6 ECTS credits
180 h study time
Offer 1 with catalog number 1022970ANR for all students in the 2nd semester at a (A) Bachelor - preliminary level.
The first objective of this course is to treat mathematical foundations of data science. These mathematical foundations are spread over different subdisciplines of mathematics. Mathematical optimization is not possible without analysis of multivariate real functions, the determination of a best rank k approximation of a set of data points in the Euclidean space is a problem in linear algebra, and modelling the internet as a (directed) graph is necessary to develop any PageRank algorithm. Hence the courses Analysis, Linear Algebra and Discrete Mathematics are a very suitable base for students to set their first steps into the mathematics for data science. The second objective of this course is to use and develop the mathematical knowledge of the courses in the first term in the context of this course. Although this course is a mathematical course, the content will be rigorous from foundation to application. Hence for a topic like spectral clustering of data, the treatment will start with the mathematical foundations and end with an implementation in python
Contents
1. Spectral graph theory (part 1): matrices associated to graphs, the spectrum of a graph, spectral properties of undirected graphs.
2. Linear Algebra (part 1): Perron-Frobenius theorem, Raleigh coefficients. Applications in spectral graph theory: equitable partitions, interlacing.
3. Spectral graph theory (part 2): spectra of graphs, cliques and co-cliques and the Delsarte-Hoffmanbound. Applications: the sensitivity conjecture, the chromatic number of a graph, the Shannon capacity of a graph.
4. Data clustering: k means algorithm, spectral clustering, mincut problem in graphs.
5. Linear Algebra (part 2): singular value decomposition. Applications: low rank approximations, principal component analysis, the power method, the Hypertext Induced Topics Search algorithm, google PageRank.
6. Mathematical optimization: linear programming and discrete optimization.
None
The final grade is composed based on the following categories:
Oral Exam determines 60% of the final mark.
Other Exam determines 40% of the final mark.
Within the Oral Exam category, the following assignments need to be completed:
Within the Other Exam category, the following assignments need to be completed:
Additional information regarding evaluation (Engels): Theory Exam (oral with the opportunity for written preparation) 60% + permanent evaluation using project work 40%
This offer is part of the following study plans:
Bachelor of Computer Science: Default track (only offered in Dutch)
Bachelor of Mathematics and Data Science: Standaard traject (only offered in Dutch)