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Play, download and edit the free video Residual2Vec: debaising graph embedding using network null models..

Graph embedding is a powerful approach to obtain a useful vector-space representation of nodes in networks. A widespread paradigm uses random walks to create sequences of nodes (``sentences''), and apply word embedding methods to obtain a node embedding Although the inherent bias of the random walk process is well known, its impact on graph embedding has not been fully understood. Here, we demonstrate that the bias in random walks has a profound impact on embedding, calling a caution in its interpretation. To obtain a bias-corrected embedding, we propose residual2vec. The residual2vec creates an embedding based on the deviation from random networks (i.e., a null model for networks). We demonstrate that the bias correction improves performance in machine learning applications such as link prediction and clustering. In an example of a citation network of journals from American Physical Society (APS), the residual2vec captures the characteristics of APS journals: at the heart of the embedding is general physics journals such as Physical Review and Physical Review Letter, with branches of more specialized journals such as Physical Review A and D. By contrast, if the bias is not suppressed, the journal vectors are aligned in time. Our results call for a more careful treatment of graph embedding to prevent artifacts arising from random walks to develop a better understanding of network geometry.

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