Bachelor-, Diplom- und Masterarbeiten

Drawing Line Diagrams through Sublattice Anchoring

Structural patterns such as n-dimensional cubes, diamonds (M3​), or pentagons (N5​) frequently occur in lattices of real-world data. Identifying and highlighting these well-known sublattices simplifies the interpretation of complex relational data by anchoring the visualization to familiar geometric forms. This project aims to develop a drawing algorithm that detects a predefined sublattice, pins its nodes to fixed positions, and subsequently arranges the remaining structure around this scaffold to investigate how different anchor choices improve lattice readability.

Inquiries: Marcel Nöhre

A Doubly-Additive Extension of Freese’s Algorithm

Doubly-additive line diagrams define a concept’s position as the sum of vectors from its extent and complement intent, which naturally produces parallelograms, making the lattice easier to read and enabling interactive features such as drag-and-drop editing. However, the core challenge lies in finding a vector assignment that yields a readable drawing rather than a cluttered one. Therefore, this project aims to extend the force-directed approach of Ralph Freese’s lattice drawing algorithm by optimizing base vectors, rather than refining node positions directly.

Inquiries: Marcel Nöhre

The Lattice of Relations between Multiple Squares

In the book Conceptual Exploration by Ganter and Obiedkov (2016), Section 4.2.2 gives the example of exploring the different ways of arranging two squares in two dimensions. Later, in Section 6.1.1, the authors also consider part of the problem for the case of three squares. In this mostly theoretical project or thesis, we want to consider the complete case of three squares and, if possible, compute the lattice for the general four square setting.

Inquiries: Tobias Hille

The Truncated Birkhoff Completion

In the Birkhoff completion, certain concepts, especially in the lower part of the lattice, are generated by new objects derived from implications. However, these objects may introduce inconsistent or unrealistic combinations of attributes. Truncating the lattice by eliminating such inconsistencies ensures a more meaningful and applicable structure, particularly in real-world scenarios. This project aims to study the truncated Birkhoff completion as a method for addressing inconsistencies that arise in lattice structures generated through the Birkhoff completion of non-distributive lattices.

Inquiries: Mo Abdulla

Formalizing Results of Formal Concept Analysis

Formalization of a large number of definitions and theorems in Algebra, Number Theory and Analysis in the lean prover brings the field of formal theorem proving to the forefront of mathematical research. However, mathematical notions and results from the field of Formal Concept Analysis are not yet included. Thus, the goal of this project (or thesis) is to formally prove the “Basic Theorem on Concept Lattices” (or a comparable result), in order to provide a stepping stone in this direction. Essentially, this involves building core definitions and necessary preliminary results by extending existing ones. We will aim to build a lean blueprint and if you are only interested in a small project, we will find a reasonable partial realization to stop at.

Inquiries: Tobias Hille

Temporal Ordinal Motifs in Topic Models

Topic models are, often, dimension reduction techniques for large corpora of textual documents. A central aspect to these models is that they allow for text based explanations of the dimensions in the reduced space. A novel technique, called ordinal motifs, interpret and visualize these dimension hierarchically with respect to (ordinal) substructures of standard shape. With your work, you extent this technique towards ordinal motifs over time, develop visualization techniques, and show their applicability in a practical setting.

Informationen: Johannes Hirth

Ordinal Motifs in Hierarchical Topic Models

Topic models are, often, dimension reduction techniques for large corpora of textual documents. A central aspect to these models is that they allow for text based explanations of the dimensions in the reduced space. A novel technique, called ordinal motifs, interpret and visualize these dimension hierarchically with respect to (ordinal) substructures of standard shape. With your work, you extent this technique towards hierarchical topic models, define hierarchical motif structures, develop visualization techniques, and show their applicability in a practical setting.

Informationen: Johannes Hirth

Network Motifs in Topic Flow Networks

In scientometrics, scientific collaboration is often analyzed by means of co-authorships. An aspect which is often overlooked and more difficult to quantify is the flow of expertise between authors from different research topics, which is an important part of scientific progress. With the Topic Flow Network (TFN) a graph structure for the analysis of research topic flows between scientific authors and their respective research fields was proposed. With your work, you identify and interpret substructures that are integral to this network.

Informationen: Johannes Hirth

Formal Concept Analysis mit Attribut und Objektordnungen

In dieser Arbeit untersuchen Sie, inwiefern sich die Theorie der formalen Begriffsanalyse auf den Fall übertragen lässt, dass wir eine lineare Ordnung auf den Attributen und den Objekten vorliegen haben.

Das Ziel ist es, die in der FCA üblichen Ideen (Begriffe, Implikationen etc.) auf solche Datensätze zu übertragen und die Theorie mit Echtwelt-Datensätzen zu evaluieren.

Informationen: Dominik Dürrschnabel

Invariants of Formal Contexts

It is not easy to recognise whether two (reduced) formal contexts are isomorphic, or given a set of formal contexts, how many different formal contexts are contained there. One aid are invariants, i.e. derived quantities, that do not depend on the concrete representation of the formal context. Simple examples are the number of attributes of the context or the number of objects of the context. If two contexts have different values for an invariant, the contexts are not isomorphic. The aim is to examine formal contexts with regard to possible invariants. Formal contexts can be represented as bipartite graphs, therefore, known graph invariants in particular are to be considered.

Inquiries: Tobias Hille