Multi-Level Graph Representation Learning Through Predictive Community-based Partitioning

One of the most important aspects of social network analysis is community detection, which is used to categorize related individuals in a social network into groups or communities. The approach is quite similar to graph partitioning and, in fact, most detection algorithms rely on concepts from graph theory and sociology. The aim of this chapter is to aid a novice in the field of community detection by providing a wider perspective on some of the different detection algorithms available, including the more recent developments in this field. Five popular algorithms have been studied and explained, and a recent novel approach that was proposed by the authors has also been included. The chapter concludes by highlighting areas suitable for further research, specifically targeting overlapping community detection algorithms.

Characterizing brain anatomical connections using diffusion weighted MRI and graph theory

During the last decades, automatic speech emotion recognition (SER) has gained an increased interest by the research community. Specifically, SER aims to recognize the emotional state of a speaker directly from a speech recording. The most prominent approaches in the literature include feature extraction of speech signals in time and/or frequency domain that are successively applied as input into a classification scheme. In this paper, we propose to exploit graph theory and structures as alternative forms of speech representations. We suggest applying the so-called Visibility Graph (VG) theory to represent speech data using an adjacency matrix and extract well-known graph-based features from the latter. Finally, these features are fed into a Support Vector Machine (SVM) classifier in a leave-one-speaker-out, multi-class fashion. Our proposed feature set is compared with a well-known acoustic feature set named the Geneva Minimalistic Acoustic Parameter Set (GeMAPS). We test both approaches on two publicly available speech datasets: SAVEE and EMOVO. The experimental results show that the proposed graph-based features provide better results, namely a classification accuracy of 70% and 98%, respectively, yielding an increase by 29.2% and 60.6%, respectively, when compared to GeMAPS.

In recent era, networks of data are growing massively and forming a shape of complex structure. Data scientists try to analyze different complex networks and utilize these networks to understand the complex structure of a network in a meaningful way. There is a need to detect and identify such a complex network in order to know how these networks provide communication means while using the complex structure. Social network analysis provides methods to explore and analyze such complex networks using graph theories, network properties and community detection algorithms. In this paper, an analysis of co-authorship network of Public Relation and Public Administration subjects of Microsoft Academic Graph (MAG) is presented, using common centrality measures. The authors belong to different research and academic institutes present all over the world. Cohesive groups of authors have been identified and ranked on the basis of centrality measures, such as betweenness, degree, page rank and closeness. Experimental results show the discovery of authors who are good in specific domain, have a strong field knowledge and maintain collaboration among their peers in the field of Public Relations and Public Administration.

Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it is shown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

Introduction/ Background The interaction between tumor and surrounding microenvironment (TME) is recognized as playing an important role in the progression of the disease. Understanding of the interaction between tumor and immune system is the focus of several studies dedicated to the improvement of cancer immunotherapy effectiveness [1]. On the other hand, it has been shown that invasion and metastasis of breast tumors is influenced by collagen organization at the tumor-stromal interface [2]. The characterization of such interactions relies on an efficient spatial distribution quantification of TME. Graph-based analysis tools are the best suitable to answer this question as they have the ability to represent spatial arrangements and neighborhood relationships of different tissue components [3]. Aims In this work, we propose a novel approach to characterize the spatial relationships between cancer cells and TME components in breast tumors, using graph theory and sparse sets’ mathematical morphology (MM). The tools of morphology on graphs were first used in [4] to study the neighborhood relationships between cells in germinal centers from lymph nodes, then in [5] for semantic spatial configuration modeling in histopathology. In our study, we propose new morphological descriptors characterizing the tumor architecture and the interactions with TME cells. Methods Towards a better evaluation and understanding, we use simulated data of different breast tumor types , , where locations of cancer nuclei (CN), fibroblasts (synthesizers of collagen, FN), and lymphocytes (LN) are already known. In order to set neighborhood relationships between different cells, Delaunay graph [3] is first reconstructed on all cells, and alpha-shape filter [5] is applied to circumvent border effects, giving new graph denoted G . The designed features are extracted basically from two different morphological operations. The first operation is composed of successive morphological erosions [4] applied to the subgraph induced by CN (denoted SGC, ), repeated until the subgraph is null. The curve given by the number of CN in terms of erosions provides 3 significant characteristics : I) The origin slope describes the number of CN on the boundary of tumor aggregates (TA) and, thus, the tumor-stromal interface ; II) The area under curve (AUC) reflects the density within TAs, and III) the number of iterations outlines the morphologic radius of the largest TA and, consequently, the geodesic distance of the farthest tumor cell from LN and/or FN. The second morphological operation is composed of successive morphological dilations applied to SGC with non-overlapping control of labeled connected-components . The goal behind this operation is to investigate the TME cells surrounding each TA. The ratio between the number of LN and the number of CN, and the means of the Euclidean and the geodesic distances of LN from CN on the boundary are calculated for each TA . Results In this work, we have briefly presented a conceptual framework for analyzing the architecture of breast tumors and the interactions with the surrounding microenvironment. New graph-based features were proposed to characterize the spatial distribution of TME components and were tested on simulated data. In our future works, we will include adipose tissue [6], blood vessels and endothelial cells. We will also focus on the anisotropic characterization of collagen, and test the approach on real dataset.

In recent years, we have witnessed an overwhelming and fast proliferation of different types of malware targeting organizations and individuals, which considerably increased the time required to detect malware. The malware developers make this issue worse by spreading many variants of the same malware [ 13 ]. To deal with this issue, graph theory techniques, and particularly community detection algorithms, can be leveraged to achieve bulk detection of malware families and variants to identify malicious communities instead of focusing on the detection of an individual instance of malware, which could significantly reduce the detection time. In this article, we review the state-of-the-art malware analysis solutions that employ community detection algorithms and provide a taxonomy that classifies the solutions with respect to five facets: analysis task, community detection approach, target platform, analysis type, and source of features. We present the solutions with respect to the analysis task, which covers malware detection, malware classification, cyber-threat infrastructure detection, and feature selection. The findings of this survey indicate that there is still room for contributions to further improve the state of the art and address research gaps. Finally, we discuss the advantages and the limitations of the solutions, identify open issues, and provide future research directions.

Community detection is an important task in the analysis of complex networks, which is significant for mining and analyzing the organization and function of networks. As an unsupervised learning algorithm based on the particle competition mechanism, stochastic competitive learning has been applied in the field of community detection in complex networks, but still has several limitations. In order to improve the stability and accuracy of stochastic competitive learning and solve the problem of community detection, we propose an unsupervised community detection algorithm LNSSCL (Local Node Similarity-Integrated Stochastic Competitive Learning). The algorithm calculates node degree as well as Salton similarity metrics to determine the starting position of particle walk; local node similarity is incorporated into the particle preferential walk rule; the particle is dynamically adjusted to control capability increments according to the control range; particles select the node with the strongest control capability within the node to be resurrected; and the LNSSCL algorithm introduces a node affiliation selection step to adjust the node community labels. Experimental comparisons with 12 representative community detection algorithms on real network datasets and synthetic networks show that the LNSSCL algorithm is overall better than other compared algorithms in terms of standardized mutual information (NMI) and modularity (Q). The improvement effect for the stochastic competition learning algorithm is evident, and it can effectively accomplish the community detection task in complex networks.

Graph representation learning models have demonstrated great capability in many real-world applications. Nevertheless, prior research reveals that these models can learn biased representations leading to unfair outcomes. A few works have been proposed to mitigate the bias in graph representations. However, most existing works require exceptional time and computing resources for training and fine-tuning. In this demonstration, we propose a framework FairMILE for efficient fair graph representation learning. FairMILE allows the user to efficiently learn fair graph representations while preserving utility. In addition, FairMILE can work in conjunction with any unsupervised embedding approach based on the user's preference and accommodate various fairness constraints. The demonstration will introduce the methodology of FairMILE, showcase how to set up and run this framework, and demonstrate our effectiveness and efficiency to the audience through both quantitative metrics and visualization.

The distributed $(\Delta + 1)$-coloring problem is one of the most fundamental and well-studied problems in distributed algorithms. Starting with the work of Cole and Vishkin in 1986, a long line of gradually improving algorithms has been published. The state-of-the-art running time, prior to our work, is $O(\Delta \log \Delta + \log^* n)$, due to Kuhn and Wattenhofer [Proceedings of the $25$th Annual ACM Symposium on Principles of Distributed Computing, Denver, CO, 2006, pp. 7--15]. Linial [Proceedings of the $28$th Annual IEEE Symposium on Foundation of Computer Science, Los Angeles, CA, 1987, pp. 331--335] proved a lower bound of $\frac{1}{2} \log^* n$ for the problem, and Szegedy and Vishwanathan [Proceedings of the 25th Annual ACM Symposium on Theory of Computing, San Diego, CA, 1993, pp. 201--207] provided a heuristic argument that shows that algorithms from a wide family of locally iterative algorithms are unlikely to achieve a running time smaller than $\Theta(\Delta \log \Delta)$. We present a deterministic $(\Delta + 1)$-coloring distributed algorithm with running time $O(\Delta) + \frac{1}{2} \log^* n$. We also present a trade-off between the running time and the number of colors, and devise an $O(\lambda\cdot\Delta)$-coloring algorithm, with running time $O(\Delta / \lambda + \log^* n)$, for any parameter $\lambda > 1$. Our algorithm breaks the heuristic barrier of Szegedy and Vishwanathan and achieves running time which is linear in the maximum degree $\Delta$. On the other hand, the conjecture of Szegedy and Vishwanathan may still be true, as our algorithm does not belong to the family of locally iterative algorithms. On the way to this result we study a generalization of the notion of graph coloring, which is called defective coloring [L. Cowen, R. Cowen, and D. Woodall, J. Graph Theory, 10 (1986), pp. 187--195]. In an $m$-defective $p$-coloring the vertices are colored with $p$ colors so that each vertex has up to $m$ neighbors with the same color. We show that an $m$-defective $p$-coloring with reasonably small $m$ and $p$ can be computed very efficiently in the distributed setting. We also develop a technique to employ multiple defective colorings of various subgraphs of the original graph $G$ for computing a $(\Delta+1)$-coloring of $G$. We believe that these techniques are of independent interest.

Community structures are inherent in social networks and finding them is an interesting and well-studied problem. Finding community structures in social networks is similar to locating densely connected clusters of nodes in a graph. One of the popular methods for finding communities is to first find the inter-community edges and then removing them to reveal the communities. It is well-known that a network centrality measure named edge betweenness can be used to detect the inter-community edges. The edges with high edge betweenness are those that fall in a large number of shortest paths out of all possible pairs of shortest paths. Finding all-pair shortest paths is a computationally expensive task, especially for large-sized graphs. So we construct a t-spanner, a known graph sparsification technique, for finding edges with high betweenness and eventually find communities by removing such edges. Using the t-spanner, we then detect the inter-community edges in O(km) running time by building a distance oracle of size O(kn1+1/k), where t = 2k-1. Compared to the traditional community detection methods dependent on calculation of betweenness values, our algorithm runs much faster. Experiments show that our algorithm finds communities of quality comparable to the other state-of-the-art community detection algorithms.

This thesis studies exponential time algorithms that give optimum solutions to optimization problems which are highly unlikely to be solvable to optimality in polynomial time. Such algorithms are designed and upper bounds on their running times are analyzed, for pro-blems from graph theory, constraint satisfaction, and computational biology. It is studied how restrictions on one computationally hard parameter affect the running time of algorithms for computing another parameter. Algorithms are obtained to compute minimum dominating sets, minimum bandwidth and topological bandwidth layouts, and other hard parameters, in time exponential only in the maximum number of leaves in a spanning tree of a graph. For sparse graphs, algorithms find minimum connected dominating sets in time exponential only in the optimum value. These algorithms are based on kernels of small size, meaning that arbitrary instances are polynomial-time compressible to equivalent instances whose size depends on the parameter alone. Lower and upper bounds on the number and size of certain combinatorial objects are proved. For minimal feedback vertex sets in tournaments, improved bounds on their number and a polynomial-space polynomial-delay algorithm for their enumeration are given. For subcubic planar graphs, fast algorithms finding large induced matchings are given. Fixed-parameter algorithms are presented for maximization problems whose optimum solution value grows as an unbounded function with the instance size. Polynomial kernels are obtained for all permutation constraint satisfaction problems with ternary constraints, and independent set problems in restricted graph classes, when these problems are parameterized above tight lower bounds on their solution value. Polynomial space algorithms with subexponential time requirement are obtained for the minimum triplet inconsistency problem in phylogenetics, and basically all bidimensional problems in sparse graphs such as graphs excluding a fixed minor.

There is a large amount of information in the network data that we can exploit. It is difficult for classical community detection algorithms to handle network data with sparse topology. Representation learning of network data is usually paired with clustering algorithms to solve the community detection problem. Meanwhile, there is always an unpredictable distribution of class clusters output by graph representation learning. Therefore, we propose an improved density peak clustering algorithm (ILDPC) for the community detection problem, which improves the local density mechanism in the original algorithm and can better accommodate class clusters of different shapes. And we study the community detection in network data. The algorithm is paired with the benchmark model Graph sample and aggregate (GraphSAGE) to show the adaptability of ILDPC for community detection. The plotted decision diagram shows that the ILDPC algorithm is more discriminative in selecting density peak points compared to the original algorithm. Finally, the performance of K-means and other clustering algorithms on this benchmark model is compared, and the algorithm is proved to be more suitable for community detection in sparse networks with the benchmark model on the evaluation criterion F1-score. The sensitivity of the parameters of the ILDPC algorithm to the low-dimensional vector set output by the benchmark model GraphSAGE is also analyzed.

Many networks exhibit small-world properties. The structure of a small-world network is characterized by short average path lengths and high clustering coefficients. Few graph layout methods capture this structure well which limits their effectiveness and the utility of the visualization itself. Here we present an extension to our novel graphTPP layout method for laying out small-world networks using only their topological properties rather than their node attributes. The Watts–Strogatz model is used to generate a variety of graphs with a small-world network structure. Community detection algorithms are used to generate six different clusterings of the data. These clusterings, the adjacency matrix and edgelist are loaded into graphTPP and, through user interaction combined with linear projections of the adjacency matrix, graphTPP is able to produce a layout which visually separates these clusters. These layouts are compared to the layouts of two force-based techniques. graphTPP is able to clearly separate each of the communities into a spatially distinct area and the edge relationships between the clusters show the strength of their relationship. As a secondary contribution, an edge-grouping algorithm for graphTPP is demonstrated as a means to reduce visual clutter in the layout and reinforce the display of the strength of the relationship between two communities.

Despite the continuous evolution and significant improvement of cybersecurity mechanisms, malware threats remain one of the most important concerns in cyberspace. Meanwhile, Android malware plays a big role in these ever-growing threats. In recent years, deep learning has become the dominant machine learning technique for malware detection and continues to make outstanding achievements. Deep graph representation learning is the task of embedding graph-structured data into a low-dimensional space using deep learning models. Recently, autoencoders have proven to be an effective way for deep representation learning. However, it is not straightforward to apply the idea of autoencoder to graph-structured data because of their irregular structure. In this paper, we present DroidMalGNN, a novel deep learning technique that combines autoencoders with graph neural networks (GNNs) to detect Android malware in an end-to-end manner. DroidMalGNN represents each Android application with an attributed function call graph (AFCG) that allows it to model complex relationships between data. For more efficiency, DroidMalGNN performs graph representation learning in a supervised manner where two autoencoders are trained with benign and malicious AFCGs separately. In this way, it generates two informative embedding vectors for each AFCG in a low-dimensional space and feeds them into a dense neural network to classify the AFCG as benign or malicious. Our experimental results show that DroidMalGNN can achieve good detection performance in terms of different evaluation measures.