Graph Mining Tasks Research Articles

Bipartite network embedding with Symmetric Neighborhood Convolution

Mining bipartite networks, a ubiquitous type of model particularly developed for networks with two different classes of nodes, is of great importance in various applications. Recently, the advance of network representation learning has provided more tractable, effective and robust methods for several graph mining tasks. However, the strength of representation learning has not been sufficiently explored for bipartite structure, since that most existing learning methods either separately treat the nodes in different classes by defective projections, or independently sample instances for learning by adopting relation-aware random walks. Both methods can lose information and they hardly leverage the symmetry property of bipartite structure directly. In this paper, a novel method called Symmetric Neighborhood Convolution is proposed to fulfill the representation learning task in bipartite networks. The method takes into consideration the topological symmetry property and utilizes one-dimensional convolution kernels to extract features from neighborhood for the nodes in each class. Three different objectives are designated to compare the performance of the proposed convolution-based mechanism. The method is evaluated on five real-world datasets by the tasks of link prediction and recommendation. Comparing to eight competitive baselines, experimental results demonstrate the effectiveness of our method.

Permutation-equivariant and Proximity-aware Graph Neural Networks with Stochastic Message Passing

Graph neural networks (GNNs) are emerging machine learning models on graphs. Permutation-equivariance and proximity-awareness are two important properties highly desirable for GNNs. Both properties are needed to tackle some challenging graph problems, such as finding communities and leaders. In this paper, we first analytically show that the existing GNNs, mostly based on the message-passing mechanism, cannot simultaneously preserve the two properties. Then, we propose Stochastic Message Passing (SMP) model, a general and simple GNN to maintain both proximity-awareness and permutation-equivariance. In order to preserve node proximities, we augment the existing GNNs with stochastic node representations. We theoretically prove that the mechanism can enable GNNs to preserve node proximities, and at the same time, maintain permutation-equivariance with certain parametrization. We report extensive experimental results on ten datasets and demonstrate the effectiveness and efficiency of SMP for various typical graph mining tasks, including graph reconstruction, node classification, and link prediction.

Exploring PIM Architecture for High-Performance Graph Pattern Mining

Graph mining applications, such as subgraph pattern matching and mining, are widely used in real-world domains such as bioinformatics, social network analysis, and computer vision. Such applications are considered as a new class of data-intensive applications that generate massive irregular computation workloads and memory accesses, which are different from many well-studied graph applications such as BFS and page rank. In this letter, we use the emerging process-in-memory architecture to accelerate data-intensive operations in graph mining tasks. We first identify the code blocks that are best suitable for PIM execution. Then, we observe a significant load imbalance on PIM architecture and analyze the root cause for such imbalance in graph mining applications. Lastly, we evaluate several scheduling schemes that help reduce the load imbalance and discuss potential optimizations to enhance performance further.

Adversarial Directed Graph Embedding

Node representation learning for directed graphs is critically important to facilitate many graph mining tasks. To capture the directed edges between nodes, existing methods mostly learn two embedding vectors for each node, source vector and target vector. However, these methods learn the source and target vectors separately. For the node with very low indegree or outdegree, the corresponding target vector or source vector cannot be effectively learned. In this paper, we propose a novel Directed Graph embedding framework based on Generative Adversarial Network, called DGGAN. The main idea is to use adversarial mechanisms to deploy a discriminator and two generators that jointly learn each node’s source and target vectors. For a given node, the two generators are trained to generate its fake target and source neighbor nodes from the same underlying distribution, and the discriminator aims to distinguish whether a neighbor node is real or fake. The two generators are formulated into a unified framework and could mutually reinforce each other to learn more robust source and target vectors. Extensive experiments show that DGGAN consistently and significantly outperforms existing state-of-the-art methods across multiple graph mining tasks on directed graphs.

Persona2vec: a flexible multi-role representations learning framework for graphs.

Graph embedding techniques, which learn low-dimensional representations of a graph, are achieving state-of-the-art performance in many graph mining tasks. Most existing embedding algorithms assign a single vector to each node, implicitly assuming that a single representation is enough to capture all characteristics of the node. However, across many domains, it is common to observe pervasively overlapping community structure, where most nodes belong to multiple communities, playing different roles depending on the contexts. Here, we propose persona2vec, a graph embedding framework that efficiently learns multiple representations of nodes based on their structural contexts. Using link prediction-based evaluation, we show that our framework is significantly faster than the existing state-of-the-art model while achieving better performance.

Learning ladder neural networks for semi-supervised node classification in social network

Graph convolutional networks (GCNs) and network embedding are the two main categories of popular methods for Semi-Supervised Node Classification (SSNC) in social network. However, the former is commonly oriented to attributed networks with efficient auxiliary information in nodes. The latter is usually not geared towards specific graph mining tasks. Therefore, these methods often perform poorly for specific tasks in non-attributed networks. To solve the above problems, in this paper, we propose a novel semi-supervised Node Classification method with Ladder Neural Networks named NCLNN for non-attributed network. We first preprocess the graph for capturing the structural information. Then we present and learn a deep ladder neural network for SSNC. Our trained ladder neural networks could combine supervised learning with unsupervised learning in deep neural networks via simultaneously minimizing the sum of supervised and unsupervised loss functions. Extensive experiments on three real-world network datasets demonstrate that the proposed NCLNN substantially outperforms the state-of-the-art methods on SSNC task.

An edge creation history retrieval based method to predict links in social networks

Link prediction is a graph mining task that aims to foretell whether pairs of non-linked nodes will connect in the future. It has many useful applications in social networks such as friend recommendation, identification of future collaborations between authors in co-authorship networks, discovery of hidden groups of terrorists and criminals, among others. In general, the state-of-the-art link prediction methods consider topological data extracted from the current state (i.e., the most recent and available snapshot) of a network. They do not take into account information that describes how the network’s topology was at the moments when the existing edges were created. Hence, those methods take the chance to disregard information about the circumstances that may have influenced the appearance of old edges, and that could be useful to predict the creation of new ones. Thus, this study raises and evaluates the hypothesis that recovering such data may contribute to improving link prediction. This hypothesis is justified since those data enrich the description of the application’s context with examples that represent exactly the kind of event to be foreseen: the creation of new connections. To this end, this paper proposes a new link prediction method that is based on edge creation history retrieval. Results from experiments with twenty scenarios of four real co-authorship social networks presented statistical evidence that indicates the effectiveness of the proposed method and confirms the raised hypothesis.

Finding dense subgraphs with maximum weighted triangle density

Finding dense subgraphs from sparse graphs is a fundamental graph mining task that has been applied in various domains, such as social networks, biology, and spam detection. Because the standard formulation of this problem is difficult to solve owing to connections with the Maximum Clique Problem, some tractable formulations have been proposed. These formulations find a dense subgraph by optimizing some density function, such as the degree density or triangle density. In this paper, we introduce the weighted k-clique density, a novel formulation for dense subgraph extraction. We show that the problem of maximizing weighted k-clique density can be solved optimally in polynomial time by solving a series of minimum cut problems. For scalability, we also propose a more efficient greedy algorithm with performance guarantee. The experimental results on real-world network datasets show that, compared with established state-of-the-art algorithms, the proposed algorithm can find a much denser subgraph in terms of edge density and triangle density.

Evolving network representation learning based on random walks

Large-scale network mining and analysis is key to revealing the underlying dynamics of networks, not easily observable before. Lately, there is a fast-growing interest in learning low-dimensional continuous representations of networks that can be utilized to perform highly accurate and scalable graph mining tasks. A family of these methods is based on performing random walks on a network to learn its structural features and providing the sequence of random walks as input to a deep learning architecture to learn a network embedding. While these methods perform well, they can only operate on static networks. However, in real-world, networks are evolving, as nodes and edges are continuously added or deleted. As a result, any previously obtained network representation will now be outdated having an adverse effect on the accuracy of the network mining task at stake. The naive approach to address this problem is to re-apply the embedding method of choice every time there is an update to the network. But this approach has serious drawbacks. First, it is inefficient, because the embedding method itself is computationally expensive. Then, the network mining task outcome obtained by the subsequent network representations are not directly comparable to each other, due to the randomness involved in the new set of random walks involved each time. In this paper, we propose EvoNRL, a random-walk based method for learning representations of evolving networks. The key idea of our approach is to first obtain a set of random walks on the current state of network. Then, while changes occur in the evolving network’s topology, to dynamically update the random walks in reserve, so they do not introduce any bias. That way we are in position of utilizing the updated set of random walks to continuously learn accurate mappings from the evolving network to a low-dimension network representation. Moreover, we present an analytical method for determining the right time to obtain a new representation of the evolving network that balances accuracy and time performance. A thorough experimental evaluation is performed that demonstrates the effectiveness of our method against sensible baselines and varying conditions.

Massively Distributed Graph Distances

Graph distance (or similarity) scores are used in several graph mining tasks, including anomaly detection, nearest neighbor and similarity search, pattern recognition, transfer learning, and clustering. Graph distances that are metrics and, in particular, satisfy the triangle inequality, have theoretical and empirical advantages. Well-known graph distances that are metrics include the chemical or the Chartrand-Kubiki-Shultz (CKS) distances. Unfortunately, both are computationally intractable. Recent efforts propose using convex relaxations of the chemical and CKS distances. Though distance computation becomes a convex optimization problem under these relaxations, the number of variables is quadratic in the graph size; this makes traditional optimization algorithms prohibitive even for small graphs. We propose a distributed method for massively parallelizing this problem using the Alternating Directions Method of Multipliers (ADMM). Our solution uses a novel, distributed bisection algorithm for computing a $p$ -norm proximal operator as a building block. We demonstrate its scalability by conducting experiments over multiple parallel environments.

A network representation method based on edge information extraction

In recent years, network representation learning has attracted extensive attention in the academic field due to its significant application potential. However, most of the methods cannot explore edge information in the network deeply, resulting in poor performance at downstream tasks such as classification, clustering and link prediction. In order to solve this problem, we propose a novel way to extract network information. First, the original network is transformed into an edge network with structure and edge information. Then, edge representation vectors can be obtained directly by using an existing network representation model with edge network as its input. Node representation vectors can also be obtained by utilizing the relationships between edges and nodes. Compared with the structure of original network, the edge network is denser, which can help solving the problems caused by sparseness. Extensive experiments on several real-world networks demonstrate that edge network outperforms original network in various graph mining tasks, i.e., node classification and node clustering.

MLNE: Multi-Label Network Embedding.

Network embedding aims to preserve topological structures of a network using low-dimensional vectors and has shown to be effective for driving a myriad of graph mining tasks (e.g., link prediction or classification) free of the stressful feature extraction procedure. Many methods have been proposed to integrate node content and/or label information, with nodes sharing similar content/labels being close to each other in the learned latent space. To date, existing methods either consider networked instances with a single label or consider a set of labels as a whole for node representation learning. Therefore, they cannot handle network of instances containing multiple labels (i.e. multi-labels), which are ubiquitous in describing complex concepts of instances. In this article, we formulate a new multi-label network embedding (MLNE) problem to learn feature representation for networked multi-label instances. We argue that the key to MLNE learning is to aggregate node topology structures, node content, and multi-label correlations. We propose a two-layer network embedding framework to couple information for effective learning. To capture higher order label correlations, we use labels to form a high-level label-label network over a low-level node-node network, in which the label network interacts with the node network through multi-labeling relations. The low-level node-node network can be enhanced by latent label-specific features from high-level label network with well-captured high-order correlations between labels. To enable the multi-label informed network embedding, we force both node and label representations being optimized under the same low-dimensional latent space by a unified training objective. Experiments on real-world data sets demonstrate that MLNE achieves better performance compared with methods with or without considering label information.

Unsupervised network embeddings with node identity awareness

A main challenge in mining network-based data is finding effective ways to represent or encode graph structures so that it can be efficiently exploited by machine learning algorithms. Several methods have focused in network representation at node/edge or substructure level. However, many real life challenges related with time-varying, multilayer, chemical compounds and brain networks involve analysis of a family of graphs instead of single one opening additional challenges in graph comparison and representation. Traditional approaches for learning representations relies on hand-crafted specialized features to extract meaningful information about the graphs, e.g. statistical properties, structural motifs, etc. as well as popular graph distances to quantify dissimilarity between networks. In this work we provide an unsupervised approach to learn graph embeddings for a collection of graphs defined on the same set of nodes so that it can be used in numerous graph mining tasks. By using an unsupervised neural network approach on input graphs, we aim to capture the underlying distribution of the data in order to discriminate between different class of networks. Our method is assessed empirically on synthetic and real life datasets and evaluated in three different tasks: graph clustering, visualization and classification. Results reveal that our method outperforms well known graph distances and graph-kernels in clustering and classification tasks, being highly efficient in runtime.

A fast and robust kernel optimization method for core\u2013periphery detection in directed and weighted graphs

Many graph mining tasks can be viewed as classification problems on high dimensional data. Within this class we consider the issue of discovering core-periphery structure, which has wide applications in the economic and social sciences. In contrast to many current approaches, we allow for weighted and directed edges and we do not assume that the overall network is connected. Our approach extends recent work on a relevant relaxed nonlinear optimization problem. In the directed, weighted setting, we derive and analyze a globally convergent iterative algorithm. We also relate the algorithm to a maximum likelihood reordering problem on an appropriate core-periphery random graph model. We illustrate the effectiveness of the new algorithm on a large scale directed email network.

An evaluation of vertex and edge modification techniques for privacy-preserving on graphs

Noise is added by privacy-preserving methods or anonymization processes to prevent adversaries from re-identifying users in anonymous networks. The noise introduced by the anonymization steps may also affect the data, reducing its utility for subsequent data mining processes. Graph modification approaches are one of the most used and well-known methods to protect the privacy of the data. These methods convert the data by means of vertex and edge modifications before releasing the perturbed data. In this paper we want to analyze the vertex and edge modification techniques found in literature covering this topic. We empirically evaluate the information loss introduced by each of these methods not only using generic metrics related to graph properties, but also using some specific metrics related to real graph-mining tasks. We want to point out how these methods affect the main properties and characteristics of the network, since it will help us to choose the best one to achieve a desired privacy level while preserving data utility.

On Graph Mining With Deep Learning: Introducing Model R for Link Weight Prediction

Abstract Deep learning has been successful in various domains including image recognition, speech recognition and natural language processing. However, the research on its application in graph mining is still in an early stage. Here we present Model R, a neural network model created to provide a deep learning approach to the link weight prediction problem. This model uses a node embedding technique that extracts node embeddings (knowledge of nodes) from the known links’ weights (relations between nodes) and uses this knowledge to predict the unknown links’ weights. We demonstrate the power of Model R through experiments and compare it with the stochastic block model and its derivatives. Model R shows that deep learning can be successfully applied to link weight prediction and it outperforms stochastic block model and its derivatives by up to 73% in terms of prediction accuracy. We analyze the node embeddings to confirm that closeness in embedding space correlates with stronger relationships as measured by the link weight. We anticipate this new approach will provide effective solutions to more graph mining tasks.

Discovering Hierarchical Subgraphs of K-Core-Truss

Discovering dense subgraphs in a graph is a fundamental graph mining task, which has a wide range of applications in social networks, biology and visualization to name a few. Even the problem of computing most cohesive subgraphs is NP-hard (like clique, quasi-clique, k-densest subgraph), there exists a polynomial time algorithm for computing the k-core and k-truss. In this paper, we propose a novel dense subgraph model, {mathsf {k}}-{mathsf {core}}-{mathsf {truss}}, which leverages on a new type of important edges based on the basis of k-core and k-truss. We investigate the structural properties of the {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} model. Compared to k-core and k-truss, {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} can significantly discover the interesting and important structural information out the scope of k-core and k-truss. We study two useful problems of {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} decomposition and {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} search. In particular, we develop a k-core-truss decomposition algorithm to find all {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} in a graph G by iteratively removing edges with the smallest {mathsf {degree}}-{mathsf {support}}. In addition, we offer a {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} search algorithm to identifying a particular {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} containing a given query node such that the core number k is the largest. Extensive experiments on several web-scale real-world datasets show the effectiveness and efficiency of {mathsf {k}}-{mathsf {core}}-{mathsf {truss}} model and proposed algorithms.

Upper approximation based privacy preserving in online social networks

Abstract With the advent of the online social network and advancement of technology, people get connected and interact on social network. To better understand the behavior of users on social network, we need to mine the interactions of users and their demographic data. Companies with less or no expertise in mining would need to share this data with the companies of expertise for mining purposes. The major challenge in sharing the social network data is maintaining the individual privacy on social network while retaining the implicit knowledge embedded in the social network. Thus, there is a need of anonymizing the social network data before sharing it to the third-party. The current study proposes to use upper approximation concept of rough sets for developing a solution for privacy preserving social network graph publishing. The proposed algorithm is capable of preserving the privacy of graph structure while simultaneously maintaining the utility or value that can be generated from the graph structure. The proposed algorithm is validated by showing its effectiveness on several graph mining tasks like clustering, classification, and PageRank computation. The set of experiments were conducted on four standard datasets, and the results of the study suggest that the proposed algorithm would maintain the both the privacy of individuals and the accuracy of the graph mining tasks.

Distributed computing of distance‐based graph invariants for analysis and visualization of complex networks

SummaryWe present a new framework for analysis and visualization of complex networks based on structural information retrieved from their distance k‐graphs and B‐matrices. The construction of B‐matrices for graphs with more than 1 million edges requires massive Breadth‐First Search (BFS) computations and is facilitated using new software prepared for distributed environments. Our framework benefits from data parallelism inherent to all‐pair shortest‐path problem and extends Cassovary, an open‐source in‐memory graph processing engine, to enable multinode computation of distance k‐graphs and related graph descriptors. We also introduce a new type of B‐matrix, constructed using clustering coefficient vertex invariant, which can be generated with a computational effort comparable with the one required for a previously known degree B‐matrix, while delivering an additional set of information about graph structure. Our approach enables efficient generation of expressive, multidimensional descriptors useful in graph embedding and graph mining tasks. The experiments showed that the new framework is scalable and for specific all‐pair shortest‐path task provides better performance than existing generic graph processing frameworks. We further present how the developed tools helped in the analysis and visualization of real‐world graphs from Stanford Large Network Dataset Collection. Copyright © 2016 John Wiley & Sons, Ltd.

GARUDA

Unraveling "interesting" subgraphs corresponding to disease/crime hotspots or characterizing habitation shift patterns is an important graph mining task. With the availability and growth of large-scale real-world graphs, mining for such subgraphs has become the need of the hour for graph miners as well as non-technical end-users. In this demo, we present GARUDA, a system capable of mining large-scale graphs for statistically significant subgraphs in a scalable manner, and provide: (1) a detailed description of the various features and user-friendly GUI of GARUDA; (2) a brief description of the system architecture; and (3) a demonstration scenario for the audience. The demonstration showcases one real graph mining task as well as its ability to scale to large real graphs, portraying speed-ups of upto 8--10 times over the state-of-the-art MSCS algorithm.