To deal simultaneously with both, the attributed network embedding and clustering, we propose a new model. It exploits both content and structure information, capitalising on their simultaneous use. The proposed model relies on the approximation of the relaxed continuous embedding solution by the true discrete clustering one. Thereby, we show that incorporating an embedding representation provides simpler and more interpretable solutions. Experiment results demonstrate that the proposed algorithm performs better, in terms of clustering and embedding, than the state-of-art algorithms, including deep learning methods devoted to similar tasks for attributed network datasets with different proprieties. In recent years, Attributed Networks (AN) (Qi et al., 2012) have been used to model a large variety of real-world networks, such as academic and health care networks where both node links and attributes/features are available for analysis. Unlike plain networks in which only node links and dependencies are observed, with AN, each node is associated with a valuable set of features. More recently, the learning representation has received a significant amount of attention as an important aim in many applications including social networks, academic citation networks and proteinprotein interaction networks. Hence, Attributed network Embedding (ANE) (Cai et al., 2018; Yan et al., 2007; aims to seek a continuous low-dimensional matrix representation for nodes in a network, such that original network topological structure and node attribute proximity can be preserved in the new low-dimensional embedding. Although, many approaches have emerged with Network Embedding (NE), the research on ANE (Attributed Network Embedding) is still remains to be explored . Unlike NE that learns from plain networks, ANE aims to capitalize both the proximity information of the network and the affinity of node attributes. Note that, due to the heterogeneity of the two information sources, it is difficult for the existing NE algorithms to be directly applied to ANE. To sum up, the learned representation has been shown to be helpful in many learning tasks such as network clustering (Wang et al., 2017) , nodes visualization (Dai et al., 2018) , nodes classification (Zhu et al., 2007; Dai et al., 2018; Huang et al., 2017) and link prediction (Singh & Gordon, 2008; Pan et al., 2018) . Therefore ANE is a challenging research problem due to the high-dimensionality, sparsity and non-linearity of the graph data. In this paper, we proposed a novel matrix decomposition framework for simultaneous attributed network data embedding and clustering. Unlike known methods that combine the objective function of AN embedding and the objective function of clustering separately, we proposed a new single framework to perform SANEC S for AN embedding and nodes clustering. We showed that the optimized objective function can be decomposed into three terms, the first is the objective function of a kind of PCA applied to M, the second is the graph embedding criterion in a low-dimensional space, and the third is the clustering criterion. We also integrated a discrete rotation functionality, which allows a smooth transformation from the relaxed continuous embedding to a discrete solution, and guarantees a tractable optimization problem with a discrete solution. Thereby, we developed an effective algorithm capitalizing on learning representation and clustering. The obtained results show the advantages of combining both tasks over other approaches. SANEC S outperforms the all recent methods devoted to the same tasks including deep learning methods which require deep models pretraining. The proposed framework offers several perspectives and investigations. We have noted that the construction of M and S is important, it highlights the introduction of W. As for the W X we have observed that it is fundamental as it makes possible to link the information from X to the network; this has been verified by many experiments. Finally, as we have stressed that Q is an embedding of attributes, this suggests to consider also a simultaneously ANE and co-clustering.
This paper propose a novel matrix decomposition framework for simultaneous attributed network data embedding and clustering. This paper proposes an algorithm to perform jointly attribute network embedding and clustering together.