Topic models are a popular tool for clustering and analyzing textual data. They allow texts to be classified on the basis of their affiliation to the previously calculated topics. Despite their widespread use in research and application, an in-depth analysis of topic models is still an open research topic. State-of-the-art methods for interpreting topic models are based on simple visualizations, such as similarity matrices, top-term lists or embeddings, which are limited to a maximum of three dimensions. In this paper, we propose an incidence-geometric method for deriving an ordinal structure from flat topic models, such as non-negative matrix factorization. These enable the analysis of the topic model in a higher (order) dimension and the possibility of extracting conceptual relationships between several topics at once. Due to the use of conceptual scaling, our approach does not introduce any artificial topical relationships, such as artifacts of feature compression. Based on our findings, we present a new visualization paradigm for concept hierarchies based on ordinal motifs. These allow for a top-down view on topic spaces. We introduce and demonstrate the applicability of our approach based on a topic model derived from a corpus of scientific papers taken from 32 top machine learning venues.

Lattices and their order diagrams are an essential tool for communicating knowledge and insights about data. This is in particular true when applying Formal Concept Analysis. Such representations, however, are difficult to comprehend by untrained users and in general in cases where lattices are large. We tackle this problem by automatically generating textual explanations for lattices using standard scales. Our method is based on the general notion of ordinal motifs in lattices for the special case of standard scales. We show the computational complexity of identifying a small number of standard scales that cover most of the lattice structure. For these, we provide textual explanation templates, which can be applied to any occurrence of a scale in any data domain. These templates are derived using principles from human-computer interaction and allow for a comprehensive textual explanation of lattices. We demonstrate our approach on the spices planner data set, which is a medium sized formal context comprised of fifty-six meals (objects) and thirty-seven spices (attributes). The resulting 531 formal concepts can be covered by means of about 100 standard scales.

The foundation of any formal analysis of data is the identification of unique and meaningful substructures and properties. The realm of ordinal structures, in particular lattices, is no exemption to that. The field of Formal Conceptual Analysis (FCA), which derives lattices from data tables, called formal contexts, is already very well equipped with tools and notions for identifying and analyzing important substructures. One essential tool of FCA is to provide a user a lattice diagram of meaningful size, which can be interpreted (or even explained). For obvious reasons, this approach defies any applicability to data sets as they are commonly used today, as the resulting lattices are comprised of thousands of elements. In addition, the lattice diagram itself, as the primary means of communication, presents a significant hurdle to interpretation for untrained users. Common approaches tackle the first problem by data set reductions within the data tables [10, 14] or within the resulting lattice structure [1, 2, 9, 15].