Data mining when each data point is a network

We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of modeling contexts, especially when coarse-graining the detailed graph information is of interest. One of the main challenges in mining graph data is the definition of a suitable pairwise similarity metric in the space of graphs. We explore two practical solutions to solving this problem: one based on finding subgraph densities, and Karthikeyan Rajendran Department of Chemical & Biological Engineering, Princeton University Present Address: 731 Lexington Avenue, 10022, New York, NY, USA, email: [email protected] Assimakis Kattis Theory Group, Department of Computer Science, University of Toronto 10 King’s College Road, M5S 3G4, Toronto, ON, Canada, email: [email protected] Alexander Holiday Department of Chemical & Biological Engineering, Princeton University 41 Olden Street, 08544, Princeton, NJ, USA, email: [email protected] Risi Kondor Machine Learning Group, Computer Science & Statistics, University of Chicago Ryerson 257B, 1100 E. 58th Street, 60637, Chicago, IL, USA, email: [email protected] Ioannis G. Kevrekidis A319 Engineering Quad, Department of Chemical & Biological Engineering and Program in Applied & Computational Mathematics, Princeton University Technische Universität München Institute for Advanced Study; Zuse Institut Berlin 41 Olden Street, 08544, Princeton, NJ, USA, email: [email protected] 1 ar X iv :1 61 2. 02 90 8v 1 [ cs .S I] 9 D ec 2 01 6 2 Authors Suppressed Due to Excessive Length one using spectral information. The approach is illustrated on three test data sets (ensembles of graphs); two of these are obtained from standard graph generating algorithms, while the graphs in the third example are sampled as dynamic snapshots from an evolving network simulation. We further incorporate these approaches with equation free techniques, demonstrating how such data mining approaches can enhance scientific computation of network evolution dynamics.