The graph matching problem seeks to find an alignment between the nodes of two graphs that minimizes the number of adjacency disagreements. Solving the graph matching is increasingly important due to it's applications in operations research, computer vision, neuroscience, and more. However, current state-of-the-art algorithms are inefficient in matching very large graphs, though they produce good accuracy. The main computational bottleneck of these algorithms is the linear assignment problem, which must be solved at each iteration. In this paper, we leverage the recent advances in the field of optimal transport to replace the accepted use of linear assignment algorithms. We present GOAT, a modification to the state-of-the-art graph matching approximation algorithm "FAQ" (Vogelstein, 2015), replacing its linear sum assignment step with the "Lightspeed Optimal Transport" method of Cuturi (2013). The modification provides improvements to both speed and empirical matching accuracy. The effectiveness of the approach is demonstrated in matching graphs in simulated and real data examples.
We present a chatbot implementing a novel dialogue management approach based on logical inference. Instead of framing conversation a sequence of response generation tasks, we model conversation as a collaborative inference process in which speakers share information to synthesize new knowledge in real time. Our chatbot pipeline accomplishes this modelling in three broad stages. The first stage translates user utterances into a symbolic predicate representation. The second stage then uses this structured representation in conjunction with a larger knowledge base to synthesize new predicates using efficient graph matching. In the third and final stage, our bot selects a small subset of predicates and translates them into an English response. This approach lends itself to understanding latent semantics of user inputs, flexible initiative taking, and responses that are novel and coherent with the dialogue context.
This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages for identifying similar arbitrary objects in compound 3D scenes and matching them. For joint reasoning, we first rephrase graph matching as a rigid point set registration problem operating on spectral graph embeddings. Consequently, we utilise efficient convex semidefinite program relaxations for aligning points in Hilbert spaces and add coupling constraints to model the mutual dependency and exploit synergies between both tasks. We outperform state of the art in challenging cases with non-perfectly matching and noisy graphs, and we show successful applications on real compound scenes with multiple 3D elements. Our source code and data are publicly available.
Although conceptualization has been widely studied in semantics and knowledge representation, it is still challenging to find the most accurate concept phrases to characterize the main idea of a text snippet on the fast-growing social media. This is partly attributed to the fact that most knowledge bases contain general terms of the world, such as trees and cars, which do not have the defining power or are not interesting enough to social media app users. Another reason is that the intricacy of natural language allows the use of tense, negation and grammar to change the logic or emphasis of language, thus conveying completely different meanings. In this paper, we present TAG, a high-quality concept matching dataset consisting of 10,000 labeled pairs of fine-grained concepts and web-styled natural language sentences, mined from the open-domain social media. The concepts we consider represent the trending interests of online users. Associated with TAG is a concept graph of these fine-grained concepts and entities to provide the structural context information. We evaluate a wide range of popular neural text matching models as well as pre-trained language models on TAG, and point out their insufficiency to tag social media content with the most appropriate concept. We further propose a novel graph-graph matching method that demonstrates superior abstraction and generalization performance by better utilizing both the structural context in the concept graph and logic interactions between semantic units in the sentence via syntactic dependency parsing. We open-source both the TAG dataset and the proposed methods to facilitate further research.
Few-Shot Remote Sensing Scene Classification (FSRSSC) is an important task, which aims to recognize novel scene classes with few examples. Recently, several studies attempt to address the FSRSSC problem by following few-shot natural image classification methods. These existing methods have made promising progress and achieved superior performance. However, they all overlook two unique characteristics of remote sensing images: (i) object co-occurrence that multiple objects tend to appear together in a scene image and (ii) object spatial correlation that these co-occurrence objects are distributed in the scene image following some spatial structure patterns. Such unique characteristics are very beneficial for FSRSSC, which can effectively alleviate the scarcity issue of labeled remote sensing images since they can provide more refined descriptions for each scene class. To fully exploit these characteristics, we propose a novel scene graph matching-based meta-learning framework for FSRSSC, called SGMNet. In this framework, a scene graph construction module is carefully designed to represent each test remote sensing image or each scene class as a scene graph, where the nodes reflect these co-occurrence objects meanwhile the edges capture the spatial correlations between these co-occurrence objects. Then, a scene graph matching module is further developed to evaluate the similarity score between each test remote sensing image and each scene class. Finally, based on the similarity scores, we perform the scene class prediction via a nearest neighbor classifier. We conduct extensive experiments on UCMerced LandUse, WHU19, AID, and NWPU-RESISC45 datasets. The experimental results show that our method obtains superior performance over the previous state-of-the-art methods.
This paper deals with the problem of graph matching or network alignment for Erd\H{o}s--R\'enyi graphs, which can be viewed as a noisy average-case version of the graph isomorphism problem. Let $G$ and $G'$ be $G(n, p)$ Erd\H{o}s--R\'enyi graphs marginally, identified with their adjacency matrices. Assume that $G$ and $G'$ are correlated such that $\mathbb{E}[G_{ij} G'_{ij}] = p(1-\alpha)$. For a permutation $\pi$ representing a latent matching between the vertices of $G$ and $G'$, denote by $G^\pi$ the graph obtained from permuting the vertices of $G$ by $\pi$. Observing $G^\pi$ and $G'$, we aim to recover the matching $\pi$. In this work, we show that for every $\varepsilon \in (0,1]$, there is $n_0>0$ depending on $\varepsilon$ and absolute constants $\alpha_0, R > 0$ with the following property. Let $n \ge n_0$, $(1+\varepsilon) \log n \le np \le n^{\frac{1}{R \log \log n}}$, and $0 < \alpha < \min(\alpha_0,\varepsilon/4)$. There is a polynomial-time algorithm $F$ such that $\mathbb{P}\{F(G^\pi,G')=\pi\}=1-o(1)$. This is the first polynomial-time algorithm that recovers the exact matching between vertices of correlated Erd\H{o}s--R\'enyi graphs with constant correlation with high probability. The algorithm is based on comparison of partition trees associated with the graph vertices.
Graph Retrieval has witnessed continued interest and progress in the past few years. In thisreport, we focus on neural network based approaches for Graph matching and retrieving similargraphs from a corpus of graphs. We explore methods which can soft predict the similaritybetween two graphs. Later, we gauge the power of a particular baseline (Shortest Path Kernel)and try to model it in our product graph random walks setting while making it more generalised.
We address the non-convex optimisation problem of finding a sparse matrix on the Stiefel manifold (matrices with mutually orthogonal columns of unit length) that maximises (or minimises) a quadratic objective function. Optimisation problems on the Stiefel manifold occur for example in spectral relaxations of various combinatorial problems, such as graph matching, clustering, or permutation synchronisation. Although sparsity is a desirable property in such settings, it is mostly neglected in spectral formulations since existing solvers, e.g. based on eigenvalue decomposition, are unable to account for sparsity while at the same time maintaining global optimality guarantees. We fill this gap and propose a simple yet effective sparsity-promoting modification of the Orthogonal Iteration algorithm for finding the dominant eigenspace of a matrix. By doing so, we can guarantee that our method finds a Stiefel matrix that is globally optimal with respect to the quadratic objective function, while in addition being sparse. As a motivating application we consider the task of permutation synchronisation, which can be understood as a constrained clustering problem that has particular relevance for matching multiple images or 3D shapes in computer vision, computer graphics, and beyond. We demonstrate that the proposed approach outperforms previous methods in this domain.
Automating the Key Information Extraction (KIE) from documents improves efficiency, productivity, and security in many industrial scenarios such as rapid indexing and archiving. Many existing supervised learning methods for the KIE task need to feed a large number of labeled samples and learn separate models for different types of documents. However, collecting and labeling a large dataset is time-consuming and is not a user-friendly requirement for many cloud platforms. To overcome these challenges, we propose a deep end-to-end trainable network for one-shot KIE using partial graph matching. Contrary to previous methods that the learning of similarity and solving are optimized separately, our method enables the learning of the two processes in an end-to-end framework. Existing one-shot KIE methods are either template or simple attention-based learning approach that struggle to handle texts that are shifted beyond their desired positions caused by printers, as illustrated in Fig.1. To solve this problem, we add one-to-(at most)-one constraint such that we will find the globally optimized solution even if some texts are drifted. Further, we design a multimodal context ensemble block to boost the performance through fusing features of spatial, textual, and aspect representations. To promote research of KIE, we collected and annotated a one-shot document KIE dataset named DKIE with diverse types of images. The DKIE dataset consists of 2.5K document images captured by mobile phones in natural scenes, and it is the largest available one-shot KIE dataset up to now. The results of experiments on DKIE show that our method achieved state-of-the-art performance compared with recent one-shot and supervised learning approaches. The dataset and proposed one-shot KIE model will be released soo
Much recent work in bilingual lexicon induction (BLI) views word embeddings as vectors in Euclidean space. As such, BLI is typically solved by finding a linear transformation that maps embeddings to a common space. Alternatively, word embeddings may be understood as nodes in a weighted graph. This framing allows us to examine a node's graph neighborhood without assuming a linear transform, and exploits new techniques from the graph matching optimization literature. These contrasting approaches have not been compared in BLI so far. In this work, we study the behavior of Euclidean versus graph-based approaches to BLI under differing data conditions and show that they complement each other when combined. We release our code at https://github.com/kellymarchisio/euc-v-graph-bli.
One of the strongest signals for automated matching of ontologies and knowledge graphs are the textual descriptions of the concepts. The methods that are typically applied (such as character- or token-based comparisons) are relatively simple, and therefore do not capture the actual meaning of the texts. With the rise of transformer-based language models, text comparison based on meaning (rather than lexical features) is possible. In this paper, we model the ontology matching task as classification problem and present approaches based on transformer models. We further provide an easy to use implementation in the MELT framework which is suited for ontology and knowledge graph matching. We show that a transformer-based filter helps to choose the correct correspondences given a high-recall alignment and already achieves a good result with simple alignment post-processing methods.
In recent years, powered by the learned discriminative representation via graph neural network (GNN) models, deep graph matching methods have made great progresses in the task of matching semantic features. However, these methods usually rely on heuristically generated graph patterns, which may introduce unreliable relationships to hurt the matching performance. In this paper, we propose a joint \emph{graph learning and matching} network, named GLAM, to explore reliable graph structures for boosting graph matching. GLAM adopts a pure attention-based framework for both graph learning and graph matching. Specifically, it employs two types of attention mechanisms, self-attention and cross-attention for the task. The self-attention discovers the relationships between features and to further update feature representations over the learnt structures; and the cross-attention computes cross-graph correlations between the two feature sets to be matched for feature reconstruction. Moreover, the final matching solution is directly derived from the output of the cross-attention layer, without employing a specific matching decision module. The proposed method is evaluated on three popular visual matching benchmarks (Pascal VOC, Willow Object and SPair-71k), and it outperforms previous state-of-the-art graph matching methods by significant margins on all benchmarks. Furthermore, the graph patterns learnt by our model are validated to be able to remarkably enhance previous deep graph matching methods by replacing their handcrafted graph structures with the learnt ones.
Several metrics have been proposed for assessing the similarity of (abstract) meaning representations (AMRs), but little is known about how they relate to human similarity ratings. Moreover, the current metrics have complementary strengths and weaknesses: some emphasize speed, while others make the alignment of graph structures explicit, at the price of a costly alignment step. In this work we propose new Weisfeiler-Leman AMR similarity metrics that unify the strengths of previous metrics, while mitigating their weaknesses. Specifically, our new metrics are able to match contextualized substructures and induce n:m alignments between their nodes. Furthermore, we introduce a Benchmark for AMR Metrics based on Overt Objectives (BAMBOO), the first benchmark to support empirical assessment of graph-based MR similarity metrics. BAMBOO maximizes the interpretability of results by defining multiple overt objectives that range from sentence similarity objectives to stress tests that probe a metric's robustness against meaning-altering and meaning-preserving graph transformations. We show the benefits of BAMBOO by profiling previous metrics and our own metrics. Results indicate that our novel metrics may serve as a strong baseline for future work.
Matching local features across images is a fundamental problem in computer vision. Targeting towards high accuracy and efficiency, we propose Seeded Graph Matching Network, a graph neural network with sparse structure to reduce redundant connectivity and learn compact representation. The network consists of 1) Seeding Module, which initializes the matching by generating a small set of reliable matches as seeds. 2) Seeded Graph Neural Network, which utilizes seed matches to pass messages within/across images and predicts assignment costs. Three novel operations are proposed as basic elements for message passing: 1) Attentional Pooling, which aggregates keypoint features within the image to seed matches. 2) Seed Filtering, which enhances seed features and exchanges messages across images. 3) Attentional Unpooling, which propagates seed features back to original keypoints. Experiments show that our method reduces computational and memory complexity significantly compared with typical attention-based networks while competitive or higher performance is achieved.
Graph matching is an important problem that has received widespread attention, especially in the field of computer vision. Recently, state-of-the-art methods seek to incorporate graph matching with deep learning. However, there is no research to explain what role the graph matching algorithm plays in the model. Therefore, we propose an approach integrating a MILP formulation of the graph matching problem. This formulation is solved to optimal and it provides inherent baseline. Meanwhile, similar approaches are derived by releasing the optimal guarantee of the graph matching solver and by introducing a quality level. This quality level controls the quality of the solutions provided by the graph matching solver. In addition, several relaxations of the graph matching problem are put to the test. Our experimental evaluation gives several theoretical insights and guides the direction of deep graph matching methods.
We consider the task of learning latent community structure from multiple correlated networks. First, we study the problem of learning the latent vertex correspondence between two edge-correlated stochastic block models, focusing on the regime where the average degree is logarithmic in the number of vertices. We derive the precise information-theoretic threshold for exact recovery: above the threshold there exists an estimator that outputs the true correspondence with probability close to 1, while below it no estimator can recover the true correspondence with probability bounded away from 0. As an application of our results, we show how one can exactly recover the latent communities using multiple correlated graphs in parameter regimes where it is information-theoretically impossible to do so using just a single graph.
Matching problems on 3D shapes and images are challenging as they are frequently formulated as combinatorial quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. In this work, we address such problems with emerging quantum computing technology and propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware. We investigate several ways to inject permutation matrix constraints in a quadratic unconstrained binary optimization problem which can be mapped to quantum hardware. We focus on obtaining a sufficient spectral gap, which further increases the probability to measure optimal solutions and valid permutation matrices in a single run. We perform our experiments on the quantum computer D-Wave 2000Q (2^11 qubits, adiabatic). Despite the observed discrepancy between simulated adiabatic quantum computing and execution on real quantum hardware, our reformulation of permutation matrix constraints increases the robustness of the numerical computations over other penalty approaches in our experiments. The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures, which opens up multiple new directions for solving matching problems in 3D computer vision and graphics.
Graph matching aims to establish node correspondence between two graphs, which has been a fundamental problem for its NP-complete nature. One practical consideration is the effective modeling of the affinity function in the presence of noise, such that the mathematically optimal matching result is also physically meaningful. This paper resorts to deep neural networks to learn the node and edge feature, as well as the affinity model for graph matching in an end-to-end fashion. The learning is supervised by combinatorial permutation loss over nodes. Specifically, the parameters belong to convolutional neural networks for image feature extraction, graph neural networks for node embedding that convert the structural (beyond second-order) information into node-wise features that leads to a linear assignment problem, as well as the affinity kernel between two graphs. Our approach enjoys flexibility in that the permutation loss is agnostic to the number of nodes, and the embedding model is shared among nodes such that the network can deal with varying numbers of nodes for both training and inference. Moreover, our network is class-agnostic. Experimental results on extensive benchmarks show its state-of-the-art performance. It bears some generalization capability across categories and datasets, and is capable for robust matching against outliers.
We address the problem of 3D shape registration and we propose a novel technique based on spectral graph theory and probabilistic matching. The task of 3D shape analysis involves tracking, recognition, registration, etc. Analyzing 3D data in a single framework is still a challenging task considering the large variability of the data gathered with different acquisition devices. 3D shape registration is one such challenging shape analysis task. The main contribution of this chapter is to extend the spectral graph matching methods to very large graphs by combining spectral graph matching with Laplacian embedding. Since the embedded representation of a graph is obtained by dimensionality reduction we claim that the existing spectral-based methods are not easily applicable. We discuss solutions for the exact and inexact graph isomorphism problems and recall the main spectral properties of the combinatorial graph Laplacian; We provide a novel analysis of the commute-time embedding that allows us to interpret the latter in terms of the PCA of a graph, and to select the appropriate dimension of the associated embedded metric space; We derive a unit hyper-sphere normalization for the commute-time embedding that allows us to register two shapes with different samplings; We propose a novel method to find the eigenvalue-eigenvector ordering and the eigenvector signs using the eigensignature (histogram) which is invariant to the isometric shape deformations and fits well in the spectral graph matching framework, and we present a probabilistic shape matching formulation using an expectation maximization point registration algorithm which alternates between aligning the eigenbases and finding a vertex-to-vertex assignment.
RGB-Infrared (IR) person re-identification aims to retrieve person-of-interest from heterogeneous cameras, easily suffering from large image modality discrepancy caused by different sensing wavelength ranges. Existing work usually minimizes such discrepancy by aligning domain distribution of global features, while neglecting the intra-modality structural relations between semantic parts. This could result in the network overly focusing on local cues, without considering long-range body part dependencies, leading to meaningless region representations. In this paper, we propose a graph-enabled distribution matching solution, dubbed Geometry-Guided Dual-Alignment (G2DA) learning, for RGB-IR ReID. It can jointly encourage the cross-modal consistency between part semantics and structural relations for fine-grained modality alignment by solving a graph matching task within a multi-scale skeleton graph that embeds human topology information. Specifically, we propose to build a semantic-aligned complete graph into which all cross-modality images can be mapped via a pose-adaptive graph construction mechanism. This graph represents extracted whole-part features by nodes and expresses the node-wise similarities with associated edges. To achieve the graph-based dual-alignment learning, an Optimal Transport (OT) based structured metric is further introduced to simultaneously measure point-wise relations and group-wise structural similarities across modalities. By minimizing the cost of an inter-modality transport plan, G2DA can learn a consistent and discriminative feature subspace for cross-modality image retrieval. Furthermore, we advance a Message Fusion Attention (MFA) mechanism to adaptively reweight the information flow of semantic propagation, effectively strengthening the discriminability of extracted semantic features.