Image categorization: Graph edit [formula omitted] direction histogram

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.

Graph edit distance (GED) is a measure for quantifying the similarity between two graphs. Because of its flexibility and versatility, GED is widely used in many real applications. However, the main disadvantage of GED is its high computational cost. Many solutions have been proposed to speed up GED computation, but most of them focus on developing serial algorithms and only very few solutions consider parallel computing. In this paper, we study a parallel GED computation to elaborate a fast and precise algorithm. Unlike existing solutions that utilize either a depth-first or a best-first search, we propose a hybrid approach that combines depth-first and best-first search paradigms. Our approach can quickly find tighter GED upper bounds, and effectively prune the search space using the upper bounds. Based on the approach, we develop an efficient parallel GED computation algorithm named ${\sf HGED}$ . To maximize thread utility, ${\sf HGED}$ is also equipped with a novel dynamic load balancing scheme whose main focus is on reducing the overhead of thread synchronization. Experimental results on widely used real datasets show that, on average, ${\sf HGED}$ outperforms the state-of-the art serial algorithm ${\sf AStar}^{+}$ - ${\sf LSa}$ by 6 times and the state-of-the parallel algorithm ${\sf PGED}$ by 4 times.

Graph edit distance is an error tolerant matching technique emerged as a powerful and flexible graph matching paradigm that can be used to address different tasks in pattern recognition, machine learning and data mining; it represents the minimum-cost sequence of basic edit operations to transform one graph into another by means of insertion, deletion and substitution of vertices and/or edges. A widely used method for exact graph edit distance computation is based on the A* algorithm. To overcome its high memory load while traversing the search tree for storing pending solutions to be explored, we propose a depth-first graph edit distance algorithm which requires less memory and searching time. An evaluation of all possible solutions is performed without explicitly enumerating them all. Candidates are discarded using an upper and lower bounds strategy. A solid experimental study is proposed; experiments on a publicly available database empirically demonstrated that our approach is better than the A* graph edit distance computation in terms of speed, accuracy and classification rate.

It is essential to identify similarity between graphs for various tasks in data mining, machine learning and pattern recognition. Graph edit distance (GED) is the most popular graph similarity measure thanks to its flexibility and versatility. In this paper, we study the problem of top-<i>k</i> graph similarity search, which finds <i>k</i> graphs most similar to a given query graph under the GED measure. We propose incremental GED computation algorithms that compute desired GED lower and upper bounds. Based on the algorithms, we develop novel search frameworks to address the top-<i>k</i> search problem. Our frameworks are also designed to use a state-of-the art indexing technique to speed up top-<i>k</i> search. By conducting extensive experiments on real datasets, we show that the proposed frameworks significantly improve the performance of top-<i>k</i> graph similarity search.

Background Graph edit distance is a methodology used to solve error-tolerant graph matching. This methodology estimates a distance between two graphs by determining the minimum number of modifications required to transform one graph into the other. These modifications, known as edit operations, have an edit cost associated that has to be determined depending on the problem.Objective This study focuses on the use of optimization techniques in order to learn the edit costs used when comparing graphs by means of the graph edit distance.Methods Graphs represent reduced structural representations of molecules using pharmacophore-type node descriptions to encode the relevant molecular properties. This reduction technique is known as extended reduced graphs. The screening and statistical tools available on the ligand-based virtual screening benchmarking platform and the RDKit were used.ResultsIn the experiments, the graph edit distance using learned costs performed better or equally good than using predefined costs. This is exemplified with six publicly available datasets: DUD-E, MUV, GLL&GDD, CAPST, NRLiSt BDB, and ULS-UDS.Conclusion This study shows that the graph edit distance along with learned edit costs is useful to identify bioactivity similarities in a structurally diverse group of molecules. Furthermore, the target-specific edit costs might provide useful structure-activity information for future drug-design efforts.

A novel hierarchical-based framework for upper bound computation of graph edit distance

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.

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.

We consider a setting where there are two parties, each party holds a private graph and they wish to jointly compute the structural dissimilarity between two graphs without revealing any information about their private input graph. Graph edit distance (GED) is a widely accepted metric for measuring the dissimilarity of graphs. It measures the minimum cost for transforming one graph into the other graph by applying graph edit operations. In this paper we present a framework for securely computing approximated GED and as an example, present a protocol based on threshold additive homomorphic encryption scheme. We develop several new sub-protocols such as private maximum computation and optimal assignment protocols to construct the main protocol. We show that our protocols are secure against semi-honest adversaries. The asymptotic complexity of the protocol is \(O(n^5\ell \log ^*(\ell ))\) where \(\ell \) is the bit length of ring elements and n is the number of nodes in the graph.

Alignment of point sets is frequently used in pattern recognition when objects are represented by sets of coordinate points. The idea behind this problem is to be able to compare two objects regardless of the effect of a given transformation on their coordinate data. This paper presents a method to align point sets based on the graph edit distance. The main idea is to learn the edit costs (in a learning step) and then apply graph edit distance (in a pattern recognition step) with the learned edit costs. Thus, the edit cost would have to incorporate the transformation parameters. In the experimental section, we show that the method is competitive if the graph edit distance parameters are automatically learned considering the learning set. These parameters are the insertion and deletion costs and also the weights on the substitution costs.

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

Learning graph edit distance by graph neural networks

Graph edit distance (GED) is an error tolerant graph matching paradigm whose methods are often evaluated in a classification context and less deeply assessed in terms of the accuracy of the found solution. To evaluate the accuracy of GED methods, low level information is required not only at the classification level but also at the matching level. Most of the publicly available repositories with associated ground truths are dedicated to evaluating graph classification or exact graph matching methods and so the matching correspondences as well as the distance between each pair of graphs are not directly evaluated. This paper consists of two parts. First, we provide a graph database repository annotated with low level information like graph edit distances and their matching correspondences. Second, we propose a set of performance evaluation metrics to assess the performance of GED methods.

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.

Random walk kernels in conjunction with Support Vector Machines are powerful methods for error-tolerant graph matching. Because of their local definition, however, the applicability of random walk kernels strongly depends on the characteristics of the underlying graph representation. In this paper, we describe a simple extension to the standard random walk kernel based on graph edit distance. The idea is to include global matching information in the local similarity evaluation of random walks in graphs. The proposed extension allows us to improve the performance of the random walk kernel significantly. We present an experimental evaluation of our method on three difficult graph datasets.