** Attributed network embedding has received much interest from the research community as most of the networks come with some content in each node, which is also known as node attributes. Existing attributed network approaches work well when the network is consistent in structure and attributes, and nodes behave as expected. But real world networks often have anomalous nodes. Typically these outliers, being relatively unexplainable, affect the embeddings of other nodes in the network. Thus all the downstream network mining tasks fail miserably in the presence of such outliers. Hence an integrated approach to detect anomalies and reduce their overall effect on the network embedding is required. Towards this end, we propose an unsupervised outlier aware network embedding algorithm (ONE) for attributed networks, which minimizes the effect of the outlier nodes, and hence generates robust network embeddings. We align and jointly optimize the loss functions coming from structure and attributes of the network. To the best of our knowledge, this is the first generic network embedding approach which incorporates the effect of outliers for an attributed network without any supervision. We experimented on publicly available real networks and manually planted different types of outliers to check the performance of the proposed algorithm. Results demonstrate the superiority of our approach to detect the network outliers compared to the state-of-the-art approaches. We also consider different downstream machine learning applications on networks to show the efficiency of ONE as a generic network embedding technique. The source code is made available at https://github.com/sambaranban/ONE. **

** Attributed graph clustering is challenging as it requires joint modelling of graph structures and node attributes. Recent progress on graph convolutional networks has proved that graph convolution is effective in combining structural and content information, and several recent methods based on it have achieved promising clustering performance on some real attributed networks. However, there is limited understanding of how graph convolution affects clustering performance and how to properly use it to optimize performance for different graphs. Existing methods essentially use graph convolution of a fixed and low order that only takes into account neighbours within a few hops of each node, which underutilizes node relations and ignores the diversity of graphs. In this paper, we propose an adaptive graph convolution method for attributed graph clustering that exploits high-order graph convolution to capture global cluster structure and adaptively selects the appropriate order for different graphs. We establish the validity of our method by theoretical analysis and extensive experiments on benchmark datasets. Empirical results show that our method compares favourably with state-of-the-art methods. **

** Network embedding is the process of learning low-dimensional representations for nodes in a network, while preserving node features. Existing studies only leverage network structure information and focus on preserving structural features. However, nodes in real-world networks often have a rich set of attributes providing extra semantic information. It has been demonstrated that both structural and attribute features are important for network analysis tasks. To preserve both features, we investigate the problem of integrating structure and attribute information to perform network embedding and propose a Multimodal Deep Network Embedding (MDNE) method. MDNE captures the non-linear network structures and the complex interactions among structures and attributes, using a deep model consisting of multiple layers of non-linear functions. Since structures and attributes are two different types of information, a multimodal learning method is adopted to pre-process them and help the model to better capture the correlations between node structure and attribute information. We employ both structural proximity and attribute proximity in the loss function to preserve the respective features and the representations are obtained by minimizing the loss function. Results of extensive experiments on four real-world datasets show that the proposed method performs significantly better than baselines on a variety of tasks, which demonstrate the effectiveness and generality of our method. **

** Network embedding aims to learn a latent, low-dimensional vector representations of network nodes, effective in supporting various network analytic tasks. While prior arts on network embedding focus primarily on preserving network topology structure to learn node representations, recently proposed attributed network embedding algorithms attempt to integrate rich node content information with network topological structure for enhancing the quality of network embedding. In reality, networks often have sparse content, incomplete node attributes, as well as the discrepancy between node attribute feature space and network structure space, which severely deteriorates the performance of existing methods. In this paper, we propose a unified framework for attributed network embedding-attri2vec-that learns node embeddings by discovering a latent node attribute subspace via a network structure guided transformation performed on the original attribute space. The resultant latent subspace can respect network structure in a more consistent way towards learning high-quality node representations. We formulate an optimization problem which is solved by an efficient stochastic gradient descent algorithm, with linear time complexity to the number of nodes. We investigate a series of linear and non-linear transformations performed on node attributes and empirically validate their effectiveness on various types of networks. Another advantage of attri2vec is its ability to solve out-of-sample problems, where embeddings of new coming nodes can be inferred from their node attributes through the learned mapping function. Experiments on various types of networks confirm that attri2vec is superior to state-of-the-art baselines for node classification, node clustering, as well as out-of-sample link prediction tasks. The source code of this paper is available at https://github.com/daokunzhang/attri2vec. **

** An attributed network enriches a pure network by encoding a part of widely accessible node auxiliary information into node attributes. Learning vector representation of each node a.k.a. Network Embedding (NE) for such an attributed network by considering both structure and attribute information has recently attracted considerable attention, since each node embedding is simply a unified low-dimension vector representation that makes downstream tasks e.g. link prediction more efficient and much easier to realize. Most of previous works have not considered the significant case of a network with incomplete structure information, which however, would often appear in our real-world scenarios e.g. the abnormal users in a social network who intentionally hide their friendships. And different networks obviously have different levels of incomplete structure information, which imposes more challenges to balance two sources of information. To tackle that, we propose a robust NE method called Attributed Biased Random Walks (ABRW) to employ attribute information for compensating incomplete structure information by using transition matrices. The experiments of link prediction and node classification tasks on real-world datasets confirm the robustness and effectiveness of our method to the different levels of the incomplete structure information. **

** Network embedding has become a hot research topic recently which can provide low-dimensional feature representations for many machine learning applications. Current work focuses on either (1) whether the embedding is designed as an unsupervised learning task by explicitly preserving the structural connectivity in the network, or (2) whether the embedding is a by-product during the supervised learning of a specific discriminative task in a deep neural network. In this paper, we focus on bridging the gap of the two lines of the research. We propose to adapt the Generative Adversarial model to perform network embedding, in which the generator is trying to generate vertex pairs, while the discriminator tries to distinguish the generated vertex pairs from real connections (edges) in the network. Wasserstein-1 distance is adopted to train the generator to gain better stability. We develop three variations of models, including GANE which applies cosine similarity, GANE-O1 which preserves the first-order proximity, and GANE-O2 which tries to preserves the second-order proximity of the network in the low-dimensional embedded vector space. We later prove that GANE-O2 has the same objective function as GANE-O1 when negative sampling is applied to simplify the training process in GANE-O2. Experiments with real-world network datasets demonstrate that our models constantly outperform state-of-the-art solutions with significant improvements on precision in link prediction, as well as on visualizations and accuracy in clustering tasks. **

** Network embedding methodologies, which learn a distributed vector representation for each vertex in a network, have attracted considerable interest in recent years. Existing works have demonstrated that vertex representation learned through an embedding method provides superior performance in many real-world applications, such as node classification, link prediction, and community detection. However, most of the existing methods for network embedding only utilize topological information of a vertex, ignoring a rich set of nodal attributes (such as, user profiles of an online social network, or textual contents of a citation network), which is abundant in all real-life networks. A joint network embedding that takes into account both attributional and relational information entails a complete network information and could further enrich the learned vector representations. In this work, we present Neural-Brane, a novel Neural Bayesian Personalized Ranking based Attributed Network Embedding. For a given network, Neural-Brane extracts latent feature representation of its vertices using a designed neural network model that unifies network topological information and nodal attributes; Besides, it utilizes Bayesian personalized ranking objective, which exploits the proximity ordering between a similar node-pair and a dissimilar node-pair. We evaluate the quality of vertex embedding produced by Neural-Brane by solving the node classification and clustering tasks on four real-world datasets. Experimental results demonstrate the superiority of our proposed method over the state-of-the-art existing methods. **

** Classifying large scale networks into several categories and distinguishing them according to their fine structures is of great importance with several applications in real life. However, most studies of complex networks focus on properties of a single network but seldom on classification, clustering, and comparison between different networks, in which the network is treated as a whole. Due to the non-Euclidean properties of the data, conventional methods can hardly be applied on networks directly. In this paper, we propose a novel framework of complex network classifier (CNC) by integrating network embedding and convolutional neural network to tackle the problem of network classification. By training the classifiers on synthetic complex network data and real international trade network data, we show CNC can not only classify networks in a high accuracy and robustness, it can also extract the features of the networks automatically. **

Enhancing Network Embedding with Auxiliary Information: An Explicit Matrix Factorization Perspective

** Recent advances in the field of network embedding have shown the low-dimensional network representation is playing a critical role in network analysis. However, most of the existing principles of network embedding do not incorporate auxiliary information such as content and labels of nodes flexibly. In this paper, we take a matrix factorization perspective of network embedding, and incorporate structure, content and label information of the network simultaneously. For structure, we validate that the matrix we construct preserves high-order proximities of the network. Label information can be further integrated into the matrix via the process of random walk sampling to enhance the quality of embedding in an unsupervised manner, i.e., without leveraging downstream classifiers. In addition, we generalize the Skip-Gram Negative Sampling model to integrate the content of the network in a matrix factorization framework. As a consequence, network embedding can be learned in a unified framework integrating network structure and node content as well as label information simultaneously. We demonstrate the efficacy of the proposed model with the tasks of semi-supervised node classification and link prediction on a variety of real-world benchmark network datasets. **

** Social network analysis provides meaningful information about behavior of network members that can be used for diverse applications such as classification, link prediction. However, network analysis is computationally expensive because of feature learning for different applications. In recent years, many researches have focused on feature learning methods in social networks. Network embedding represents the network in a lower dimensional representation space with the same properties which presents a compressed representation of the network. In this paper, we introduce a novel algorithm named "CARE" for network embedding that can be used for different types of networks including weighted, directed and complex. Current methods try to preserve local neighborhood information of nodes, whereas the proposed method utilizes local neighborhood and community information of network nodes to cover both local and global structure of social networks. CARE builds customized paths, which are consisted of local and global structure of network nodes, as a basis for network embedding and uses the Skip-gram model to learn representation vector of nodes. Subsequently, stochastic gradient descent is applied to optimize our objective function and learn the final representation of nodes. Our method can be scalable when new nodes are appended to network without information loss. Parallelize generation of customized random walks is also used for speeding up CARE. We evaluate the performance of CARE on multi label classification and link prediction tasks. Experimental results on various networks indicate that the proposed method outperforms others in both Micro and Macro-f1 measures for different size of training data. **