Bachelor-, Diplom- und Masterarbeiten

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

Detecting Graphs in Images

The project aims to develop a machine learning model that can detect (simple) graphs in images. This involves not only an extensive literature review but also gathering useful training data. Moreover we need to train the model to recognize and segment images containing graphs. The project will use image classification algorithms and techniques to achieve this goal. Completing individual parts may already be enough for a successful conclusion. You will build upon work done by previous participants.
Most (if not all) of the programming will be done in Python.

Inquiries: Tobias Hille

Generators for and Properties of random bipartite Graphs

In this project, we will conduct a practical investigation into the random generation of bipartite graphs. We will build upon previous works in the field and analyze the properties of the produced distributions. Additionally, we will simulate real-world data, potentially using approaches like GAN training.
Most (if not all) of the programming will be done in Python.

Inquiries: Tobias Hille

Implications in Conceptual Scaling

One way of computing dependencies in data set are implications. To extract implications from data sets, we first have to interpret the data on the ordinal level via a method called conceptual scaling. The implication that we find in the scaled data set can have two origins. The first are dependencies in the many-valued data set and the second are artifacts from the scaling process. With your work you develop a method to analyze these sets of implications separately.

Informationen: Johannes Hirth

Decomposition of Concept Lattices

Conceptual structures are great hierarchical tools to analyze complex relations between data point. Recent approaches focus on identifying ordinal sub-structures of concept lattices that have specific shape, e.g., chains, cubes, cycles etc. The sub-structures are then used to derive highler level relations between data point or to explain the hierarchical structure. With your work, you study how this approach can be used to decompose concept lattices into sub-structures.

Informationen: Johannes Hirth