  Node influence metrics have been applied to many applications, including
ranking web pages on internet, or locations on spatial networks. PageRank is a
popular and effective algorithm for estimating node influence. However,
conventional PageRank method considers neither the heterogeneity of network
structures nor additional network information, causing a major impedance to
performance improvement and an underestimation of non-hub nodes' importance. As
these problems are only partially studied, existing solutions are still not
satisfying. This paper addresses the problems by presenting a general
PageRank-based model framework, dubbed Hetero-NodeRank, that accounts for
heterogeneous network topology and incorporates node attribute information to
capture both link- and node-based effects in measuring node influence.
Moreover, the framework enables the calibration of the proposed model against
empirical data, which transforms the original deductive approach into an
inductive one that could be useful for hypothesis testing and causal-effect
analysis. As the original unsupervised task becomes a supervised one,
optimization methods can be leveraged for model calibrations. Experiments on
real data from the national city network of China demonstrated that the
proposed model outperforms several widely used algorithms.

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