Optimizing the Induced Correlation in Omnibus Joint Graph Embeddings
研究了全连接联合图嵌入框架中算法诱导的相关性，提出自动构建方法以解决平坦相关性和相关性到全连接问题，通过理论和实验证明新算法优于经典方法。
Theoretical and empirical evidence suggests that joint graph embedding algorithms induce correlation across networks in the embedding space. In the Omnibus joint graph embedding framework, previous results delineated the dual effects of algorithm-induced and model-inherent correlations on the total correlation across embedded networks. Accounting for the algorithm-induced correlation is practically important, as suboptimal Omnibus constructions can lead to inferential losses. This work presents the first efforts to automate the Omnibus construction in order to address two key questions: the correlation–to–Omni problem and the flat correlation problem. In the flat correlation problem, we seek the minimum algorithm-induced flat correlation (i.e., the same across all graph pairs) produced via an Omnibus embedding, as minimal flat correlation best preserves individual graph structure in the embedding space. 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 maximal flat correlation. In the correlation–to–Omni problem, we present the corr2Omni algorithm to construct Omnibus embeddings that best preserve a given matrix of estimated pairwise graph correlations in the embedding space. In simulated and real data settings, we demonstrate the increased effectiveness of corr2Omni versus the classical Omnibus construction.