Projekt Knowledge Discovery and Data Engineering Wintersemester 2024/25

Simulating “Kommunaler Finanzausgleich”

How much a municipality or city receives in its annual budget through the federal equalization mechanism depends on a huge number of factors, the interaction of which is difficult for out- and insiders to understand. For example, it is not only the municipality’s own tax revenue that is decisive, but also indirectly the population in the other municipalities. The aim of the project is to provide a tool with which the calculations can be carried out automatically and, if possible, presented in a graphically appealing way. In addition to finding and entering raw data, the difficulties of the project are the sometimes changing legal regulations over time. Nevertheless the main scientific focus will be on how sensitive the system is to the parameter of the “Grundsteuer Hebesatz”, which can be set by each local authority.

Note: In terms of content, this project is very much geared towards dual students of the tax office, as a great deal of specialized knowledge will be required. Nevertheless, the topic is of course open to all students.

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: Mohammad Abdulla

To be (distributive) or not to be: Distributivity of Real World Data

In this work, we propose a series of experiments aimed at exploring some structural properties of non-distributive lattices on real-world datasets. Our primary objective is to implement and evaluate methods that measure how far a given lattice deviates from being distributive. These methods will provide a quantitative understanding of non-distributivity . The effectiveness of these techniques will be tested on real datasets from various domains, allowing us to assess their practical applicability.

Inquiries: Mohammad 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

Implementierung von Algorithmen für die Ordnungsdimension

Es gibt diverse Algorithmen zur Berechnung der Ordnungsdimension. In diesem Projekt implementieren Sie diese und evaluieren ihre Qualität im Hinblick auf Laufzeit und Speicherplatzbedarf.

Informationen: Dominik Dürrschnabel

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

Tag Combination and Synthesis in OpenStreetMap

The geographically organised objects in OpenStreetMap are usually tagged with a large number of tags. A side effect of the wiki ethos, however, is that tags are not used consistently and there is a lot of duplication and overlap. Building on previous work analysing tags, we will now look for tags that that have similar meanings or serve the same purpose. A demonstration application is to be developed for the project, which will give suggestions for combining or changing the current tags assigned to an object.
Most (if not all) of the programming will be done in Python.

Inquiries: Tobias Hille

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

Python-Bindings for fcaR

The package fcaR is a software to perform various computations for formal concept analysis in R. Thereby, the algorithms are implemented in C. The goal of this project is to develop python bindings for this C-backend, such that the package can be used in python without relying on R.

Informationen: Dominik Dürrschnabel

Stabilität von Formalen Kontexten

Wir nennen einen formalen Kontext stabil, wenn sich beim Setzen oder Entfernen jedes Kreuzes die Größe des Begriffsverbandes nicht verkleinert. Untersuchen Sie Echtweltdaten auf Stabilität und untersuchen Sie, inwiefern sich die Stabilität als Bewertungsmaß für intrinsisch sinnvolle Daten eignet.

Informationen: Dominik Dürrschnabel

Evaluierung von Graphzeichnungen

Ziel dieser Arbeit ist es, zu evaluieren, welche “weichen” Kriterien für Graphzeichnungen in der Praxis wie stark mit als “schön” wahrgenommenen Zeichnungen korellieren. Außerdem soll untersucht werden, inwieweit die “wichtigen” Kriterien sich beim Zeichnen von Graphen und Ordnungsdiagrammen unterscheiden.

Informationen: Dominik Dürrschnabel

Intrinsic Triangulation of Loss Landscapes of Neural Networks

Recent work investigating geometry and topology of loss landscapes of neural networks revealed interesting properties regarding connectivity of clusters of local minima [1], [2]. In this work you will try to apply advances in computation intrinsic triangulation for 3d rendering [3] towards those surfaces (or reasonable hyperplane projections). One possible motivation for this is the change for an ability to construct geodesic paths on the constructed approximation.
Most (if not all) of the programming will be done in Python.

Inquiries: Tobias Hille