Learning graph edit distance by graph neural networks

Graph representations have been widely used in pattern recognition thanks to their powerful representation formalism and rich theoretical background. A number of error-tolerant graph matching algorithms such as graph edit distance have been proposed for computing a distance between two labelled graphs. However, they typically suffer from a high computational complexity, which makes it difficult to apply these matching algorithms in a real scenario. In this paper, we propose an efficient graph distance based on the emerging field of geometric deep learning. Our method employs a message passing neural network to capture the graph structure and learns a metric with a siamese network approach. The performance of the proposed graph distance is validated in two application cases, graph classification and graph retrieval of handwritten words, and shows a promising performance when compared with (approximate) graph edit distance benchmarks.

Graph neural networks (GNNs) are increasingly used to model complex patterns in graph-structured data. However, enabling them to ''forget'' designated information remains challenging, especially under privacy regulations such as the GDPR. Existing unlearning methods largely optimize for efficiency and scalability, yet they offer little transparency, and the black-box nature of GNNs makes it difficult to verify whether forgetting has truly occurred. We propose an explainability-driven verifier for GNN unlearning that snapshots the model before and verifies after deletion, using attribution shifts and localized structural changes (e.g., graph edit distance) as transparent evidence. The verifier uses five explainability metrics—residual attribution, heatmap shift, explainability score deviation, graph edit distance, and (diagnostic) graph rule shift. We evaluate two backbones (GCN, GAT) and four unlearning strategies (Retrain, GraphEditor, GNNDelete, IDEA) across five benchmarks (Cora, Citeseer, Pubmed, Coauthor?CS, Coauthor?Physics). Results show that Retrain and GNNDelete achieve near-complete forgetting, GraphEditor provides partial erasure, and IDEA leaves residual signals. These explanation deltas provide the primary, human-readable evidence of forgetting; we also report membership?inference ROC?AUC as a complementary, graph?wide privacy signal. The code is available at https://github.com/ImranAhsan23/F-E

Graph edit distance (GED) is a fundamental measure for graph similarity analysis in many real applications. GED computation has known to be NP-hard and many heuristic methods are proposed. GED has two inherent characteristics: multiple optimum node matchings and one-to-one node matching constraints. However, these two characteristics have not been well considered in the existing learning-based methods, which leads to suboptimal models. In this paper, we propose a novel GED-specific loss function that simultaneously encodes the two characteristics. First, we propose an optimal partial node matching-based regularizer to encode multiple optimum node matchings. Second, we propose a plane intersection-based regularizer to impose the one-to-one constraints for the encoded node matchings. We use the graph neural network on the association graph of the two input graphs to learn the cross-graph representation. Our experiments show that our method is 4.2x-103.8x more accurate than the state-of-the-art methods on real-world benchmark graphs.

Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently, the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation, we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.

AI-Driven molecule generation and bioactivity prediction: A multi-model approach combining VAE, graph and language-based neural networks.

The study of graph neural networks has revealed that they can unleash new applications in a variety of disciplines using such a basic process that we cannot imagine in the context of other deep learning designs. Many limitations limit their expressiveness, and researchers are working to overcome them to fully exploit the power of graph data. There are a number of publications that explore graph neural networks (GNNs) restrictions and bottlenecks, but the common thread that runs through them all is that they can all be traced back to message passing, which is the key technique we use to train our graph models. We outline the general GNN design pipeline in this study as well as discuss solutions to the over-smoothing problem, categorize the solutions, and identify open challenges for further research. Abbreviations: CGNN: Continuous Graph Neural Networks; CNN: Convolution NeuralNetwork; DeGNN: Decomposition Graph Neural Network; DGN: Directional GraphNetworks; DGN: Differentiable Group Normalization; DL: Deep Learning; EGAI:Enhancing GNNs by a High-quality Aggregation of Beneficial Information; GAT: GraphAttention Network; GCN: Graph Convolutional Network; GDC: Graph Drop Connect; GDR: Group Distance Ratio; GNN: Graph Neural Network; GRAND: GraphRandom Neural Networks; IIG: Instance Information Gain; MAD: Man AverageDistance; PDE-GCN: Partial Differential Equations-GCN; PTDNet: ParameterizedTopological Denoising network; TDGNN: Tree Decomposition Graph NeuralNetwork;

The first step to building a scientific application based on machine learning is to numerically represent input data in order to enter the input data into machine learning algorithms. However, the input representation should be carefully designed for successful machine learning because the input representation directly affects the prediction accuracy of the machine learning algorithms. In this chapter, we will explore various input representations from classical feature vectors to composite data formats to understand the benefits of each data representation. In particular, we focus on graph-based input representations that can preserve both the chemical and geometric characteristics of the molecular structures. Also, we will extend the graph-based input representations into general mathematical graphs to represent the molecular structures, the crystal structures, and their composite data formats. In addition to the graph-based representations, we will explore advanced deep neural networks to process such graph data, which is called graph neural networks, and several chemical applications based on graph neural networks will be introduced. As future research, we will discuss how to feed the inter-atomic geometry into graph neural networks to prevent the information loss in geometric information of the molecules. The contents of this chapter will be useful to understand the design principles in constructing chemical databases for successful machine learning.

Graph neural networks (GNNs) is an information - processing system that uses message passing among graph nodes. In recent years, GNN variants including graph attention network (GAT), graph convolutional network (GCN), and graph recurrent network (GRN) have shown revolutionary performance in computer vision applications using deep learning and artificial intelligence. These neural network model extensions, collect information in the form of graphs. GNN may be divided into three groups based on the challenges it solves: link prediction, node classification, graph classification. Machines can differentiate and recognise objects in image and video using standard CNNs. Extensive amount of research work needs to be done before robots can have same visual intuition as humans. GNN architectures, on the other hand, may be used to solve various image categorization and video challenges. The number of GNN applications in computer vision not limited, continues to expand. Human-object interaction, actin understanding, image categorization from a few shots and many more. In this paper use of GNN in image and video understanding, design aspects, architecture, applications and implementation challenges towards computer vision is described. GNN is a strong tool for analysing graph data and is still a relatively active area that needs further researches attention to solve many computer vision applications.

Past events have revealed that widespread blackouts are mostly a result of cascading failures in the power grid. Understanding the underlining mechanisms of cascading failures can help in developing strategies to minimize the risk of such events. Moreover, a real-time detection of precursors to cascading failures will help operators take measures to prevent their propagation. Currently, the well-established probabilistic and physics-based models of cascading failures offer low computational efficiency, hindering them to be used only as offline tools. In this work, we develop a data-driven methodology for online estimation of the risk of cascading failures. We utilize a physics-based cascading failure model to generate a cascading failure dataset considering different operating conditions and failure scenarios, thus obtaining a sample space covering a large set of power grid states that are labeled as safe or unsafe. We use the synthetic data to train deep learning architectures, namely Feed-forward Neural Networks (FNN) and Graph Neural Networks (GNN). With the development of GNNs, improved performance is achieved with graph-structured data, and GNNs can generalize to graphs of diverse sizes. A comparison between FNN and GNN is made and the GNNs inductive capability is demonstrated via test grids. Furthermore, we apply transfer learning to improve the performance of a pre-trained GNN model on power grids not seen in the training process. The GNN model shows accuracy and balanced accuracy above 96% on selected test datasets not used in the training. Conversely, the FNN shows accuracy above 85% and balanced accuracy above 81% on test datasets unseen during training. Overall, the GNN model is successful in determining, if one or several simultaneous outages result in a critical grid state, under specific grid operating conditions.

The definition of efficient similarity or dissimilarity measures between graphs is a key problem in structural pattern recognition. This problem is nicely addressed by the graph edit distance, which constitutes one of the most flexible graph dissimilarity measure in this field. Unfortunately, the computation of an exact graph edit distance is known to be exponential in the number of nodes. In the early beginning of this decade, an efficient heuristic based on a bipartite assignment algorithm has been proposed to find efficiently a suboptimal solution. This heuristic based on an optimal matching of nodes' neighborhood provides a good approximation of the exact edit distance for graphs with a large number of different labels and a high density. Unfortunately, this heuristic works poorly on unlabeled graphs or graphs with a poor diversity of neighborhoods. In this work we propose to extend this heuristic by considering a mapping of bags of walks centered on each node of both graphs.

The secure computation of the graph structure is an important element in the field of secure calculation of graphs, which is important in querying data in graphs, since there are no algorithms for the graph edit distance problem that can resist attacks by malicious adversaries. In this paper, for the problem of secure computation of similarity edit distance of graphs, firstly, the encoding method applicable to the Paillier encryption algorithm is proposed, and the XOR operation scheme is proposed according to the Paillier homomorphic encryption algorithm. Then, the security algorithm under the semi-honest model is designed, which adopts the new encoding method and the XOR operation scheme. Finally, for the malicious behaviors that may be implemented by malicious participants in the semi-honest algorithm, using the hash function, a algorithm for secure computation of graph editing distance under the malicious model is designed, and the security of the algorithm is proved, and the computational complexity and the communication complexity of the algorithm are analyzed, which is more efficient compared with the existing schemes, and has practical value. The algorithm designed in this paper fills the research gap in the existing literature on the problem of graph edit distance and contributes to solving the problem.

The emergence of deep learning has not only brought great changes in the field of image recognition, but also achieved excellent node classification performance in graph neural networks. However, the existing graph neural network framework often uses methods based on spatial domain or spectral domain to capture network structure features. This process captures the local structural characteristics of graph data, and the convolution process has a large amount of calculation. It is necessary to use multi-channel or deep neural network structure to achieve the goal of modeling the high-order structural characteristics of the network. Therefore, this paper proposes a linear graph neural network framework [Linear Graph Neural Network (LGNN)] with superior performance. The model first preprocesses the input graph, and uses symmetric normalization and feature normalization to remove deviations in the structure and features. Then, by designing a high-order adjacency matrix propagation mechanism, LGNN enables nodes to iteratively aggregate and learn the feature information of high-order neighbors. After obtaining the node representation of the network structure, LGNN uses a simple linear mapping to maintain computational efficiency and obtain the final node representation. The experimental results show that the performance of the LGNN algorithm in some tasks is slightly worse than that of the existing mainstream graph neural network algorithms, but it shows or exceeds the machine learning performance of the existing algorithms in most graph neural network performance evaluation tasks, especially on sparse networks.

Deep learning on graphs is an upcoming area of study. This chapter provides an introduction to graph neural networks (GNNs), a type of neural network that is designed to process data represented in the form of graphs. First, it summarizes the explanation of deep learning on graphs. The fundamental concepts of graph neural networks, as well as GNN theories, are then explained. In this chapter, different types of graph neural network (GNN) are also explained. At the end, the applications of graph neural network where GNN is used and for what purpose it is going to be used are explained. This also explores the various applications of GNNs in fields such as social network analysis, recommendation systems, drug discovery, computer vision, and natural language processing. With the increasing prevalence of graph data, GNNs are becoming increasingly important and will likely continue to play a significant role in many fields in the future.

Traffic forecasting is a crucial aspect of modern Intelligent Transportation Systems (ITS) and the Internet of Vehicles (IoV), playing a vital role in improving the safety and efficiency of daily transportation activities. Despite the valuable contributions of traditional machine learning (ML) models and advanced deep learning (DL) techniques, there persist challenges in capturing the intricate spatial and temporal dependencies inherent in traffic flow. In response to these challenges, we present GRAPHITE, an innovative framework that combines Graph Neural Networks (GNNs) and Generative Adversarial Networks (GANs) to leverage generative reasoning for efficient traffic management. Our model seamlessly integrates historical traffic volume data collected by road sensors with local spatial information encoded through knowledge graphs (KGs) associated with each sensor. These KGs offer a structured representation of relationships between traffic sensors and points of interest (POIs) in their neighborhood, thereby enhancing the comprehension of the urban context and leading to more accurate traffic predictions. Extensive experiments conducted on diverse datasets underscore the efficacy of GRAPHITE. Notably, we achieved a maximum decrease in RMSE of 31.05% compared to GAN-GRU and a maximum increase in R2 of 8.15% compared to GAN-RNN, positioning GRAPHITE as a standout solution among the current state-of-the-art approaches. Our code is available at: https://github.com/MODAL-UNINA/GRAPHITE.

In the "blind review" mode for technical bid evaluation within the power industry, review experts must make impartial judgments based on anonymized technical response documents. However, these documents often contain a large amount of complex graphical content, which existing general Optical Character Recognition (OCR) technology struggles to accurately identify. To address this, this study first constructs a specialized image dataset covering typical power industry response document scenarios. Subsequently, an improved You Only Look Once (YOLO) object detection model is developed, incorporating an anchor box clustering strategy optimized for small, densely packed power symbols and a multi-scale feature fusion mechanism. Then, a local contextual relationship inference module based on Graph Neural Networks is designed and integrated. Finally, an end-to-end recognition pipeline from image input to structured information output is constructed. Experimental results indicate that the improved model achieves a mean Average Precision (mAP) of 90.0% in key equipment detection tasks; in topology relationship restoration experiments, the average Graph Edit Distance (GED) is 0.172; in end-to-end efficiency experiments simulating real blind review scenarios, the average processing time per document is only 8.7 seconds, with an information completeness rate of 98.2%. The research demonstrates that the YOLO-based object detection and relationship modeling method, customized for the blind review mode, can effectively address the challenge of recognizing complex image content in power response documents, providing reliable technical support for the efficiency and fairness of blind reviews.