Computational Modeling of Hierarchically Polarized Groups by Structured Matrix Factorization.

The paper extends earlier work on modeling hierarchically polarized groups on social media. An algorithm is described that 1) detects points of agreement and disagreement between groups, and 2) divides them hierarchically to represent nested patterns of agreement and disagreement given a structural guide. For example, two opposing parties might disagree on core issues. Moreover, within a party, despite agreement on fundamentals, disagreement might occur on further details. We call such scenarios hierarchically polarized groups. An (enhanced) unsupervised Non-negative Matrix Factorization (NMF) algorithm is described for computational modeling of hierarchically polarized groups. It is enhanced with a language model, and with a proof of orthogonality of factorized components. We evaluate it on both synthetic and real-world datasets, demonstrating ability to hierarchically decompose overlapping beliefs. In the case where polarization is flat, we compare it to prior art and show that it outperforms state of the art approaches for polarization detection and stance separation. An ablation study further illustrates the value of individual components, including new enhancements.