Knowledge graphs have recently become the state-of-the-art tool for representing the diverse and complex knowledge of the world. Examples include the proprietary knowledge graphs of companies such as Google, Facebook, IBM, or Microsoft, but also freely available ones such as YAGO, DBpedia, and Wikidata. A distinguishing feature of Wikidata is that the knowledge is collaboratively edited and curated. While this greatly enhances the scope of Wikidata, it also makes it impossible for a single individual to grasp complex connections between properties or understand the global impact of edits in the graph. We apply Formal Concept Analysis to efficiently identify comprehensible implications that are implicitly present in the data. Although the complex structure of data modelling in Wikidata is not amenable to a direct approach, we overcome this limitation by extracting contextual representations of parts of Wikidata in a systematic fashion. We demonstrate the practical feasibility of our approach through several experiments and show that the results may lead to the discovery of interesting implicational knowledge. Besides providing a method for obtaining large real-world data sets for FCA, we sketch potential applications in offering semantic assistance for editing and curating Wikidata.

The annual number of publications at scientific venues, for example, conferences and journals, is growing quickly. Hence, even for researchers it becomes harder and harder to keep track of research topics and their progress. In this task, researchers can be supported by automated publication analysis. Yet, many such methods result in uninterpretable, purely numerical representations. As an attempt to support human analysts, we present topic space trajectories, a structure that allows for the comprehensible tracking of research topics. We demonstrate how these trajectories can be interpreted based on eight different analysis approaches. To obtain comprehensible results, we employ non-negative matrix factorization as well as suitable visualization techniques. We show the applicability of our approach on a publication corpus spanning 50 years of machine learning research from 32 publication venues. In addition to a thorough introduction of our method, our focus is on an extensive analysis of the results we achieved. Our novel analysis method may be employed for paper classification, for the prediction of future research topics, and for the recommendation of fitting conferences and journals for submitting unpublished work. An advantage in these applications over previous methods lies in the good interpretability of the results obtained through our methods.

In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a consortium, based on closure systems of attribute sets and the well-known attribute exploration algorithm from formal concept analysis. To this end, we introduce (weak) local experts for subdomains of a given knowledge domain. These entities are able to refute and potentially accept a given (implicational) query for some closure system that is a restriction of the whole domain. On this we build up a consortial expert and show first insights about the ability of such an expert to answer queries. Furthermore, we depict techniques on how to cope with falsely accepted implications and on combining counterexamples. Using notions from combinatorial design theory we further expand those insights as far as providing first results on the decidability problem if a given consortium is able to explore some target domain. Applications in conceptual knowledge acquisition as well as in collaborative interactive ontology learning are at hand.

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For localization and mapping of indoor environments through WiFi signals, locations are often represented as likelihoods of the received signal strength indicator. In this work we compare various measures of distance between such likelihoods in combination with different methods for estimation and representation. In particular, we show that among the considered distance measures the Earth Mover's Distance seems the most beneficial for the localization task. Combined with kernel density estimation we were able to retain the topological structure of rooms in a real-world office scenario.