  Higher-order proximity preserved network embedding has attracted increasing
attention. In particular, due to the superior scalability, random-walk-based
network embedding has also been well developed, which could efficiently explore
higher-order neighborhoods via multi-hop random walks. However, despite the
success of current random-walk-based methods, most of them are usually not
expressive enough to preserve the personalized higher-order proximity and lack
a straightforward objective to theoretically articulate what and how network
proximity is preserved. In this paper, to address the above issues, we present
a general scalable random-walk-based network embedding framework, in which
random walk is explicitly incorporated into a sound objective designed
theoretically to preserve arbitrary higher-order proximity. Further, we
introduce the random walk with restart process into the framework to naturally
and effectively achieve personalized-weighted preservation of proximities of
different orders. We conduct extensive experiments on several real-world
networks and demonstrate that our proposed method consistently and
substantially outperforms the state-of-the-art network embedding methods.
