Abstract: Learning representations of nodes in a low dimensional space is a crucial
task with numerous interesting applications in network analysis, including link
prediction, node classification, and visualization. Two popular approaches for
this problem are matrix factorization and random walk-based models. In this
paper, we aim to bring together the best of both worlds, towards learning node
representations. In particular, we propose a weighted matrix factorization
model that encodes random walk-based information about nodes of the network.
The benefit of this novel formulation is that it enables us to utilize kernel
functions without realizing the exact proximity matrix so that it enhances the
expressiveness of existing matrix decomposition methods with kernels and
alleviates their computational complexities. We extend the approach with a
multiple kernel learning formulation that provides the flexibility of learning
the kernel as the linear combination of a dictionary of kernels in data-driven
fashion. We perform an empirical evaluation on real-world networks, showing
that the proposed model outperforms baseline node embedding algorithms in
downstream machine learning tasks.