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Abstract:
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Network representation learning (NRL) is an important machine learning task that seeks meaningful low-dimensional representations, or embeddings, of network data. Despite its recent prominence, NRL methods generally suffer from a lack of interpretability. Inferential analyses of identified embeddings are difficult, limiting the application of NRL strategies. In this talk, we introduce a decomposition technique called Principal Component Analysis for Networks (PCAN) that identifies statistically meaningful embeddings of network samples. Not only does PCAN inherit interpretability from PCA, it also provides a straightforward strategy to visualize, cluster, and train predictive algorithms on a sample of complex networks. We provide a central limit theorem for the identified embeddings of PCAN when the observed sample is a collection of kernel-based random graphs, enabling a hypothesis testing for two sample comparisons. We investigate the utility of the PCAN through simulation studies and applications to network samples of functional connectivity of the brain and political co-voting behavior. Our findings reveal that PCAN is useful and straightforward for analyzing network samples.
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