MVEX01-21-17 Functional PCA vs Convolution Neural Networks

​Convolution Neural Network CNN belongs to the most popular frameworks in the deep learning methodology. Through the operation of convolution on a signal, the CNNs allow for more efficient accounting for local dependence in the data.  On the other hand, the functional principal component analysis uses the methods of functional analysis to model complex relations between functional data. Fitting a functional model and then using eigenfunction to capture the relations aims at complex interaction within high-dimensional data.

The purpose of this project is to compare these two, at the first sight completely unrelated, methods. The comparison will be performed on the simulated data and/or on some empirical control data set. In the functional data analysis, different functional bases will be utilized including the spline bases adopted to the data through the machine learning methodology. The assessment of the two methodologies will be based on their prediction power, interpretability, and mathematical simplicity.

The project is in the area of the so-called artificial intelligence and aims at showing the interplay between machine learning and abstract mathematics.

The project requires probability, matrix calculus, and some fundamentals in scientific programming proficiency since a large part of it assumes computer simulations. The project has many potential directions to be the first stage of a master project. The project's team can benefit from interactions with the team on the project entitled "Orthonormal bases for functional analysis''.
Rapporten skrivs på svenska (men handledning sker på engelska).

Projektkod MVEX01-21-17
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  Sannolikhetsteori och matematisk statistik, kunskap om datorsimuleringar.
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.