Figure 2

Hierarchical topic models and decisions as distributions over topics. (A) Using a network-based topic modeling approach that uses hierarchical stochastic block models [29], we infer hierarchical partitions in the bipartite network of judicial decisions and words. We show word topics in the housing decisions corpus. The hierarchical structure of the model is illustrated by expanding a particular topic: from left to right, we take a topic at the highest level of the hierarchy (level 3) and expand specific sub-topics at successively lower levels. (At level 3, only the top words in each subtopic are shown.) Topics contain words that are used in similar contexts, and this similarity increases as we go down in the hierarchy. (B) Given the membership of each word in a given topic, decisions can be characterized as distributions over topics by measuring the number of times each word appears in a document (Section 2). For example, topic 131 accounts for 11% of the words in Decision A, and for 17% of the words in Decision B. We follow the same procedure for the bipartite network of documents and legislation (Fig. 1 and Fig. S12 in Additional file 1). Likewise, we infer the word topics and the legislation topics for the other two corpora: homicides and condominium. Tables S1-S4 in Additional file 1 in provide the number of topics at each hierarchical level for each topic model