Graph Matching Techniques Research Articles

A graph decomposition-based approach for the graph-fused lasso

We propose a new algorithm for solving the graph-fused lasso (GFL), a regularized model that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. The proposed method applies a novel decomposition of the objective function for the alternating direction method of multipliers (ADMM) algorithm. While ADMM has been widely used in fused lasso problems, existing works such as the network lasso decompose the objective function into the loss function component and the total variation penalty component. In contrast, based on the graph matching technique in graph theory, we propose a new method of decomposition that separates the objective function into two components, where one component is the loss function plus part of the total variation penalty, and the other component is the remaining total variation penalty. We develop an exact convergence rate of the proposed algorithm by developing a general theory on the local convergence of ADMM. Compared with the network lasso algorithm, our algorithm has a faster exact linear convergence rate (although in the same order as for the network lasso). It also enjoys a smaller computational cost per iteration, thus converges overall faster in most numerical examples.

Learning symmetry-aware atom mapping in chemical reactions through deep graph matching

Accurate atom mapping, which establishes correspondences between atoms in reactants and products, is a crucial step in analyzing chemical reactions. In this paper, we present a novel end-to-end approach that formulates the atom mapping problem as a deep graph matching task. Our proposed model, AMNet (Atom Matching Network), utilizes molecular graph representations and employs various atom and bond features using graph neural networks to capture the intricate structural characteristics of molecules, ensuring precise atom correspondence predictions. Notably, AMNet incorporates the consideration of molecule symmetry, enhancing accuracy while simultaneously reducing computational complexity. The integration of the Weisfeiler-Lehman isomorphism test for symmetry identification refines the model’s predictions. Furthermore, our model maps the entire atom set in a chemical reaction, offering a comprehensive approach beyond focusing solely on the main molecules in reactions. We evaluated AMNet’s performance on a subset of USPTO reaction datasets, addressing various tasks, including assessing the impact of molecular symmetry identification, understanding the influence of feature selection on AMNet performance, and comparing its performance with the state-of-the-art method. The result reveals an average accuracy of 97.3% on mapped atoms, with 99.7% of reactions correctly mapped when the correct mapped atom is within the top 10 predicted atoms.Scientific contributionThe paper introduces a novel end-to-end deep graph matching model for atom mapping, utilizing molecular graph representations to capture structural characteristics effectively. It enhances accuracy by integrating symmetry detection through the Weisfeiler-Lehman test, reducing the number of possible mappings and improving efficiency. Unlike previous methods, it maps the entire reaction, not just main components, providing a comprehensive view. Additionally, by integrating efficient graph matching techniques, it reduces computational complexity, making atom mapping more feasible.

Topology change detection in networks due to false data injections: a priori assessment based on graph matching techniques

Topology change detection in networks due to false data injections: a priori assessment based on graph matching techniques

Hybrid Base Complex: Extract and Visualize Structure of Hex-dominant Meshes.

Hex-dominant mesh generation has received significant attention in recent research due to its superior robustness compared to pure hex-mesh generation techniques. In this work, we introduce the first structure for analyzing hex-dominant meshes. This structure builds on the base complex of pure hex-meshes but incorporates the non-hex elements for a more comprehensive and complete representation. We provide its definition and describe its construction steps. Based on this structure, we present an extraction and categorization of sheets using advanced graph matching techniques to handle the non-hex elements. This enables us to develop an enhanced visual analysis of the structure for any hex-dominant meshes.We apply this structure-based visual analysis to compare hex-dominant meshes generated by different methods to study their advantages and disadvantages. This complements the standard quality metric based on the non-hex element percentage for hex-dominant meshes. Moreover, we propose a strategy to extract a cleaned (optimized) valence-based singularity graph wireframe to analyze the structure for both mesh and sheets. Our results demonstrate that the proposed hybrid base complex provides a coarse representation for mesh element, and the proposed valence singularity graph wireframe provides a better internal visualization of hex-dominant meshes.

EAGMN: Coronary artery semantic labeling using edge attention graph matching network

Coronary artery disease (CAD) is one of the primary causes leading deaths worldwide. The presence of atherosclerotic lesions in coronary arteries is the underlying pathophysiological basis of CAD, and accurate extraction of individual arterial branches using invasive coronary angiography (ICA) is crucial for stenosis detection and CAD diagnosis. However, deep-learning-based models face challenges in generating semantic segmentation for coronary arteries due to the morphological similarity among different types of arteries. To address this challenge, we propose an innovative approach called the Edge Attention Graph Matching Network (EAGMN) for coronary artery semantic labeling. Inspired by the learning process of interventional cardiologists in interpreting ICA images, our model compares arterial branches between two individual graphs generated from different ICAs. We begin with extracting individual graphs based on the vascular tree obtained from the ICA. Each node in the individual graph represents an arterial segment, and the EAGMN aims to learn the similarity between nodes from the two individual graphs. By converting the coronary artery semantic segmentation task into a graph node similarity comparison task, identifying the node-to-node correspondence would assign semantic labels for each arterial branch. More specifically, the EAGMN utilizes the association graph constructed from the two individual graphs as input. A graph attention module is employed for feature embedding and aggregation, while a decoder generates the linear assignment for node-to-node semantic mapping. Based on the learned node-to-node relationships, unlabeled coronary arterial segments are classified using the labeled coronary arterial segments, thereby achieving semantic labeling. A dataset with 263 labeled ICAs is used to train and validate the EAGMN. Experimental results indicate the EAGMN achieved a weighted accuracy of 0.8653, a weighted precision of 0.8656, a weighted recall of 0.8653 and a weighted F1-score of 0.8643. Furthermore, we employ ZORRO to provide interpretability and explainability of the graph matching for artery semantic labeling. These findings highlight the potential of the EAGMN for accurate and efficient coronary artery semantic labeling using ICAs. By leveraging the inherent characteristics of ICAs and incorporating graph matching techniques, our proposed model provides a promising solution for improving CAD diagnosis and treatment.

Bisected graph matching improves automated pairing of bilaterally homologous neurons from connectomes.

Graph matching algorithms attempt to find the best correspondence between the nodes of two networks. These techniques have been used to match individual neurons in nanoscale connectomes-in particular, to find pairings of neurons across hemispheres. However, since graph matching techniques deal with two isolated networks, they have only utilized the ipsilateral (same hemisphere) subgraphs when performing the matching. Here, we present a modification to a state-of-the-art graph matching algorithm that allows it to solve what we call the bisected graph matching problem. This modification allows us to leverage the connections between the brain hemispheres when predicting neuron pairs. Via simulations and experiments on real connectome datasets, we show that this approach improves matching accuracy when sufficient edge correlation is present between the contralateral (between hemisphere) subgraphs. We also show how matching accuracy can be further improved by combining our approach with previously proposed extensions to graph matching, which utilize edge types and previously known neuron pairings. We expect that our proposed method will improve future endeavors to accurately match neurons across hemispheres in connectomes, and be useful in other applications where the bisected graph matching problem arises.

Graph-matching distance between individuals' functional connectomes varies with relatedness, age, and cognitive score.

Functional connectomes (FCs), represented by networks or graphs that summarize coactivation patterns between pairs of brain regions, have been related at a population level to age, sex, cognitive/behavioral scores, life experience, genetics, and disease/disorders. However, quantifying FC differences between individuals also provides a rich source of information with which to map to differences in those individuals' biology, experience, genetics or behavior. In this study, graph matching is used to create a novel inter-individual FC metric, called swap distance, that quantifies the distance between pairs of individuals' partial FCs, with a smaller swap distance indicating the individuals have more similar FC. We apply graph matching to align FCs between individuals from the the Human Connectome Project and find that swap distance (i) increases with increasing familial distance, (ii) increases with subjects' ages, (iii) is smaller for pairs of females compared to pairs of males, and (iv) is larger for females with lower cognitive scores compared to females with larger cognitive scores. Regions that contributed most to individuals' swap distances were in higher-order networks, that is, default-mode and fronto-parietal, that underlie executive function and memory. These higher-order networks' regions also had swap frequencies that varied monotonically with familial relatedness of the individuals in question. We posit that the proposed graph matching technique provides a novel way to study inter-subject differences in FC and enables quantification of how FC may vary with age, relatedness, sex, and behavior.

Uncovering illicit supply networks and their interfaces to licit counterparts through graph-theoretic algorithms

The rapid market growth of different illicit trades in recent years can be attributed to their discreet, yet effective, supply chains. This article presents a graph-theoretic approach for investigating the composition of illicit supply networks using limited information. Two key steps constitute our strategy. The first is the construction of a broad network that comprises entities suspected of participating in the illicit supply chain. Two intriguing concepts are involved here: unification of alternate Bills-of-materials and identification of entities positioned at the interface of licit and illicit supply chain; logical graph representation and graph matching techniques are applied to achieve those objectives. In the second step, we search for a set of dissimilar supply chain structures that criminals might likely adopt. We provide an integer linear programming formulation as well as a graph-theoretic representation for this problem, the latter of which leads us to a new variant of Steiner Tree problem: Generalized Group Steiner Tree Problem. Additionally, a three-step algorithmic approach of extracting single (cheapest), multiple and dissimilar trees is proposed to solve the problem. We conclude this work with a semi-real case study on counterfeit footwear to illustrate the utility of our approach in uncovering illicit trades. We also present extensive numerical studies to demonstrate scalability of our algorithms.

Hierarchical graph representation for unsupervised crop row detection in images

Crop row detection is an important aspect of smart farming. An accurate method of crop row detection ensures better navigation of the robot in the field as well as accurate weed control between rows, and crop monitoring. Recent deep learning approaches have emerged as the indispensable methods for most computer vision tasks. Therefore, crop row detection using neural networks is currently the most frequently studied approach. However, these methods require a large amount of labeled data, which is not suitable for many situations such as agriculture, where labeling data is tedious and expensive. Unsupervised techniques such as graph-based represent a promising alternative to tackle such a problem. Indeed, the crop rows represent relationships between plants (relative position, co-occurrence...), that could be integrated as structured information with an unsupervised approach. However, little attention has been paid to graph-based techniques for crop row structures representation. In this paper we propose a new method based on hierarchical approach and unsupervised graph representation for crop row detection. The idea is to transform the field into a structured data where each plant can be linked to its neighbors according to their spatial relationships. Then, with a hierarchical clustering and a criterion of exploring the nodes of the graph we extract subgraphs that represent the aligned structures. We show that the graph matching technique can discard inconsistent structures such as weed aggregations. The results obtained show the validity of the proposed method, with higher performances.

Classification and Recognition of Bilingual Text Using Graph Edit Distance Based Degree of Similarity

Objectives: Graph Edit distance-based classification and recognition method is introduced in this study for bilingual characters. Specifically, this method aims to classify characters first and then recognize them in the 2nd level. Methods: This study combines both exact graph matching and inexact graph matching techniques to achieve better Recognition. The exact graph matching technique classifies characters by considering the number of vertices and edges as features to classify. Inexact graph matching uses an algorithmic model to measure the degree of similarity in the length of edit operations. Findings: The proposed model can compute, if not optimal, sequences all the time, at least near-optimal edit sequence. The proposed model is based on dynamic programming. Edit distance is estimated by comparing preorder sequences of the respective binary trees. Finally, this model uses the loss function to recognize text accurately. To bring out the practicality of the proposed model, we present a case study on the classification of English alphabets and Kannada conjunct consonants. Novelty: (i) A hybrid approach for converting a large class classification problem into a small classification problem that takes advantage of both exact and inexact graph matching techniques. (ii) An algorithmic model is designed to represent each character as a unique string. (iii) Uses dynamic programming in the right places to get the optimal tree, and (iv) to convert the graph matching problem to a string matching problem reduces the time complexity of the problem. Keywords: Bilingual text; Character Recognition; Degree of Similarity; Graph Edit Distance; Graph Matching

Lane-based estimation of travel time distributions by vehicle type via vehicle re-identification using low-resolution video images

Travel time estimation plays an essential role in the high-granular traffic control and management of urban roads with distinct lane-changing conditions among lanes. However, little attention has been given to the estimation of distributions of travel times among different lanes and different vehicle types in addition to their expected values. This paper proposes a new method for estimating lane-based travel time distributions with consideration of different vehicle types through matching low-resolution vehicle video images taken by conventional traffic surveillance cameras. The vehicle type classification is based on vehicle sizes and deep learning features extracted by densely connected convolutional neural networks, and the vehicle re-identification is conducted through a lane-based bipartite graph matching technique. A case study is carried out on a congested urban road in Hong Kong. Results show that the proposed method performs well in estimating the lane-level travel time distributions by vehicle type which can be very helpful for various lane-based and vehicle type-specific traffic management schemes.

AMG Preconditioners for Linear Solvers towards Extreme Scale

Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are a popular ingredient of such linear solvers; this is the motivation for the present work where we examine some recent developments in a package of AMG preconditioners to improve efficiency, scalability, and robustness on extreme-scale problems. The main novelty is the design and implementation of a parallel coarsening algorithm based on aggregation of unknowns employing weighted graph matching techniques; this is a completely automated procedure, requiring no information from the user, and applicable to general symmetric positive definite (s.p.d.) matrices. The new coarsening algorithm improves in terms of numerical scalability at low operator complexity over decoupled aggregation algorithms available in previous releases of the package. The preconditioners package is built on the parallel software framework \texttt{PSBLAS}, which has also been updated to progress towards exascale. We present weak scalability results on one of the most powerful supercomputers in Europe, for linear systems with sizes up to $O(10^{10})$ unknowns.

M2A2: Microscale Modular Assembled ASICs for High-Mix, Low-Volume, Heterogeneously Integrated Designs

With CMOS process technology scaling, the mask cost for fabricating nano-scale transistors, contacts, and interconnects has become prohibitively expensive, especially, for low volume designs. Moreover, higher transistor density has resulted in higher design complexity and large-sized die, which has led to an increase in the design cycle time and degradation in the process yield. These challenges are forcing low-volume application-specific integrated circuits (ASICs) toward highly suboptimal field-programmable gate arrays (FPGAs). In this article, we propose a new approach for designing and fabricating high-mix, low-volume heterogeneously integrated ASICs, referred to as Microscale Modular Assembled ASIC (M2A2), consisting of: 1) pick-and-place assembly of prefabricated blocks (PFBs) which utilizes the nano-precision placement capabilities developed in jet-and-flash imprint lithography (J-FIL) and 2) EDA design methodology utilizing unsupervised learning and graph-matching techniques. The EDA methodology leverages existing CAD tool infrastructure for easy adoption into the current EDA ecosystem. The proposed fabrication technology makes use of pick-and-place assembly technique to allow nano-precise assembly of PFBs. The PFBs can be fabricated in advanced process nodes and then knitted together on a wafer substrate. Custom-designed low-cost back-end metal layers can then be created/placed on top of the PFB knitted layer to realize a variety of high-mix, low-volume ASIC designs. M2A2 would allow more flexibility in front-end design by optimal PFB selection and knitting compared to the earlier proposed approaches such as structured ASICs (sASICs). In this article, the performance of M2A2-based designs are compared with different design technologies, such as baseline ASICs, FPGAs, and sASICs at 16 nm, 40 nm, and 130 nm CMOS process nodes. The post-PNR simulation results achieved over 15 IWLS benchmarks show that the proposed M2A2 designs achieve 27.11x -34.89x reduced power-delay-product (PDP) compared to FPGAs, and incur 1.69x -2.36x larger area compared to the baseline ASICs. The M2A2 designs achieve 15%-68.5% smaller area and 8.5%-52% higher performance compared to the sASIC methodologies. Moreover, the key fabrication steps in the proposed M2A2 technology are presented. The experimental fab results along with the proposed EDA flow simulations show promising results for the proposed M2A2 technology. Design tradeoffs and process challenges for large scale deployment of the M2A2 technology are discussed along with their mitigation strategies.

CRecSys: A Context-Based Recommender System Using Collaborative Filtering and LOD

Linked Open Data (LOD) is an emerging Web technology to store and publish structured data in the form of interlinked knowledgebases like DBpedia, Freebase, Wikidata, and Yago. It uses structured data from multiple domains, and it can be used to conceptualize a concept of interest. Recently, researchers have shown that incorporating contextual features in recommender systems improves rating prediction accuracy. However, identification of contextual features for building context-aware recommender systems is a major bottleneck. To this end, in this article, we present the development of a context-based recommender system, CRecSys, for item ratings prediction in movie domain. CRecSys extracts item-based contextual features from the underlying dataset and generates an RDF graph to model items and their contextual features for computing context-based items similarity using graph matching techniques and item-based collaborative filtering. It uses LOD and two well-known movie data sources - Rotten Tomatoes and IMDB for item profiling using a dataset of 1300 movies. CRecSys is experimentally evaluated over two movie datasets, one is generated by the authors and second is the MovieLens-1M benchmark dataset. CRecSys is also compared with ten baselines and two state-of-the-art recommendation methods, and performs significantly better. It is also empirically established that CRecSys is able to effectively deal with some of the open challenges like cold-start and limited content problems of the traditional recommender systems.

Exergy graph-based fault detection and isolation of a gas-to-liquids process

With the sheer size of modern process plants, the Fault Detection and Isolation (FDI) field continues to gain popularity. FDI is a sophisticated concept which aims to detect and isolate anomalies that occur within a plant to avoid losses of personnel, damages to the environment, and financial implications. It does so in a way which is more direct, efficient and safer than what human operators are capable of. One approach to FDI is to consider the exergy characterisation of a system. By describing the exergy of the system units and streams, in this case a gas-to-liquids (GTL) process plant, the various process variables are encapsulated under a universal energy-domain parameter. The advantage of this being that it can describe the physical states as well as the chemical characteristics of the process. Previous work which utilised exergy characterisation along with a fixed-threshold approach showed promise. This study however, shows that the approach falls short when presented with 3 % faults. These results motivated the investigation of utilising attributed graphs, which package exergy data into a framework that preserves structural information of the plant. The usefulness of finding similarities (called graph matching) between the graphs constructed of operational conditions and pre-collected fault conditions to detect and isolate faulty conditions, is demonstrated. The technique performs well when considering fault magnitudes bigger than 8 % but deteriorates when applied to smaller, 3 % faults. The poor performance could be ascribed to the graph matching aspect, which is described by a single distance value that discards dimensionality. Future work will therefore look into the graph matching technique specifically, aiming to retain more informative dimensions.

Learning a Fixed-Length Fingerprint Representation.

We present DeepPrint, a deep network, which learns to extract fixed-length fingerprint representations of only 200 bytes. DeepPrint incorporates fingerprint domain knowledge, including alignment and minutiae detection, into the deep network architecture to maximize the discriminative power of its representation. The compact, DeepPrint representation has several advantages over the prevailing variable length minutiae representation which (i) requires computationally expensive graph matching techniques, (ii) is difficult to secure using strong encryption schemes (e.g., homomorphic encryption), and (iii) has low discriminative power in poor quality fingerprints where minutiae extraction is unreliable. We benchmark DeepPrint against two top performing COTS SDKs (Verifinger and Innovatrics) from the NIST and FVC evaluations. Coupled with a re-ranking scheme, the DeepPrint rank-1 search accuracy on the NIST SD4 dataset against a gallery of 1.1 million fingerprints is comparable to the top COTS matcher, but it is significantly faster (DeepPrint: 98.80% in 0.3 seconds vs. COTS A: 98.85% in 27 seconds). To the best of our knowledge, the DeepPrint representation is the most compact and discriminative fixed-length fingerprint representation reported in the academic literature.

A unified formulation of a class of graph matching techniques

In this paper, we show that graph matching methods based on relaxation labeling, spectral graph theory and tensor theory have the same mathematical form by employing power iteration technique. Besides, the differences among these methods are also fully discussed and can be proven that distinctions have little impact on the final matching result. Moreover, we propose a fast compatibility building procedure to accelerate the preprocessing speed which is considered to be the main time consuming part of graph matching. Finally, several experiments are conducted to verify our findings.

Advanced Driving Behavior Analytics for an Improved Safety Assessment and Driver Fingerprinting

The recent computerizations of cars, together with the development of sensor technologies and car communication devices have transformed the cars into wealthy sources of information. The analysis of data generated continuously by cars can contribute greatly in improving driving safety and drivers comfort. Even though different analytical solutions have emerged recently, there still exist some important issues in driving safety that we assume were poorly addressed, as well as diverse mathematical methodologies whose application in driving behavior analysis is to be investigated. In this paper, we developed a methodology to process and analyze car-generated data, with focus on two analysis goals: 1) automatic verification of drivers’ behavior conformity to traffic rules; and 2) visualization and comparison of drivers’ behaviors. The proposed methodology is divided into three steps. At first, the abstraction using numerical domains is used to reduce the size of the generated data. Then, the probabilistic graphical models (Probabilistic Automata, and Labeled Directed Graphs) combined with a machine-learning algorithm are used for building a formal model of the driver behavior. Finally, two indepth analyses are carried out by applying automatic model checking and graph matching techniques. Early experimental results point out that the design of numerical domains considered influences hugely the analysis results.

Applying graph matching techniques to enhance reuse of plant design information

This article investigates how graph matching can be applied to process plant design data in order to support the reuse of previous designs. A literature review of existing graph matching algorithms is performed, and a group of algorithms is chosen for further testing. A use case from early phase plant design is presented. A methodology for addressing the use case is proposed, including graph simplification algorithms and node similarity measures, so that existing graph matching algorithms can be applied in the process plant domain. The proposed methodology is evaluated empirically on an industrial case consisting of design data from several pulp and paper plants.

New graph distance for deformable 3D objects recognition based on triangle-stars decomposition

We address the problem of comparing deformable 3D objects represented by graphs such as triangular tessellations. We propose a new graph matching technique to measure the distance between these graphs. The proposed approach is based on a new decomposition of triangular tessellations into triangle-stars. The algorithm ensures a minimum number of disjoint triangle-stars, provides improved dissimilarity by covering larger neighbors and allows the creation of descriptors that are invariant or at least oblivious under the most common deformations. The present approach is based on an approximation of the Graph Edit Distance, which is fault-tolerant to noise and distortion, thus making our technique particularly suitable for the comparison of deformable objects. Classification is performed with supervised machine learning techniques. Our approach defines a metric space using graph embedding and graph kernel techniques. It is proved that the proposed distance is a pseudo-metric. Its time complexity is determined and the method is evaluated against benchmark databases. Our experimental results confirm the performances and the accuracy of our system.