In this paper, we focus on the matching recovery problem between a pair of correlated Gaussian Wigner matrices with a latent vertex correspondence. We are particularly interested in a robust version of this problem such that our observation is a perturbed input $(A+E,B+F)$ where $(A,B)$ is a pair of correlated Gaussian Wigner matrices and $E,F$ are adversarially chosen matrices supported on an unknown $\epsilon n * \epsilon n$ principle minor of $A,B$, respectively. We propose a vector approximate message passing (vector AMP) algorithm that succeeds in polynomial time as long as the correlation $\rho$ between $(A,B)$ is a non-vanishing constant and $\epsilon = o\big( \tfrac{1}{(\log n)^{20}} \big)$. The main methodological inputs for our result are the iterative random graph matching algorithm proposed in \cite{DL22+, DL23+} and the spectral cleaning procedure proposed in \cite{IS24+}. To the best of our knowledge, our algorithm is the first efficient random graph matching type algorithm that is robust under any adversarial perturbations of $n^{1-o(1)}$ size.
Modelling information from complex systems such as humans social interaction or words co-occurrences in our languages can help to understand how these systems are organized and function. Such systems can be modelled by networks, and network theory provides a useful set of methods to analyze them. Among these methods, graph embedding is a powerful tool to summarize the interactions and topology of a network in a vectorized feature space. When used in input of machine learning algorithms, embedding vectors help with common graph problems such as link prediction, graph matching, etc. Word embedding has the goal of representing the sense of words, extracting it from large text corpora. Despite differences in the structure of information in input of embedding algorithms, many graph embedding approaches are adapted and inspired from methods in NLP. Limits of these methods are observed in both domains. Most of these methods require long and resource greedy training. Another downside to most methods is that they are black-box, from which understanding how the information is structured is rather complex. Interpretability of a model allows understanding how the vector space is structured without the need for external information, and thus can be audited more easily. With both these limitations in mind, we propose a novel framework to efficiently embed network vertices in an interpretable vector space. Our Lower Dimension Bipartite Framework (LDBGF) leverages the bipartite projection of a network using cliques to reduce dimensionality. Along with LDBGF, we introduce two implementations of this framework that rely on communities instead of cliques: SINr-NR and SINr-MF. We show that SINr-MF can perform well on classical graphs and SINr-NR can produce high-quality graph and word embeddings that are interpretable and stable across runs.
We study the problem of learning latent community structure from multiple correlated networks, focusing on edge-correlated stochastic block models with two balanced communities. Recent work of Gaudio, R\'acz, and Sridhar (COLT 2022) determined the precise information-theoretic threshold for exact community recovery using two correlated graphs; in particular, this showcased the subtle interplay between community recovery and graph matching. Here we study the natural setting of more than two graphs. The main challenge lies in understanding how to aggregate information across several graphs when none of the pairwise latent vertex correspondences can be exactly recovered. Our main result derives the precise information-theoretic threshold for exact community recovery using any constant number of correlated graphs, answering a question of Gaudio, R\'acz, and Sridhar (COLT 2022). In particular, for every $K \geq 3$ we uncover and characterize a region of the parameter space where exact community recovery is possible using $K$ correlated graphs, even though (1) this is information-theoretically impossible using any $K-1$ of them and (2) none of the latent matchings can be exactly recovered.
We study learning problems on correlated stochastic block models with two balanced communities. Our main result gives the first efficient algorithm for graph matching in this setting. In the most interesting regime where the average degree is logarithmic in the number of vertices, this algorithm correctly matches all but a vanishing fraction of vertices with high probability, whenever the edge correlation parameter $s$ satisfies $s^2 > \alpha \approx 0.338$, where $\alpha$ is Otter's tree-counting constant. Moreover, we extend this to an efficient algorithm for exact graph matching whenever this is information-theoretically possible, positively resolving an open problem of R\'acz and Sridhar (NeurIPS 2021). Our algorithm generalizes the recent breakthrough work of Mao, Wu, Xu, and Yu (STOC 2023), which is based on centered subgraph counts of a large family of trees termed chandeliers. A major technical challenge that we overcome is dealing with the additional estimation errors that are necessarily present due to the fact that, in relevant parameter regimes, the latent community partition cannot be exactly recovered from a single graph. As an application of our results, we give an efficient algorithm for exact community recovery using multiple correlated graphs in parameter regimes where it is information-theoretically impossible to do so using just a single graph.
Scene graphs have proven to be highly effective for various scene understanding tasks due to their compact and explicit representation of relational information. However, current methods often overlook the critical importance of preserving symmetry when generating scene graphs from 3D point clouds, which can lead to reduced accuracy and robustness, particularly when dealing with noisy, multi-view data. This work, to the best of our knowledge, presents the first implementation of an Equivariant Scene Graph Neural Network (ESGNN) to generate semantic scene graphs from 3D point clouds, specifically for enhanced scene understanding. Furthermore, a significant limitation of prior methods is the absence of temporal modeling to capture time-dependent relationships among dynamically evolving entities within a scene. To address this gap, we introduce a novel temporal layer that leverages the symmetry-preserving properties of ESGNN to fuse scene graphs across multiple sequences into a unified global representation by an approximate graph-matching algorithm. Our combined architecture, termed the Temporal Equivariant Scene Graph Neural Network (TESGNN), not only surpasses existing state-of-the-art methods in scene estimation accuracy but also achieves faster convergence. Importantly, TESGNN is computationally efficient and straightforward to implement using existing frameworks, making it well-suited for real-time applications in robotics and computer vision. This approach paves the way for more robust and scalable solutions to complex multi-view scene understanding challenges. Our source code is publicly available at: https://github.com/HySonLab/TESGraph
Zero-shot learning (ZSL) aims to leverage additional semantic information to recognize unseen classes. To transfer knowledge from seen to unseen classes, most ZSL methods often learn a shared embedding space by simply aligning visual embeddings with semantic prototypes. However, methods trained under this paradigm often struggle to learn robust embedding space because they align the two modalities in an isolated manner among classes, which ignore the crucial class relationship during the alignment process. To address the aforementioned challenges, this paper proposes a Visual-Semantic Graph Matching Net, termed as VSGMN, which leverages semantic relationships among classes to aid in visual-semantic embedding. VSGMN employs a Graph Build Network (GBN) and a Graph Matching Network (GMN) to achieve two-stage visual-semantic alignment. Specifically, GBN first utilizes an embedding-based approach to build visual and semantic graphs in the semantic space and align the embedding with its prototype for first-stage alignment. Additionally, to supplement unseen class relations in these graphs, GBN also build the unseen class nodes based on semantic relationships. In the second stage, GMN continuously integrates neighbor and cross-graph information into the constructed graph nodes, and aligns the node relationships between the two graphs under the class relationship constraint. Extensive experiments on three benchmark datasets demonstrate that VSGMN achieves superior performance in both conventional and generalized ZSL scenarios. The implementation of our VSGMN and experimental results are available at github: https://github.com/dbwfd/VSGMN
Graph similarity computation (GSC) aims to quantify the similarity score between two graphs. Although recent GSC methods based on graph neural networks (GNNs) take advantage of intra-graph structures in message passing, few of them fully utilize the structures presented by edges to boost the representation of their connected nodes. Moreover, previous cross-graph node embedding matching lacks the perception of the overall structure of the graph pair, due to the fact that the node representations from GNNs are confined to the intra-graph structure, causing the unreasonable similarity score. Intuitively, the cross-graph structure represented in the assignment graph is helpful to rectify the inappropriate matching. Therefore, we propose a structure-enhanced graph matching network (SEGMN). Equipped with a dual embedding learning module and a structure perception matching module, SEGMN achieves structure enhancement in both embedding learning and cross-graph matching. The dual embedding learning module incorporates adjacent edge representation into each node to achieve a structure-enhanced representation. The structure perception matching module achieves cross-graph structure enhancement through assignment graph convolution. The similarity score of each cross-graph node pair can be rectified by aggregating messages from structurally relevant node pairs. Experimental results on benchmark datasets demonstrate that SEGMN outperforms the state-of-the-art GSC methods in the GED regression task, and the structure perception matching module is plug-and-play, which can further improve the performance of the baselines by up to 25%.
Partial graph matching extends traditional graph matching by allowing some nodes to remain unmatched, enabling applications in more complex scenarios. However, this flexibility introduces additional complexity, as both the subset of nodes to match and the optimal mapping must be determined. While recent studies have explored deep learning techniques for partial graph matching, a significant limitation remains: the absence of an optimization objective that fully captures the problem's intrinsic nature while enabling efficient solutions. In this paper, we propose a novel optimization framework for partial graph matching, inspired by optimal partial transport. Our approach formulates an objective that enables partial assignments while incorporating matching biases, using weighted total variation as the divergence function to guarantee optimal partial assignments. Our method can achieve efficient, exact solutions within cubic worst case time complexity. Our contributions are threefold: (i) we introduce a novel optimization objective that balances matched and unmatched nodes; (ii) we establish a connection between partial graph matching and linear sum assignment problem, enabling efficient solutions; (iii) we propose a deep graph matching architecture with a novel partial matching loss, providing an end-to-end solution. The empirical evaluations on standard graph matching benchmarks demonstrate the efficacy of the proposed approach.
Solving point-wise feature correspondence in visual data is a fundamental problem in computer vision. A powerful model that addresses this challenge is to formulate it as graph matching, which entails solving a Quadratic Assignment Problem (QAP) with node-wise and edge-wise constraints. However, solving such a QAP can be both expensive and difficult due to numerous local extreme points. In this work, we introduce a novel linear model and solver designed to accelerate the computation of graph matching. Specifically, we employ a positive semi-definite matrix approximation to establish the structural attribute constraint.We then transform the original QAP into a linear model that is concave for maximization. This model can subsequently be solved using the Sinkhorn optimal transport algorithm, known for its enhanced efficiency and numerical stability compared to existing approaches. Experimental results on the widely used benchmark PascalVOC showcase that our algorithm achieves state-of-the-art performance with significantly improved efficiency. Source code: https://github.com/xmlyqing00/clap
This letter proposes a method of global localization on a map with semantic object landmarks. One of the most promising approaches for localization on object maps is to use semantic graph matching using landmark descriptors calculated from the distribution of surrounding objects. These descriptors are vulnerable to misclassification and partial observations. Moreover, many existing methods rely on inlier extraction using RANSAC, which is stochastic and sensitive to a high outlier rate. To address the former issue, we augment the correspondence matching using Vision Language Models (VLMs). Landmark discriminability is improved by VLM embeddings, which are independent of surrounding objects. In addition, inliers are estimated deterministically using a graph-theoretic approach. We also incorporate pose calculation using the weighted least squares considering correspondence similarity and observation completeness to improve the robustness. We confirmed improvements in matching and pose estimation accuracy through experiments on ScanNet and TUM datasets.
Histopathological imaging is vital for cancer research and clinical practice, with multiplexed Immunofluorescence (MxIF) and Hematoxylin and Eosin (H&E) providing complementary insights. However, aligning different stains at the cell level remains a challenge due to modality differences. In this paper, we present a novel framework for multimodal image alignment using cell segmentation outcomes. By treating cells as point sets, we apply Coherent Point Drift (CPD) for initial alignment and refine it with Graph Matching (GM). Evaluated on ovarian cancer tissue microarrays (TMAs), our method achieves high alignment accuracy, enabling integration of cell-level features across modalities and generating virtual H&E images from MxIF data for enhanced clinical interpretation.
Ensuring that the outputs of neural networks satisfy specific constraints is crucial for applying neural networks to real-life decision-making problems. In this paper, we consider making a batch of neural network outputs satisfy bounded and general linear constraints. We first reformulate the neural network output projection problem as an entropy-regularized linear programming problem. We show that such a problem can be equivalently transformed into an unconstrained convex optimization problem with Lipschitz continuous gradient according to the duality theorem. Then, based on an accelerated gradient descent algorithm with numerical performance enhancement, we present our architecture, GLinSAT, to solve the problem. To the best of our knowledge, this is the first general linear satisfiability layer in which all the operations are differentiable and matrix-factorization-free. Despite the fact that we can explicitly perform backpropagation based on automatic differentiation mechanism, we also provide an alternative approach in GLinSAT to calculate the derivatives based on implicit differentiation of the optimality condition. Experimental results on constrained traveling salesman problems, partial graph matching with outliers, predictive portfolio allocation and power system unit commitment demonstrate the advantages of GLinSAT over existing satisfiability layers. Our implementation is available at \url{https://github.com/HunterTracer/GLinSAT}.
Underwater object-level mapping requires incorporating visual foundation models to handle the uncommon and often previously unseen object classes encountered in marine scenarios. In this work, a metric of semantic uncertainty for open-set object detections produced by visual foundation models is calculated and then incorporated into an object-level uncertainty tracking framework. Object-level uncertainties and geometric relationships between objects are used to enable robust object-level loop closure detection for unknown object classes. The above loop closure detection problem is formulated as a graph-matching problem. While graph matching, in general, is NP-Complete, a solver for an equivalent formulation of the proposed graph matching problem as a graph editing problem is tested on multiple challenging underwater scenes. Results for this solver as well as three other solvers demonstrate that the proposed methods are feasible for real-time use in marine environments for the robust, open-set, multi-object, semantic-uncertainty-aware loop closure detection. Further experimental results on the KITTI dataset demonstrate that the method generalizes to large-scale terrestrial scenes.
Contactless fingerprint is a newly developed type of fingerprint, and has gained lots of attention in recent fingerprint studies. However, most existing contactless fingerprint algorithms treat contactless fingerprints as 2D plain fingerprints, and utilize similar recognition methods as traditional contact-based 2D fingerprints. This recognition approach does not consider the modality difference between contactless and contact fingerprints, especially the intrinsic 3D characteristic of contactless fingerprints. This paper proposes a novel contactless fingerprint recognition algorithm that captures the revealed 3D feature of contactless fingerprints rather than the plain 2D feature. The proposed method first recovers 3D features from the input contactless fingerprint, including the 3D shape model and 3D fingerprint feature (minutiae, orientation, etc.). Then, a novel 3D graph matching is conducted in 3D space according to the extracted 3D feature. Our method captures the real 3D nature of contactless fingerprints as the whole feature extraction and matching algorithms are completed in real 3D space. Experiments results on contactless fingerprint databases show that the proposed method successfully improves the matching accuracy of contactless fingerprints. Exceptionally, our method performs stably across multiple poses of contactless fingerprints due to 3D graph matching, which is a great advantage compared to previous contactless fingerprint recognition algorithms.
With the emergence of data marketplaces, the demand for methods to assess the value of data has increased significantly. While numerous techniques have been proposed for this purpose, none have specifically addressed graphs as the main data modality. Graphs are widely used across various fields, ranging from chemical molecules to social networks. In this study, we break down graphs into two main components: structural and featural, and we focus on evaluating data without relying on specific task-related metrics, making it applicable in practical scenarios where validation requirements may be lacking. We introduce a novel framework called blind message passing, which aligns the seller's and buyer's graphs using a shared node permutation based on graph matching. This allows us to utilize the graph Wasserstein distance to quantify the differences in the structural distribution of graph datasets, called the structural disparities. We then consider featural aspects of buyers' and sellers' graphs for data valuation and capture their statistical similarities and differences, referred to as relevance and diversity, respectively. Our approach ensures that buyers and sellers remain unaware of each other's datasets. Our experiments on real datasets demonstrate the effectiveness of our approach in capturing the relevance, diversity, and structural disparities of seller data for buyers, particularly in graph-based data valuation scenarios.
Cross-domain NER is a practical yet challenging problem since the data scarcity in the real-world scenario. A common practice is first to learn a NER model in a rich-resource general domain and then adapt the model to specific domains. Due to the mismatch problem between entity types across domains, the wide knowledge in the general domain can not effectively transfer to the target domain NER model. To this end, we model the label relationship as a probability distribution and construct label graphs in both source and target label spaces. To enhance the contextual representation with label structures, we fuse the label graph into the word embedding output by BERT. By representing label relationships as graphs, we formulate cross-domain NER as a graph matching problem. Furthermore, the proposed method has good applicability with pre-training methods and is potentially capable of other cross-domain prediction tasks. Empirical results on four datasets show that our method outperforms a series of transfer learning, multi-task learning, and few-shot learning methods.
More and more end-to-end text spotting methods based on Transformer architecture have demonstrated superior performance. These methods utilize a bipartite graph matching algorithm to perform one-to-one optimal matching between predicted objects and actual objects. However, the instability of bipartite graph matching can lead to inconsistent optimization targets, thereby affecting the training performance of the model. Existing literature applies denoising training to solve the problem of bipartite graph matching instability in object detection tasks. Unfortunately, this denoising training method cannot be directly applied to text spotting tasks, as these tasks need to perform irregular shape detection tasks and more complex text recognition tasks than classification. To address this issue, we propose a novel denoising training method (DNTextSpotter) for arbitrary-shaped text spotting. Specifically, we decompose the queries of the denoising part into noised positional queries and noised content queries. We use the four Bezier control points of the Bezier center curve to generate the noised positional queries. For the noised content queries, considering that the output of the text in a fixed positional order is not conducive to aligning position with content, we employ a masked character sliding method to initialize noised content queries, thereby assisting in the alignment of text content and position. To improve the model's perception of the background, we further utilize an additional loss function for background characters classification in the denoising training part.Although DNTextSpotter is conceptually simple, it outperforms the state-of-the-art methods on four benchmarks (Total-Text, SCUT-CTW1500, ICDAR15, and Inverse-Text), especially yielding an improvement of 11.3% against the best approach in Inverse-Text dataset.
With the rapid development of the short video industry, traditional e-commerce has encountered a new paradigm, video-driven e-commerce, which leverages attractive videos for product showcases and provides both video and item services for users. Benefitting from the dynamic and visualized introduction of items,video-driven e-commerce has shown huge potential in stimulating consumer confidence and promoting sales. In this paper, we focus on the video retrieval task, facing the following challenges: (1) Howto handle the heterogeneities among users, items, and videos? (2)How to mine the complementarity between items and videos for better user understanding? In this paper, we first leverage the dual graph to model the co-existing of user-video and user-item interactions in video-driven e-commerce and innovatively reduce user preference understanding to a graph matching problem. To solve it, we further propose a novel bi-level Graph Matching Network(GMN), which mainly consists of node- and preference-level graph matching. Given a user, node-level graph matching aims to match videos and items, while preference-level graph matching aims to match multiple user preferences extracted from both videos and items. Then the proposed GMN can generate and improve user embedding by aggregating matched nodes or preferences from the dual graph in a bi-level manner. Comprehensive experiments show the superiority of the proposed GMN with significant improvements over state-of-the-art approaches (e.g., AUC+1.9% and CTR+7.15%). We have developed it on a well-known video-driven e-commerce platform, serving hundreds of millions of users every day
Object re-identification is of increasing importance in visual surveillance. Most existing works focus on re-identify individual from multiple cameras while the application of group re-identification (Re-ID) is rarely discussed. We redefine Group Re-identification as a process which includes pedestrian detection, feature extraction, graph model construction, and graph matching. Group re-identification is very challenging since it is not only interfered by view-point and human pose variations in the traditional re-identification tasks, but also suffered from the challenges in group layout change and group member variation. To address the above challenges, this paper introduces a novel approach which leverages the multi-granularity information inside groups to facilitate group re-identification. We first introduce a multi-granularity Re-ID process, which derives features for multi-granularity objects (people/people-subgroups) in a group and iteratively evaluates their importances during group Re-ID, so as to handle group-wise misalignments due to viewpoint change and group dynamics. We further introduce a multi-order matching scheme. It adaptively selects representative people/people-subgroups in each group and integrates the multi-granularity information from these people/people-subgroups to obtain group-wise matching, hence achieving a more reliable matching score between groups. Experimental results on various datasets demonstrate the effectiveness of our approach.
In this paper, we propose a novel graph-based methodology to evaluate the functional correctness of SQL generation. Conventional metrics for assessing SQL code generation, such as matching-based and execution-based methods (e.g., exact set match and execution accuracy), are subject to two primary limitations. Firstly, the former fails to effectively assess functional correctness, as different SQL queries may possess identical functionalities. Secondly, the latter is susceptible to producing false positive samples in evaluations. Our proposed evaluation method, \texttt{FuncEvalGMN}, does not depend on the sufficient preparation of the test data, and it enables precise testing of the functional correctness of the code. Firstly, we parse SQL using a relational operator tree (ROT) called \textit{Relnode}, which contains rich semantic information from the perspective of logical execution.Then, we introduce a GNN-based approach for predicting the functional correctness of generated SQL. This approach incorporates global positional embeddings to address the limitations with the loss of topological information in conventional graph matching frameworks. As an auxiliary contribution, we propose a rule-based matching algorithm, Relnode Partial Matching (\texttt{RelPM}) as a baseline. Finally, we contribute a dataset, \texttt{Pair-Aug-Spider} with a training set and two testing sets, each comprising pairs of SQL codes to simulate various SQL code evaluation scenarios. The training set and one testing dataset focus on code generation using large language models (LLMs), while the other emphasizes SQL equivalence rewriting.