Lecture notes on high-dimensional data
It provides educational material for students learning mathematical data science, but is incremental as it compiles existing knowledge into lecture notes.
The paper presents lecture notes covering mathematical foundations for high-dimensional data analysis, including concentration of measure and random projections, based on a course taught to BSc students.
These are lecture notes based on the first part of a course on 'Mathematical Data Science', which I taught to final year BSc students in the UK in 2019-2020. Topics include: concentration of measure in high dimensions; Gaussian random vectors in high dimensions; random projections; separation/disentangling of Gaussian data. A revised version has been published as part of the textbook [Mathematical Introduction to Data Science, Springer, Berlin, Heidelberg, 2024, https://link.springer.com/book/10.1007/978-3-662-69426-8].