Network Prediction with Degree Distributional Metric Learning

Introduction. Real-world networks often consist of nodes with informative attributes as well as links. To properly model these networks, it is necessary to learn how attributes of the nodes relate to the connectivity structure. Metric learning is a natural framework for transforming the raw node features to match the structural properties of a graph. Traditional metric learning algorithms primarily model the similarity between nodes and not structural properties, such as degree distributions. Degree distributions play a central role in graph structure analysis [1]. The degree distribution for some nodes may be non-stationary and depend on their attributes, particularly if some attributes naturally relate to connectedness. For example, in the LinkedIn network, an individual whose job area is “Software Sales” is likely to have more connections than an individual whose area is “Software Programmer”. We propose degree distributional metric learning (DDML), a method for simultaneously learning a metric and degree preference functions such that the combination captures the structure of the input graph and allows for more accurate link prediction from only node features.