Correspondence analysis on sparse bipartite graphs with hyperspecialization

Correspondence analysis (CA) and its covariate-based counterpart, canonical correspondence analysis (CCA), are classic yet popular scaling methods in the natural, social, and biomedical sciences to estimate latent gradients that drive the formation of edges in a bipartite graph. However, these methods struggle to identify latent gradients when they exist in sparse graphs where small subsets of nodes are hyperspecialized to each other. This paper proposes a new computational method to prevent hyperspecialized nodes from obscuring latent gradient solutions based on a Markov chain interpretation of the CA eigenvalue problem. This approach identifies small subsets of hyperspecialized nodes with greater precision than traditional graph clustering techniques, and outperforms existing regularization techniques at identifying a latent gradient on a real-world political fundraising network of candidates for U.S. federal office, which spans three decades and includes nearly 20,000 candidates for federal office and 3 million of their donors.