MVEX01-21-18 Orthonormal bases for functional data analysis

​The functional data are the observations that by its nature or by convenience are considered to be samples of functions in a continuous argument. Examples are measurements of drug concentration of a patient, two-dimensional images, or movies. The analysis of such data in the functional data analysis starts with the decomposition of observations using some functional bases. In particular, the orthogonal bases are convenient due to their optimality in the function representation. However, there are many possible choices such as Fourier bases, various polynomial bases, wavelets, splines, etc.

In the project different orthogonal bases are examined on their efficiency in the data representation. In particular, the data-driven bases developed by machine learning methods will be compared with the classical analytical bases. The students will have a task to process the functional data and investigate the efficiency through the norm minimization. The understanding of general concepts of linear algebra, as well as an ability to use numerical methods in implementing abstract mathematical concepts, is a general prerequisite. The project has some overlap with the project entitled "Functional PCA vs. Convolution Neural Networks'' so some collaboration between the teams is possible and even encouraged. 
Rapporten skrivs på svenska (men handledning sker på engelska).

Projektkod MVEX01-21-18
Gruppstorlek 3-6 studenter
Målgrupp GU- och Chalmersstudenter. För GU-studenter räknas projektet som ett projekt i Tillämpad matematik (MMG900/MMG920) eller Matematisk statistik (MSG900/MSG910). 
Projektspecifika förkunskapskrav Matematisk statistik. Viss programmeringsvana, i Python, Matlab, R, eller liknande, är nödvändigt.
Se respektive kursplan för allmänna förkunskapskrav. Utöver de allmänna förkunskapskraven i MVEX01 ska Chalmersstudenter ha avklarat kurser i en- och flervariabelanalys, linjär algebra och matematisk statistik.
Handledare Krzysztof Podgorski, krys.podgorski@gmail.com
Examinator Maria Roginskaya, Ulla Dinger
Institution Matematiska vetenskaper

Publicerad: ti 03 nov 2020.