A comparison between two representatives of a set of graphs: median vs barycenter graph

Trabajo presentado al Joint IAPR International Workshop on Structural, Syntactic and Statistical Pattern Recognition (SSPR&SPR) celebrado en Esmirna (Turquía) del 18 al 20 de agosto de 2010.In this paper we consider two existing methods to generate a representative of a given set of graphs, that satisfy the following two conditions. On the one hand, that they are applicable to graphs with any kind of labels in nodes and edges and on the other hand, that they can handle relatively large amount of data. Namely, the approximated algorithms to compute the Median Graph via graph embedding and a new method to compute the Barycenter Graph. Our contribution is to give a new algorithm for the barycenter computation and to compare it to the median Graph. To compare these two representatives, we take into account algorithmic considerations and experimental results on the quality of the representative and its robustness, on several datasets.This work was supported by projects: 'CONSOLIDER-INGENIO 2010 Multimodal interaction in pattern recognition and computer vision' (V-00069), 'Robotica ubicua para entornos urbanos' (J-01225).Peer Reviewe

Building Multiple Classifier Systems Using Linear Combinations of Reduced Graphs.

Despite great efforts done in research in the last decades, the classification of general graphs, i.e., graphs with unconstrained labeling and structure, remains a challenging task. Due to the inherent relational structure of graphs it is difficult, or even impossible, to apply standard pattern recognition methods to graphs to achieve high recognition accuracies. Common methods to solve the non-trivial problem of graph classification employ graph matching in conjunction with a distance-based classifier or a kernel machine. In the present paper, we address the specific task of graph classification by means of a novel framework that uses information acquired from a broad range of reduced graph subspaces. Our novel approach can be roughly divided into three successive steps. In the first step, differently reduced graphs are created out of the original graphs relying on node centrality measures. In the second step, we compute the graph edit distance between each reduced graph and all the other graphs of the corresponding graph subspace. Finally, we linearly combine the distances in the third step and feed them into a distance-based classifier to obtain the final classification result. On six graph data sets, we empirically confirm that the proposed multiple classifier system directly benefits from the combined distances computed in the various graph subspaces

Structural Data Recognition with Graph Model Boosting

This paper presents a novel method for structural data recognition using a large number of graph models. In general, prevalent methods for structural data recognition have two shortcomings: 1) Only a single model is used to capture structural variation. 2) Naive recognition methods are used, such as the nearest neighbor method. In this paper, we propose strengthening the recognition performance of these models as well as their ability to capture structural variation. The proposed method constructs a large number of graph models and trains decision trees using the models. This paper makes two main contributions. The first is a novel graph model that can quickly perform calculations, which allows us to construct several models in a feasible amount of time. The second contribution is a novel approach to structural data recognition: graph model boosting. Comprehensive structural variations can be captured with a large number of graph models constructed in a boosting framework, and a sophisticated classifier can be formed by aggregating the decision trees. Consequently, we can carry out structural data recognition with powerful recognition capability in the face of comprehensive structural variation. The experiments shows that the proposed method achieves impressive results and outperforms existing methods on datasets of IAM graph database repository.Comment: 8 page

Learning from graphs with structural variation

We study the effect of structural variation in graph data on the predictive performance of graph kernels. To this end, we introduce a novel, noise-robust adaptation of the GraphHopper kernel and validate it on benchmark data, obtaining modestly improved predictive performance on a range of datasets. Next, we investigate the performance of the state-of-the-art Weisfeiler-Lehman graph kernel under increasing synthetic structural errors and find that the effect of introducing errors depends strongly on the dataset.Comment: Presented at the NIPS 2017 workshop "Learning on Distributions, Functions, Graphs and Groups

funcGNN: A Graph Neural Network Approach to Program Similarity

Program similarity is a fundamental concept, central to the solution of software engineering tasks such as software plagiarism, clone identification, code refactoring and code search. Accurate similarity estimation between programs requires an in-depth understanding of their structure, semantics and flow. A control flow graph (CFG), is a graphical representation of a program which captures its logical control flow and hence its semantics. A common approach is to estimate program similarity by analysing CFGs using graph similarity measures, e.g. graph edit distance (GED). However, graph edit distance is an NP-hard problem and computationally expensive, making the application of graph similarity techniques to complex software programs impractical. This study intends to examine the effectiveness of graph neural networks to estimate program similarity, by analysing the associated control flow graphs. We introduce funcGNN, which is a graph neural network trained on labeled CFG pairs to predict the GED between unseen program pairs by utilizing an effective embedding vector. To our knowledge, this is the first time graph neural networks have been applied on labeled CFGs for estimating the similarity between high-level language programs. Results: We demonstrate the effectiveness of funcGNN to estimate the GED between programs and our experimental analysis demonstrates how it achieves a lower error rate (0.00194), with faster (23 times faster than the quickest traditional GED approximation method) and better scalability compared with the state of the art methods. funcGNN posses the inductive learning ability to infer program structure and generalise to unseen programs. The graph embedding of a program proposed by our methodology could be applied to several related software engineering problems (such as code plagiarism and clone identification) thus opening multiple research directions.Comment: 11 pages, 8 figures, 3 table

Filtering graphs to check isomorphism and extracting mapping by using the Conductance Electrical Model

© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper presents a new method of filtering graphs to check exact graph isomorphism and extracting their mapping. Each graph is modeled by a resistive electrical circuit using the Conductance Electrical Model (CEM). By using this model, a necessary condition to check the isomorphism of two graphs is that their equivalent resistances have the same values, but this is not enough, and we have to look for their mapping to find the sufficient condition. We can compute the isomorphism between two graphs in O(N-3), where N is the order of the graph, if their star resistance values are different, otherwise the computational time is exponential, but only with respect to the number of repeated star resistance values, which usually is very small. We can use this technique to filter graphs that are not isomorphic and in case that they are, we can obtain their node mapping. A distinguishing feature over other methods is that, even if there exists repeated star resistance values, we can extract a partial node mapping (of all the nodes except the repeated ones and their neighbors) in O(N-3). The paper presents the method and its application to detect isomorphic graphs in two well know graph databases, where some graphs have more than 600 nodes. (C) 2016 Elsevier Ltd. All rights reserved.Postprint (author's draft