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Learning representations of nodes in a low dimensional space is a crucial task with many interesting applications in network analysis, including link prediction and node classification. Two popular approaches for this problem include matrix factorization and random walk-based models.

In this work, we aim to bring together the best of both worlds, towards learning latent node representations. In particular, we propose a weighted matrix factorization model which encodes random walk-based information about the nodes of the graph. The main benefit of this formulation is that it allows to utilize kernel functions on the computation of the embeddings. We perform an empirical evaluation on real-world networks, showing that the proposed model outperforms baseline node embedding algorithms in two downstream machine learning tasks.