A1026
Title: Optimizing the induced correlation in omnibus joint graph embeddings
Authors: Konstantinos Pantazis - Johns Hopkins University (United States)
Michael Trosset - Indiana University Bloomington (United States)
William Frost - Rosalind Franklin University (United States)
Carey Priebe - Johns Hopkins University (United States)
Vince Lyzinski - University of Maryland, College Park (United States) [presenting]
Abstract: Theoretical and empirical evidence suggests that joint graph embedding algorithms induce correlation across the networks in the embedding space. In the Omnibus joint graph embedding framework, previous results explicitly delineated the dual effects of the algorithm-induced and model-inherent correlations on the correlation across the embedded networks. This algorithm-induced correlation is key to subsequent inference, as sub-optimal Omnibus matrix constructions can lead to a loss in inference fidelity. We present the first efforts to automate the Omnibus construction in order to address two key questions in this joint embedding framework: the correlation--to--OMNI problem and the flat correlation problem. In the flat correlation problem, we seek to understand the minimum algorithm-induced flat correlation (i.e., the same across all graph pairs) produced by a generalized Omnibus embedding. Working in a subspace of the fully general Omnibus matrices, we prove a lower bound for this flat correlation and that the classical Omnibus construction induces the maximal flat correlation. In the correlation--to--OMNI problem, we present an algorithm named corr2Omni that, from estimated pairwise graph correlations, estimates the generalized Omnibus weights that induce optimal correlation in the embedding space. Moreover, in both simulated and real data settings, we demonstrate the increased effectiveness of our corr2Omni algorithm versus the classical Omnibus construction.
