Nodes in networks may have one or more functions that determine their role in the system. As opposed to local proximity, which captures the local context of nodes, the role identity captures the functional role that nodes play in a network, such as being the center of a group, or the bridge between two groups. This means that nodes far apart in a network can have similar structural role identities. Several recent works have explored methods for embedding the roles of nodes in networks. However, these methods all rely on either approximating or indirect modeling of structural equivalence. In this paper, we present a novel and flexible framework using stress majorization, to transform the high-dimensional role identities in networks directly (without approximation or indirect modeling) to a low-dimensional embedding space. Our method is also flexible, in that it does not rely on specific structural similarity definitions. We evaluated our method on the tasks of node classification, clustering, and visualization, using three real-world and five synthetic networks. Our experiments show that our framework achieves superior results than existing methods in learning node role representations.
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