Interpretable Feature Learning of Graphs using Tensor Decomposition In recent years, node embedding algorithms, which learn low dimensional vector representations for nodes in a graph, have been one of the key research interests of the graph mining community. The existing algorithms either rely on computationally expensive eigendecomposition of the large matrices, or require tuning of the word embeddingbased hyperparameters as a result of representing the graph as a node sequence similar to the sentences in a document. Moreover, the latent features produced by these algorithms are hard to interpret. In this paper, we present two novel tensor decompositionbased node embedding algorithms, that can learn node features from arbitrary types of graphs: undirected, directed, andor weighted, without relying on eigendecomposition or word embeddingbased hyperparameters. Both algorithms preserve the local and global structural properties of the graph by using kstep transition probability matrices to construct thirdorder multidimensional arrays or tensors and perform CANDECOMPPARAFAC (CP) decomposition in order to produce an interpretable and low dimensional vector space for the nodes. Our experiments encompass different types of graphs (undirecteddirected, unweightedweighted, sparsedense) of different domains such as social networking and neuroscience. Our experimental evaluation proves our models to be interpretable with respect to the understandability of the feature space, precise with respect to the network reconstruction and link prediction, and accurate with respect to node classification and graph classification.

Joint embedding of structure and features via graph convolutional networks The creation of social ties is largely determined by the entangled effects of peopleu0027s similarities in terms of individual characters and friends. However, feature and structural characters of people usually appear to be correlated, making it difficult to determine which has greater responsibility in the formation of the emergent network structure. We propose emphAN2VEC, a node embedding method which ultimately aims at disentangling the information shared by the structure of a network and the features of its nodes. Building on the recent developments of Graph Convolutional Networks (GCN), we develop a multitask GCN Variational Autoencoder where different dimensions of the generated embeddings can be dedicated to encoding feature information, network structure, and shared featurenetwork information. We explore the interaction between these disentangled characters by comparing the embedding reconstruction performance to a baseline case where no shared information is extracted. We use synthetic datasets with different levels of interdependency between feature and network characters and show (i) that shallow embeddings relying on shared information perform better than the corresponding reference with unshared information, (ii) that this performance gap increases with the correlation between network and feature structure, and (iii) that our embedding is able to capture joint information of structure and features. Our method can be relevant for the analysis and prediction of any featured network structure ranging from online social systems to network medicine.