-complicated questions according to an image is challenging in Visual Question Answering (VQA) task. Although the image can be well represented by deep learning, the question is always simply embedded and cannot well indicate its meaning. Besides, the visual and textual features have a gap for different modalities, it is difficult to align and utilize the cross-modality information. In this paper, we focus on these two problems and propose a Graph Matching Attention (GMA) network. Firstly, it not only builds graph for the image, but also constructs graph for the question in terms of both syntactic and embedding information. Next, we explore the intra-modality relationships by a dual-stage graph encoder and then present a bilateral cross-modality graph matching attention to infer the relationships between the image and the question. The updated cross-modality features are then sent into the answer prediction module for final answer prediction. Experiments demonstrate that our network achieves state-of-the-art performance on the GQA dataset and the VQA 2.0 dataset. The ablation studies verify the effectiveness of each modules in our GMA network.
Point cloud registration for 3D objects is a challenging task due to sparse and noisy measurements, incomplete observations and large transformations. In this work, we propose \textbf{G}raph \textbf{M}atching \textbf{C}onsensus \textbf{Net}work (\textbf{GMCNet}), which estimates pose-invariant correspondences for full-range Partial-to-Partial point cloud Registration (PPR) in the object-level registration scenario. To encode robust point descriptors, \textbf{1)} we first comprehensively investigate transformation-robustness and noise-resilience of various geometric features. \textbf{2)} Then, we employ a novel {T}ransformation-robust {P}oint {T}ransformer (\textbf{TPT}) module to adaptively aggregate local features regarding the structural relations, which takes advantage from both handcrafted rotation-invariant ({\textit{RI}}) features and noise-resilient spatial coordinates. \textbf{3)} Based on a synergy of hierarchical graph networks and graphical modeling, we propose the {H}ierarchical {G}raphical {M}odeling (\textbf{HGM}) architecture to encode robust descriptors consisting of i) a unary term learned from {\textit{RI}} features; and ii) multiple smoothness terms encoded from neighboring point relations at different scales through our TPT modules. Moreover, we construct a challenging PPR dataset (\textbf{MVP-RG}) based on the recent MVP dataset that features high-quality scans. Extensive experiments show that GMCNet outperforms previous state-of-the-art methods for PPR. Notably, GMCNet encodes point descriptors for each point cloud individually without using cross-contextual information, or ground truth correspondences for training. Our code and datasets are available at: https://github.com/paul007pl/GMCNet.
We consider the problem of graph-matching on a network of 3D shapes with uncertainty quantification. We assume that the pairwise shape correspondences are efficiently represented as \emph{functional maps}, that match real-valued functions defined over pairs of shapes. By modeling functional maps between nearly isometric shapes as elements of the Lie group $SO(n)$, we employ \emph{synchronization} to enforce cycle consistency of the collection of functional maps over the graph, hereby enhancing the accuracy of the individual maps. We further introduce a tempered Bayesian probabilistic inference framework on $SO(n)$. Our framework enables: (i) synchronization of functional maps as maximum-a-posteriori estimation on the Riemannian manifold of functional maps, (ii) sampling the solution space in our energy based model so as to quantify uncertainty in the synchronization problem. We dub the latter \emph{Riemannian Langevin Functional Map (RLFM) Sampler}. Our experiments demonstrate that constraining the synchronization on the Riemannian manifold $SO(n)$ improves the estimation of the functional maps, while our RLFM sampler provides for the first time an uncertainty quantification of the results.
Protein complex formation is a central problem in biology, being involved in most of the cell's processes, and essential for applications, e.g. drug design or protein engineering. We tackle rigid body protein-protein docking, i.e., computationally predicting the 3D structure of a protein-protein complex from the individual unbound structures, assuming no conformational change within the proteins happens during binding. We design a novel pairwise-independent SE(3)-equivariant graph matching network to predict the rotation and translation to place one of the proteins at the right docked position relative to the second protein. We mathematically guarantee a basic principle: the predicted complex is always identical regardless of the initial locations and orientations of the two structures. Our model, named EquiDock, approximates the binding pockets and predicts the docking poses using keypoint matching and alignment, achieved through optimal transport and a differentiable Kabsch algorithm. Empirically, we achieve significant running time improvements and often outperform existing docking software despite not relying on heavy candidate sampling, structure refinement, or templates.
While there have been many studies on hardware acceleration for deep learning on images, there has been a rather limited focus on accelerating deep learning applications involving graphs. The unique characteristics of graphs, such as the irregular memory access and dynamic parallelism, impose several challenges when the algorithm is mapped to a CPU or GPU. To address these challenges while exploiting all the available sparsity, we propose a flexible architecture called SPA-GCN for accelerating Graph Convolutional Networks (GCN), the core computation unit in deep learning algorithms on graphs. The architecture is specialized for dealing with many small graphs since the graph size has a significant impact on design considerations. In this context, we use SimGNN, a neural-network-based graph matching algorithm, as a case study to demonstrate the effectiveness of our architecture. The experimental results demonstrate that SPA-GCN can deliver a high speedup compared to a multi-core CPU implementation and a GPU implementation, showing the efficiency of our design.