Dr. James Wilson

Assocate Professor 

Department of Mathematics and Statistics

University of San Francisco

ABSTRACT: In the last decade, network representation learning (NRL) has become a common and important learning task for network-valued data. The goal of network representation learning is to identify low-dimensional representations of an observed network that preserve various aspects of the original graph like its topology, vertex attributes, or community structure. In this talk, I consider the problem of interpretable NRL for samples of network- valued data. We propose the Principal Component Analysis for Networks (PCAN) algorithm to identify statistically meaningful low-dimensional representations of a network sample via subgraph count statistics. The PCAN procedure provides an interpretable framework for which one can readily visualize, explore, and formulate predictive models for network samples. We furthermore introduce a fast sampling-based algorithm, sPCAN, which is significantly more computationally efficient than its counterpart, but still enjoys advantages of interpretability. We investigate the relationship between these two methods and analyze their large-sample properties under the common regime where the sample of networks is a collection of kernel-based random graphs. We show that under this regime, the embeddings of the sPCAN method enjoy a central limit theorem and more- over that the population level embeddings of PCAN and sPCAN are equivalent. We assess PCAN’s ability to visualize, cluster, and classify observations in network samples arising in nature, including functional connectivity network samples and dynamic networks describing the political co-voting habits of the U.S. Senate. Our analyses reveal that our proposed algorithm provides informative and discriminatory features describing the networks in each sample.