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Preprint
Iceberg query lattices for datalog
(2004)
In this paper we study two orthogonal extensions of the classical data
mining problem of mining association rules, and show how they naturally interact. The first is the extension from a propositional representation to datalog, and the second is the condensed representation of frequent itemsets by means of Formal Concept Analysis (FCA). We combine the notion of frequent datalog queries with iceberg concept lattices (also called closed itemsets) of FCA and introduce two kinds of iceberg query lattices as condensed ...
Preprint
A finite state model for on-line analytical processing in triadic contexts
(2005)
About ten years ago, triadic contexts were presented by Lehmann and Wille as an extension of Formal Concept Analysis. However, they have rarely been used up to now, which may be due to the rather complex structure of the resulting diagrams. In this paper, we go one step back and discuss how traditional line diagrams of standard (dyadic) concept lattices can be used for exploring and navigating triadic data. Our approach is inspired by the slice & dice paradigm of On-Line-Analytical Processing (OLAP). We recall the ...
Preprint
Off to new shores
(2003)
In the last years, the main orientation of Formal Concept Analysis (FCA) has turned from mathematics towards computer science. This article provides a review of this new orientation and analyzes why and how FCA and computer science attracted each other. It discusses FCA as a knowledge representation formalism using five knowledge representation principles provided by Davis, Shrobe, and Szolovits [DSS93]. It then studies how and why mathematics-based researchers got attracted by computer science. We will argue for ...
Dissertation
Investigation and Elimination of Substructures in Formal Concept Analysis focusing on Boolean Suborders and Subcontexts
(2023)
In the field of Formal Concept Analysis, data is mainly presented in so-called formal contexts, which assign to a set of objects their respective attributes. From those concept lattices can be generated, where the objects are grouped with respect to their common attributes to represent the relationships in the data in a way that enhances the understandability for humans. However, since a concept lattice can be of exponential size compared to its associated formal context, the presented relationships often become hard ...
Dissertation
Trajectory Mapping in Physical and Topical Spaces
(2023)
In this dissertation, two different types of trajectories are investigated. In the engfirst part of this work, we investigate methods for the analysis of physical trajectories. We focus on scenarios, in which signal strengths ofWiFi access points are recorded. In detail, they are recorded through smartphone devices by people moving through a building. By means of theWiFi signal strengths, (physical) trajectories of humans are reconstructed, which reflect the locations visited over time. Accurate localization based ...
Dissertation
Orometry, Intrinsic Dimensionality and Learning: Novel Insights into Network Data
(2023-11)
Today, networks are an integral part of our world. Let it be real-life friendship networks or social connections that are based on social media. In this thesis, we contribute to the understanding of networks by studying networks from three different perspectives. First, we adapt notions and concepts from orometry to metric data and networks to gain novel insights from a local perspective. Specifically, we study measures of local outstandingness and propose concepts to derive small hierarchies from larger networks. ...