Patterns stored within pre-trained deep neural networks compose large and powerful descriptive languages that can be used for many different purposes. Typically, deep network representations are implemented within vector embedding spaces, which enables the use of traditional machine learning algorithms on top of them. In this short paper we propose the construction of a graph embedding space instead, introducing a methodology to transform the knowledge coded within a deep convolutional network into a topological space (i.e. a network). We outline how such graph can hold data instances, data features, relations between instances and features, and relations among features. Finally, we introduce some preliminary experiments to illustrate how the resultant graph embedding space can be exploited through graph analytics algorithms.
The relation between graphs and deep neural networks have been previously explored, but most contributions do so from a different perspective. While our proposal is to obtain a graph representation of the embedding produced by a CNN when processing an image, most related work focuses on training DNNs for processing graph data. For example, DeepWalk @cite_1 uses random walks in a graph ( Flickr or YouTube networks) to feed a SkipGram model, and then evaluate community detection methods on those graphs. Similarly to DeepWalk, the work of also processes graphs as input, but it uses a probabilistic approach on weighted graphs to feed an autoencoder. In contrast, we are performing community detection on a dataset of images, something that, to the best of our knowledge, had not been done before.
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We present DeepWalk, a novel approach for learning latent representations of vertices in a network. These latent representations encode social relations in a continuous vector space, which is easily exploited by statistical models. DeepWalk generalizes recent advancements in language modeling and unsupervised feature learning (or deep learning) from sequences of words to graphs. DeepWalk uses local information obtained from truncated random walks to learn latent representations by treating walks as the equivalent of sentences. We demonstrate DeepWalk's latent representations on several multi-label network classification tasks for social networks such as BlogCatalog, Flickr, and YouTube. Our results show that DeepWalk outperforms challenging baselines which are allowed a global view of the network, especially in the presence of missing information. DeepWalk's representations can provide F1 scores up to 10 higher than competing methods when labeled data is sparse. In some experiments, DeepWalk's representations are able to outperform all baseline methods while using 60 less training data. DeepWalk is also scalable. It is an online learning algorithm which builds useful incremental results, and is trivially parallelizable. These qualities make it suitable for a broad class of real world applications such as network classification, and anomaly detection. We present WALKLETS, a novel approach for learning multiscale representations of vertices in a network. In contrast to previous works, these representations explicitly encode multi-scale vertex relationships in a way that is analytically derivable. WALKLETS generates these multiscale relationships by sub-sampling short random walks on the vertices of a graph. By 'skipping' over steps in each random walk, our method generates a corpus of vertex pairs which are reachable via paths of a fixed length. This corpus can then be used to learn a series of latent representations, each of which captures successively higher order relationships from the adjacency matrix. We demonstrate the efficacy of WALKLETS's latent representations on several multi-label network classification tasks for social networks such as BlogCatalog, DBLP, Flickr, and YouTube. Our results show that WALKLETS outperforms new methods based on neural matrix factorization. Specifically, we outperform DeepWalk by up to 10 and LINE by 58 Micro-F1 on challenging multi-label classification tasks. Finally, WALKLETS is an online algorithm, and can easily scale to graphs with millions of vertices and edges. Community detection is a common problem in various types of big graphs. It is meaningful to understand the functions and dynamics of networks. The challenges of detecting community for big graphs include high computational cost, no prior information, etc.. In this work, we analyze the process of random walking in graphs, and find out that the weight of an edge gotten by processing the vertices visited by the walker could be an indicator to measure the closeness of vertex connection. Based on this idea, we propose a community detection algorithm for undirected big graphs which consists of three steps, including random walking using a single walker, weight calculating for edges and community detecting. Our algorithm is running in O(n2) without prior information. Experimental results show that our algorithm is capable of detecting the community structure and the overlapping parts of graphs in real-world effectively, and handling the challenges of community detection in big graph era. Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factorization framework with closed forms. Our analysis and proofs reveal that: (1) DeepWalk empirically produces a low-rank transformation of a network's normalized Laplacian matrix; (2) LINE, in theory, is a special case of DeepWalk when the size of vertices' context is set to one; (3) As an extension of LINE, PTE can be viewed as the joint factorization of multiple networks» Laplacians; (4) node2vec is factorizing a matrix related to the stationary distribution and transition probability tensor of a 2nd-order random walk. We further provide the theoretical connections between skip-gram based network embedding algorithms and the theory of graph Laplacian. Finally, we present the NetMF method as well as its approximation algorithm for computing network embedding. Our method offers significant improvements over DeepWalk and LINE for conventional network mining tasks. This work lays the theoretical foundation for skip-gram based network embedding methods, leading to a better understanding of latent network representation learning. We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information (from social networks, user-item graphs, knowledge bases, etc.) in many machine learning tasks. Unlike previous work, we (1) explicitly model an edge as a function of node embeddings, and we (2) propose a novel objective, the graph likelihood, which contrasts information from sampled random walks with non-existent edges. Individually, both of these contributions improve the learned representations, especially when there are memory constraints on the total size of the embeddings. When combined, our contributions enable us to significantly improve the state-of-the-art by learning more concise representations that better preserve the graph structure. We evaluate our method on a variety of link-prediction task including social networks, collaboration networks, and protein interactions, showing that our proposed method learn representations with error reductions of up to 76 and 55 , on directed and undirected graphs. In addition, we show that the representations learned by our method are quite space efficient, producing embeddings which have higher structure-preserving accuracy but are 10 times smaller. In this paper, we present GraRep , a novel model for learning vertex representations of weighted graphs. This model learns low dimensional vectors to represent vertices appearing in a graph and, unlike existing work, integrates global structural information of the graph into the learning process. We also formally analyze the connections between our work and several previous research efforts, including the DeepWalk model of as well as the skip-gram model with negative sampling of We conduct experiments on a language network, a social network as well as a citation network and show that our learned global representations can be effectively used as features in tasks such as clustering, classification and visualization. Empirical results demonstrate that our representation significantly outperforms other state-of-the-art methods in such tasks. Deep neural networks (DNNs) have been widely applied in various applications involving image, text, audio, and graph data. However, recent studies have shown that DNNs are vulnerable to adversarial attack. Though there are several works studying adversarial attack and defense on domains such as images and text processing, it is difficult to directly transfer the learned knowledge to graph data due to its representation challenge. Given the importance of graph analysis, increasing number of works start to analyze the robustness of machine learning models on graph. Nevertheless, current studies considering adversarial behaviors on graph data usually focus on specific types of attacks with certain assumptions. In addition, each work proposes its own mathematical formulation which makes the comparison among different methods difficult. Therefore, in this paper, we aim to survey existing adversarial attack strategies on graph data and provide an unified problem formulation which can cover all current adversarial learning studies on graph. We also compare different attacks on graph data and discuss their corresponding contributions and limitations. Finally, we discuss several future research directions in this area. We present HARP, a novel method for learning low dimensional embeddings of a graph's nodes which preserves higher-order structural features. Our proposed method achieves this by compressing the input graph prior to embedding it, effectively avoiding troublesome embedding configurations (i.e. local minima) which can pose problems to non-convex optimization. HARP works by finding a smaller graph which approximates the global structure of its input. This simplified graph is used to learn a set of initial representations, which serve as good initializations for learning representations in the original, detailed graph. We inductively extend this idea, by decomposing a graph in a series of levels, and then embed the hierarchy of graphs from the coarsest one to the original graph. HARP is a general meta-strategy to improve all of the state-of-the-art neural algorithms for embedding graphs, including DeepWalk, LINE, and Node2vec. Indeed, we demonstrate that applying HARP's hierarchical paradigm yields improved implementations for all three of these methods, as evaluated on both classification tasks on real-world graphs such as DBLP, BlogCatalog, CiteSeer, and Arxiv, where we achieve a performance gain over the original implementations by up to 14 Macro F1. Graph Embedding methods are aimed at mapping each vertex into a low dimensional vector space, which preserves certain structural relationships among the vertices in the original graph. Recently, several works have been proposed to learn embeddings based on sampled paths from the graph, e.g., DeepWalk, Line, Node2Vec. However, their methods only preserve symmetric proximities, which could be insufficient in many applications, even the underlying graph is undirected. Besides, they lack of theoretical analysis of what exactly the relationships they preserve in their embedding space. In this paper, we propose an asymmetric proximity preserving (APP) graph embedding method via random walk with restart, which captures both asymmetric and high-order similarities between node pairs. We give theoretical analysis that our method implicitly preserves the Rooted PageRank score for any two vertices. We conduct extensive experiments on tasks of link prediction and node recommendation on open source datasets, as well as online recommendation services in Alibaba Group, in which the training graph has over 290 million vertices and 18 billion edges, showing our method to be highly scalable and effective. Graphs are a fundamental abstraction for modeling relational data. However, graphs are discrete and combinatorial in nature, and learning representations suitable for machine learning tasks poses statistical and computational challenges. In this work, we propose Graphite an algorithmic framework for unsupervised learning of representations over nodes in a graph using deep latent variable generative models. Our model is based on variational autoencoders (VAE), and differs from existing VAE frameworks for data modalities such as images, speech, and text in the use of graph neural networks for parameterizing both the generative model (i.e., decoder) and inference model (i.e., encoder). The use of graph neural networks directly incorporates inductive biases due to the spatial, local structure of graphs directly in the generative model. Moreover, we draw novel connections between graph neural networks and approximate inference via kernel embeddings of distributions. We demonstrate empirically that Graphite outperforms state-of-the-art approaches for the tasks of density estimation, link prediction, and node classification on synthetic and benchmark datasets. We propose a generalization of convolutional neural networks (CNNs) to irregular domains, through the use of an inferred graph structure. In more details, we introduce a three-step methodology to create convolutional layers that are adapted to the signals to process: 1) From a training set of signals, infer a graph representing the topology on which they evolve; 2) Identify translation operators in the vertex domain; 3) Emulate a convolution operator by translating a localized kernel on the graph. Using these layers, a convolutional neural network is built, and is trained on the initial signals to perform a classification task. Contributions are twofold. First, we adapt a definition of translations on graphs to make them more robust to irregularities, and to take into account locality of the kernel. Second, we introduce a procedure to build CNNs from data. We apply our methodology on a scrambled version of the CIFAR-10 and Haxby datasets. Without using any knowledge on the signals, we significantly outperform existing methods. Moreover, our approach extends classical CNNs on images in the sense that such networks are a particular case of our approach when the inferred graph is a grid. Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures currently produce state-of-the-art performance on a variety of image analysis tasks such as object detection and recognition. Most of deep learning research has so far focused on dealing with 1D, 2D, or 3D Euclidean-structured data such as acoustic signals, images, or videos. Recently, there has been an increasing interest in geometric deep learning, attempting to generalize deep learning methods to non-Euclidean structured data such as graphs and manifolds, with a variety of applications from the domains of network analysis, computational social science, or computer graphics. In this paper, we propose a unified framework allowing to generalize CNN architectures to non-Euclidean domains (graphs and manifolds) and learn local, stationary, and compositional task-specific features. We show that various non-Euclidean CNN methods previously proposed in the literature can be considered as particular instances of our framework. We test the proposed method on standard tasks from the realms of image-, graph-and 3D shape analysis and show that it consistently outperforms previous approaches. Deep learning on graphs has become a popular research topic with many applications. However, past work has concentrated on learning graph embedding tasks only, which is in contrast with advances in generative models for images and text. Is it possible to transfer this progress to the domain of graphs? We propose to sidestep hurdles associated with linearization of such discrete structures by having a decoder output a probabilistic fully-connected graph of a predefined maximum size directly at once. Our method is formulated as a variational autoencoder. We evaluate on the challenging task of conditional molecule generation. We propose a novel subgraph image representation for classification of network fragments with the target being their parent networks. The graph image representation is based on 2D image embeddings of adjacency matrices. We use this image representation in two modes. First, as the input to a machine learning algorithm. Second, as the input to a pure transfer learner. Our conclusions from multiple datasets are that 1. deep learning using structured image features performs the best compared to graph kernel and classical features based methods; and, 2. pure transfer learning works effectively with minimum interference from the user and is robust against small data. In this paper, we focus on fraud detection on a signed graph with only a small set of labeled training data. We propose a novel framework that combines deep neural networks and spectral graph analysis. In particular, we use the node projection (called as spectral coordinate) in the low dimensional spectral space of the graph's adjacency matrix as input of deep neural networks. Spectral coordinates in the spectral space capture the most useful topology information of the network. Due to the small dimension of spectral coordinates (compared with the dimension of the adjacency matrix derived from a graph), training deep neural networks becomes feasible. We develop and evaluate two neural networks, deep autoencoder and convolutional neural network, in our fraud detection framework. Experimental results on a real signed graph show that our spectrum based deep neural networks are effective in fraud detection. Steganography aims to conceal the very fact that the communication takes place, by embedding a message into a digit object such as image without introducing noticeable artifacts. A number of steganographic systems have been developed in past years, most of which, however, are confined to the laboratory conditions where the real-world use of steganography are rarely concerned. In this paper, we introduce an alternative perspective to steganography. A graph-theoretic model to steganography on social networks is presented to analyze real-world steganographic scenarios. In the graph, steganographic participants are corresponding to the vertices with meaningless unique identifiers. Each edge allows the two vertices to communicate with each other by any steganographic algorithm. Meanwhile, the edges are associated with weights to quantize the corresponding communication risk (or say cost). The optimization task is to minimize the overall risk, which is modeled as additive over the social network. We analyze different scenarios on a social network, and provide the suited solutions to the corresponding optimization tasks. We prove that a multiplicative probabilistic graph is equivalent to an additive weighted graph. From the viewpoint of an attacker, he may hope to detect suspicious communication channels, the data encoder(s) and the data decoder(s). We present limited detection analysis to steganographic communication on a network. Abstract Graphs, such as social networks, word co-occurrence networks, and communication networks, occur naturally in various real-world applications. Analyzing them yields insight into the structure of society, language, and different patterns of communication. Many approaches have been proposed to perform the analysis. Recently, methods which use the representation of graph nodes in vector space have gained traction from the research community. In this survey, we provide a comprehensive and structured analysis of various graph embedding techniques proposed in the literature. We first introduce the embedding task and its challenges such as scalability, choice of dimensionality, and features to be preserved, and their possible solutions. We then present three categories of approaches based on factorization methods, random walks, and deep learning, with examples of representative algorithms in each category and analysis of their performance on various tasks. We evaluate these state-of-the-art methods on a few common datasets and compare their performance against one another. Our analysis concludes by suggesting some potential applications and future directions. We finally present the open-source Python library we developed, named GEM ( Graph Embedding Methods , available at https: github.com palash1992 GEM ), which provides all presented algorithms within a unified interface to foster and facilitate research on the topic. Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike. Detecting communities in graphs is a fundamental tool to understand the structure of Web-based systems and predict their evolution. Many community detection algorithms are designed to process undirected graphs (i.e., graphs with bidirectional edges) but many graphs on the Web-e.g., microblogging Web sites, trust networks or the Web graph itself-are often directed . Few community detection algorithms deal with directed graphs but we lack their experimental comparison. In this paper we evaluated some community detection algorithms across accuracy and scalability. A first group of algorithms (Label Propagation and Infomap) are explicitly designed to manage directed graphs while a second group (e.g., WalkTrap) simply ignores edge directionality; finally, a third group of algorithms (e.g., Eigenvector) maps input graphs onto undirected ones and extracts communities from the symmetrized version of the input graph. We ran our tests on both artificial and real graphs and, on artificial graphs, WalkTrap achieved the highest accuracy, closely followed by other algorithms; Label Propagation has outstanding performance in scalability on both artificial and real graphs. The Infomap algorithm showcased the best trade-off between accuracy and computational performance and, therefore, it has to be considered as a promising tool for Web Data Analytics purposes. Modern deep transfer learning approaches have mainly focused on learning generic feature vectors from one task that are transferable to other tasks, such as word embeddings in language and pretrained convolutional features in vision. However, these approaches usually transfer unary features and largely ignore more structured graphical representations. This work explores the possibility of learning generic latent relational graphs that capture dependencies between pairs of data units (e.g., words or pixels) from large-scale unlabeled data and transferring the graphs to downstream tasks. Our proposed transfer learning framework improves performance on various tasks including question answering, natural language inference, sentiment analysis, and image classification. We also show that the learned graphs are generic enough to be transferred to different embeddings on which the graphs have not been trained (including GloVe embeddings, ELMo embeddings, and task-specific RNN hidden unit), or embedding-free units such as image pixels.