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Node embedding is the task of extracting informative and descriptive featuresover the nodes of a graph. The importance of node embeddings for graphanalytics, as well as learning tasks such as node classification, linkprediction and community detection, has led to increased interest on theproblem leading to a number of recent advances. Much like PCA in the featuredomain, node embedding is an inherently \emph{unsupervised} task; in lack ofmetadata used for validation, practical methods may require standardization andlimiting the use of tunable hyperparameters. Finally, node embedding methodsare faced with maintaining scalability in the face of large-scale real-worldgraphs of ever-increasing sizes. In the present work, we propose an adaptivenode embedding framework that adjusts the embedding process to a givenunderlying graph, in a fully unsupervised manner. To achieve this, we adopt thenotion of a tunable node similarity matrix that assigns weights on paths ofdifferent length. The design of the multilength similarities ensures that theresulting embeddings also inherit interpretable spectral properties. Theproposed model is carefully studied, interpreted, and numerically evaluatedusing stochastic block models. Moreover, an algorithmic scheme is proposed fortraining the model parameters effieciently and in an unsupervised manner. Weperform extensive node classification, link prediction, and clusteringexperiments on many real world graphs from various domains, and compare withstate-of-the-art scalable and unsupervised node embedding alternatives. Theproposed method enjoys superior performance in many cases, while also yieldinginterpretable information on the underlying structure of the graph.

Node Embedding with Adaptive Similarities for Scalable Learning over Graphs