# Optimizing the Induced Correlation in Omnibus Joint Graph Embeddings

arXiv: https://arxiv.org/abs/2409.17544 · HTML: https://mlsanity.com/paper/2409.17544/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 26 Sep 2024.

## Builds on (most cited first, 14 of 14)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Statistical inference on random dot product graphs: a survey](https://mlsanity.com/paper/1709.05454/) (2017)
- [Inference for multiple heterogeneous networks with a common invariant subspace](https://mlsanity.com/paper/1906.10026/) (2019)
- [Network cross-validation by edge sampling](https://mlsanity.com/paper/1612.04717/) (2016)
- [Community Detection and Classification in Hierarchical Stochastic Blockmodels](https://mlsanity.com/paper/1503.02115/) (2015)
- [Joint Embedding of Graphs](https://mlsanity.com/paper/1703.03862/) (2017)
- [PIQP: A Proximal Interior-Point Quadratic Programming Solver](https://mlsanity.com/paper/2304.00290/) (2023)
- [Multiple Network Embedding for Anomaly Detection in Time Series of Graphs](https://mlsanity.com/paper/2008.10055/) (2020)
- [Estimating Graph Dimension with Cross-validated Eigenvalues](https://mlsanity.com/paper/2108.03336/) (2021)
- [Euclidean mirrors and dynamics in network time series](https://mlsanity.com/paper/2205.06877/) (2022)
- [The Importance of Being Correlated: Implications of Dependence in Joint Spectral Inference across Multiple Networks](https://mlsanity.com/paper/2008.00163/) (2020)
- [Euclidean mirrors and first-order changepoints in network time series](https://mlsanity.com/paper/2405.11111/) (2024)
- [The Multiple Random Dot Product Graph Model](https://mlsanity.com/paper/1811.12172/) (2018)
- [A central limit theorem for an omnibus embedding of multiple random graphs and implications for multiscale network inference](https://mlsanity.com/paper/1705.09355/) (2017)

## Abstract (arXiv)

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. Accounting for and mitigating the algorithm-induced correlation is key to subsequent inference, as sub-optimal Omnibus matrix constructions have been demonstrated to lead to loss in inference fidelity. This work presents 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 both 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 a given matrix of estimated pairwise graph correlations, estimates the matrix of generalized Omnibus weights that induces 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.