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Much work on social media opinion polarization focuses on a flat categorization of stances (or orthogonal beliefs) of different communities from media traces. We extend in this work in two important respects. First, we detect not only points of disagreement between communities, but also points of agreement. In other words, we estimate community beliefs in the presence of overlap. Second, in lieu of flat categorization, we consider hierarchical belief estimation, where communities might be hierarchically divided. For example, two opposing parties might disagree on core issues, but within a party, despite agreement on fundamentals, disagreement might occur on further details. We call the resulting combined problem a hierarchical overlapping belief estimation problem. To solve it, this paper develops a new class of unsupervised Non-negative Matrix Factorization (NMF) algorithms, we call Belief Structured Matrix Factorization (BSMF). Our proposed unsupervised algorithm captures both the latent belief intersections and dissimilarities, as well as a hierarchical structure. We discuss the properties of the algorithm and evaluate it on both synthetic and real-world datasets. In the synthetic dataset, our model reduces error by 40%. In real Twitter traces, it improves accuracy by around 10%. The model also achieves 96.08% self-consistency in a sanity check.