Disentangling Overlapping Beliefs by Structured Matrix Factorization

Much work on social media opinion polarization focuses on identifying separate or orthogonal beliefs from media traces, thereby missing points of agreement among different communities. This paper develops a new class of Non-negative Matrix Factorization (NMF) algorithms that allow identification of both agreement and disagreement points when beliefs of different communities partially overlap. Specifically, we propose a novel Belief Structured Matrix Factorization algorithm (BSMF) to identify partially overlapping beliefs in polarized public social media. BSMF is totally unsupervised and considers three types of information: (i) who posted which opinion, (ii) keyword-level message similarity, and (iii) empirically observed social dependency graphs (e.g., retweet graphs), to improve belief separation. In the space of unsupervised belief separation algorithms, the emphasis was mostly given to the problem of identifying disjoint (e.g., conflicting) beliefs. The case when individuals with different beliefs agree on some subset of points was less explored. We observe that social beliefs overlap even in polarized scenarios. Our proposed unsupervised algorithm captures both the latent belief intersections and dissimilarities. We discuss the properties of the algorithm and conduct extensive experiments on both synthetic data and real-world datasets. The results show that our model outperforms all compared baselines by a great margin.