Graph Similarity Measures Research Articles

On efficient network similarity measures

This paper presents novel graph similarity measures which can be applied to simple directed and undirected networks. To define the graph similarity measures, we first map graphs to real numbers by utilizing structural graph measures. Then, we define measures of similarity between real numbers and prove that they can be used as proxies for graph similarity. Numerical results are derived to show the domain coverage of these measures as well as their clustering ability. The latter relates to the efficient grouping of graphs according to certain structural properties. Our numerical results are sensitive to these properties and offer insights useful for designing effective graph similarity measures.

A saliency-weighted orthogonal regression-based similarity measure for entropic graphs

Various measures are used to determine similarity ratios among images before and after image registration. Image registration methods are based on finding the translation, rotation, and scaling parameters that maximize the similarity between two images by taking advantage of the feature points and densities that are found. While the similarity criterion is calculated, it is possible and advantageous to use approximation methods on the graphs based on information theory. The current study proposes a new similarity measure based on saliency-weighted orthogonal regression derived from the weighted sums of the saliency map of the orthogonal regression residuals formed on the entropic graph. It is evaluated in terms of both quantitative and qualitative methods and compared with other graph-based similarity measures.

Relational social recommendation: Application to the academic domain

This paper outlines RSR, a relational social recommendation approach applied to a social graph comprised of relational entity profiles. RSR uses information extraction and learning methods to obtain relational facts about persons of interest from the Web, and generates an associative entity-relation social network from their extracted personal profiles. As a case study, we consider the task of peer recommendation at scientific conferences. Given a social graph of scholars, RSR employs graph similarity measures to rank conference participants by their relatedness to a user. Unlike other recommender systems that perform social rankings, RSR provides the user with detailed supporting explanations in the form of relational connecting paths. In a set of user studies, we collected feedbacks from participants onsite of scientific conferences, pertaining to RSR quality of recommendations and explanations. The feedbacks indicate that users appreciate and benefit from RSR explainability features. The feedbacks further indicate on recommendation serendipity using RSR, having it recommend persons of interest who are not apriori known to the user, oftentimes exposing surprising inter-personal associations. Finally, we outline and assess potential gains in recommendation relevance and serendipity using path-based relational learning within RSR.

GERoMe-a Method for Evaluating Stability of Graph Extraction Algorithms Without Ground Truth

The extraction of graph structures in Euclidean vector space is a topic of interest with applications in many fields, such as the analysis of vascular networks in the biomedical domain. While a number of approaches have been proposed to tackle the problem of graph extraction, a quantitative evaluation of those algorithms remains a challenging task: In many cases, manual generation of ground truth for real-world data is time-consuming, error-prone, and thus not feasible. While tools for generating synthetic datasets with corresponding ground truth exist, the resulting data often does not reflect the complexity that real-world scenarios show in morphology and topology. As a complementary or even alternative approach, we propose GERoMe, the graph extraction robustness measure, which provides a means of quantifying the stability of algorithms that extract (multi-)graphs with associated node positions from non-graph structures. Our method takes edge-associated properties into consideration and does not necessarily require ground truth data, although available ground truth information can be incorporated to additionally evaluate the correctness of the graph extraction algorithm. We evaluate the behavior of the proposed graph similarity measure and demonstrate the usefulness and applicability of our method in an exemplary study on both synthetic and real-world data.

A Graph Representation Composed of Geometrical Components for Household Furniture Detection by Autonomous Mobile Robots

This study proposes a framework to detect and recognize household furniture using autonomous mobile robots. The proposed methodology is based on the analysis and integration of geometric features extracted over 3D point clouds. A relational graph is constructed using those features to model and recognize each piece of furniture. A set of sub-graphs corresponding to different partial views allows matching the robot’s perception with partial furniture models. A reduced set of geometric features is employed: horizontal and vertical planes and the legs of the furniture. These features are characterized through their properties, such as: height, planarity and area. A fast and linear method for the detection of some geometric features is proposed, which is based on histograms of 3D points acquired from an RGB-D camera onboard the robot. Similarity measures for geometric features and graphs are proposed, as well. Our proposal has been validated in home-like environments with two different mobile robotic platforms; and partially on some 3D samples of a database.

A novel edge-centric approach for graph edit similarity computation

Graph similarity is an important notion with many applications. Graph edit distance is one of the most flexible graph similarity measures available. The main problem with this measure is that in practice it can only be computed for small graphs due to its exponential time complexity. This paper addresses the high complexity of graph edit distance computations. Specifically, we present CSI_GED, a novel edge-centric approach for computing graph edit distance through common sub-structure isomorphisms enumeration. CSI_GED utilizes backtracking search combined with a number of heuristics to reduce memory requirements and quickly prune away a large portion of the mapping search space. Experiments show that CSI_GED is highly efficient for computing graph edit distance; it outperforms the state-of-the-art methods by over three orders of magnitude. It also shows that CSI_GED scales the computation gracefully to larger and distant graphs on which current methods fail to run. Moreover, we evaluated CSI_GED as a stand-alone graph edit similarity search query method. The experiments show that CSI_GED is effective and scalable, and outperforms the state-of-the-art indexing-based methods by over two orders of magnitude.

A swarm intelligence-based approach to anomaly detection of dynamic systems

Abstract We propose a novel Swarm Intelligence-based approach for anomaly detection of dynamic systems. Specifically, we consider observation processes for dynamic systems from a foraging perspective, and ant foraging behavior-based search techniques are applied to the discovery of the ‘intrinsic communication topology’ of systems. The key idea exploited here is that systems can be viewed as ‘communication networks’ where interconnected elements communicate with one another through physical phenomena and the elements ‘process’ the communications through their dynamics; this defines the ‘intrinsic communication topology’ of the system. The behaviors of individual elements can be at least partially observed in the dynamics of other communicating system elements and, hence, condition changes will be reflected in changes in the intrinsic communications. Anomaly detection is then performed by observing the changes in the intrinsic communication topology by tracking graph similarity measures and using change point detection to determine when statistically significant changes have occurred. The performance of the proposed approach is investigated in simulation where we consider a system composed of multiple networks, each with different topologies and connection strengths, and where the individual networks comprising the system can be switched at arbitrary times. The proposed methodology is applied to this system to detect the switches between the networks and to discover the communication topologies associated with each of the network configurations.

Comments to “Quantification of network structural dissimilarities” published by Schieber et al

Recently, we came across the paper entitled “Quantification of network structural dissimilarities” published by Nature Communications. In this paper, Schieber et al claimed to propose a novel technique for measuring the structural similarity of networks. The authors of this commentary are familiar with this special area of network analysis. After reading the paper, we doubt that the graph similarity (distance) measure due to Schieber et al is entirely novel. Instead, parts thereof are very similar to contributions we have authored. Unfortunately, they have not been cited nor acknowledged in Schieber et al.

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

Graph similarity is an important notion with many applications. Graph edit distance is one of the most flexible graph similarity measure available. The main problem with this measure is that in practice it can only be computed for small graphs due to its exponential time complexity. The present paper is concerned with efficient solutions with high quality approximation of graph edit distance. In particular, we present a novel upper bound computation framework for graph edit distance. It is based on breadth-first hierarchical views of the graphs and a novel hierarchical traversing and matching method to build a graph mapping. The main advantage of this framework is that it combines map construction with edit counting in easy and straightforward manner. It also allows to compare the graphs from different hierarchical views to improve the bound. Furthermore, to avoid the complexity of multi-view comparisons and preserve distance accuracy, two new view-selection methods, based on the vertex and edge star structures, are introduced to scale the computations. Contrasting our approach with the state-of-the-art overestimation methods, experiments show that it delivers comparable upper bounds with over three orders of magnitude speedup on real data graphs. Experiments also show that this approach improves the classification accuracy of the KNN classifiers by over 15 percent when compared with the state-of-the-art overestimation methods.

Fast Top-K Graph Similarity Search Via Representative Matrices

Graph similarity search is a crucial problem in many applications, such as cheminformatics, data mining, and pattern recognition. Top-k graph similarity search aims to find the most similar $k$ graphs to a query graph in graph databases. In this paper, we present a fast top-k graph similarity search algorithm with high classification accuracy. We introduce a new graph similarity measure based upon the number of occurrences of subtree patterns in graphs. In order to accelerate search, we also construct hierarchical representative matrices for graph databases, where each row of the matrices represents a graph set. Using representative matrices, we can derive a similarity upper bound of a query graph and the graph set so as to reduce search space. Comprehensive experiments on real data sets demonstrate that our algorithm has a better performance than compared methods on classification accuracy and query time, and it also can scale to large data sets including 15 million chemical structure graphs.

Conceptual Graphs Based Approach for Subjective Answers Evaluation

Automated evaluation systems for objective type tests already exist. However, it is challenging to make an automated evaluation system for subjective type tests. Therefore, focus of this paper is on evaluation of simple text based subjective answers using Natural Language Processing techniques. A student's answer is evaluated by comparing it with a model answer of the question. Model answers cannot exactly match with the students' answers due to variability in writing. Therefore, researchers create conceptual graphs for both student as well as model answer and compute similarity between these graphs using techniques of graph similarity measures. Based on the similarity, marks are assigned to an answer. Lastly, in this manuscript authors compare the results obtained by human graders and the proposed system using Pearson correlation coefficient. Also, comparison has been drawn between the results of proposed system with other existing evaluation systems. The experimental evaluation of the proposed system shows promising results.

A Graph-based approach for Kite recognition

Kites are huge archaeological structures of stone visible from satellite images. Because of their important number and their wide geographical distribution, automatic recognition of these structures on images is an important step towards understanding these enigmatic remnants. This paper presents a complete identification tool relying on a graph representation of the Kites. As Kites are naturally represented by graphs, graph matching methods are thus the main building blocks in the Kite identification process. However, Kite graphs are disconnected geometric graphs for which traditional graph matching methods are useless. To address this issue, we propose a graph similarity measure adapted for Kite graphs. The proposed approach combines graph invariants with a geometric graph edit distance computation leading to an efficient Kite identification process. We analyze the time complexity of the proposed algorithms and conduct extensive experiments both on real and synthetic Kite graph data sets to attest the effectiveness of the approach. We also perform a set of experimentations on other data sets in order to show that the proposed approach is extensible and quite general.

An Exploratory Study of Financial Reporting Structures: A Graph Similarity Approach Using XBRL

Financial reporting information is crucial to both investors and regulators for their decision-making purposes as it reveals corporate financial position and performance over a period of time. This study proposes a quantitative method to identify companies who opt for different financial statement reporting structures from their industry peers. We first introduce a graph similarity measure to quantify structural differences of financial disclosures chosen by firms, and then we conduct two experiments focusing on reported balance sheets as examples to validate effectiveness of our proposed method in identifying discrepancies between reporting structures. The first experiment shows the proposed method is sensitive to changes made on balance sheets and helps capture major structural differences. The second experiment shows this method is able to cluster more than 92% of firms under study from 2011 to 2014 correctly into their respective industries based on their common reporting structures. We also show that the “misaligned” firms are true outliers who either opted for different reporting structures than their industrial peers or simply made technical errors. The novel approach presented in this paper provides an automated means to identify unique financial disclosure structural patterns and therefore offers a potential method to help information users to identify distinct business strategies or financial fraud.

Author verification using a Graph-based Representation

This paper presents a methodology for tackling the authorship verification problem. The approach is based on comparing the similarity between a given unknown document against the known documents using a graph representation that captures the syntactic sequence of texts and a graph similarity measure. An unknown document can be classified as having been written by the same author if the majority of the comparisons surpass a predefined threshold. The best results were obtained on the Clef PAN 2014 dataset: 79% for the Spanish and 68% for English, showing that the proposed methodology could be a way for determining a document authorship.

Community detection for graph-based similarity: Application to protein binding pockets classification

This paper addresses the problem of similarity assessment between node-labeled and edge-weighted graphs representing protein binding pockets. A novel approach is proposed for predicting the functional family of proteins on the basis of the properties of their binding pockets using graphs as models to depict their geometry and physicochemical composition without information loss. State of the art graph similarity measure based on the maximum common subgraph is relaxed by the use of an another concept: the so-called community, or in our context, the maximum densest common community “MDCC”, which is used as an almost common subgraph. The latter is more convenient since it allows to take into account the flexible nature of proteins on the 3D-level. With our approach, tolerance towards noise and structural variation is increased. Furthermore, the MDCC is detected with low computation time. The performance of our method is validated on real world data.

Selecting Graph Cut Solutions via Global Graph Similarity

Graph cut is a common way of clustering nodes on similarity graphs. As a clustering method, it does not give a unique solution under usually used loss functions. We specifically show the problem in similarity graph-based clustering setting that the resulting clusters might be even disconnected. This is counter-intuitive as one wish to have good clustering solutions in the sense that each cluster is well connected and the clusters are balanced. The key property of good clustering solutions is that the resulting graphs (after clustering) share large components with the original ones. We wish to detect this case by deriving a graph similarity measure that shows high similarity values to the original graph for good clustering solutions. The similarity measure considers global connectivities of graphs by treating graphs as distributions in (potentially different) Euclidean spaces. The global graph comparison is then turned into distribution comparison. Simulation shows that the similarity measure could consistently distinguish different qualities of clustering solution beyond what could be done with the usually used loss functions of clustering algorithms.

Comparison of Different Graph Distance Metrics for Semantic Text Based Classification

Nowadays semantic information of text is used largely for text classification task instead of bag-of-words approaches. This is due to having some limitations of bag of word approaches to represent text appropriately for certain kind of documents. On the other hand, semantic information can be represented through feature vectors or graphs. Among them, graph is normally better than traditional feature vector due to its powerful data structure. However, very few methodologies exist in the literature for semantic representation of graph. Error tolerant graph matching techniques such as graph similarity measures can be utilised for text classification. However, the techniques like Maximum Common Subgraph (mcs) and Minimum Common Supergraph (MCS) for graph similarity measures are computationally NP-hard problem. In the present paper summarized texts are used during extraction of semantic information to make it computationally faster. The semantic information of texts are represented through the discourse representation structures and later transformed into graphs. Five different graph distance measures based on Maximum Common Subgraph (mcs) and Minimum Common Supergraph (MCS) are used with k-NN classifier to evaluate text classification task. The text documents are taken from Reuters21578 text database distributed over 20 classes. Ten documents of each class for both training and testing purpose are used in the present work. From the results, it has been observed that the techniques have more or less equivalent potential to do text classification and as good as traditional bag-of-words approaches.

Graph context and its application in graph similarity measurement

Feature extraction and similarity measurement for graphs are important issues in computer vision and pattern recognition.However,traditional methods could not describe the graphs under some non-rigid transformation adequately,so a new graph feature descriptor and its similarity measurement method were proposed based on Graph Context(GC) descriptor.Firstly,a sample point set was obtained by discretely sampling.Secondly,graph context descriptor was presented based on the sample point set.At last,improved Earth Mover's Distance(EMD) was used to measure the similarity for graph context descriptor.Different from the graph edit distance methods,the proposed method did not need to define cost function which was difficult to set in those methods.The experimental results demonstrate that the proposed method performs better for the graphs under some non-rigid transformation.

Automatic design quality evaluation using graph similarity measures

This paper contributes to the problem of assisting the designer in dealing with evaluating the quality of a design. Especially, spatial relationships and arrangements of components within a design are explicitly dealt with. Hierarchical graphs are used as the design representation to enable capturing different ways components can be related by taking into account the fact that a component can form a part of another one. As the human evaluation is often based on the experience gained from seeing and analyzing many designs a similar approach is proposed in this paper. This approach uses methods drawn from machine learning, in particular kernels for structured data. Kernel functions are used to calculate similarity of new designs to other designs for which the evaluation is known thus simulating the process of learning from experience. The proposed approach is illustrated by experimental results obtained for the task of floor layout design.

Modules in the metabolic network of E.coli with regulatory interactions

We examine the modular structure of the metabolic network when combined with the regulatory network representing direct regulation of enzymes by small metabolites in E. coli. We introduce novel clustering algorithm and compare it with mainstream module detection method based on simulated annealing. Both methods identify the similar modular core. Slight but significant increase in modularity is observed after regulatory interactions addition. We also identify new functional modules in the combined network, which cannot be detected in the metabolic network only. Regulatory loops in the modules are the source of their autonomy, and allow us to hypothesise about module function.