Manifold learning aim at computing non-linear dimensionality reduction. It can be used to visualize high dimensional dataset, see Figure 1, extract low-dimensional trend or to remove noise from highly degraded dataset, see Figure 2.

Description

Figure 1: Isomap embedding of digits images. The $32\times 32$ images are naturally distributed according to the number they represent.

 

Figure 2: Blur from wide-field microscope (left) can be expressed in a low-dimensional space composed of elementary blur operators (right).

 
Description of the project


Non-linear embedding such as Isomap, Graph Laplacian or Principal Component Analysis (PCA) are rely on the computation of Euclidean distance between the high-dimensional datapoint.  However, several practical dataset are naturally defined on non-Euclidean domain.
This is the case in cryogenic Electron Microscopy (cryo-EM). The observed images can be defined as point on the manifold of 3-dimensional rotations SO(3).
In this project, we will investigate original approaches to handle dataset that are not defined on non-Euclidean domain.

This project requires strong interest for mathematical analysis.

 

Organisation

Organisation

Any of the above project can be adapted into either a Bachelor or a Master thesis.

You will be supervised by at least two different person. Please reach out with one of the following for a first inquiry:

  • Valentin Debarnot, valentin.debarnot[@]unibas.ch.
  • Ivan Dokmanić, ivan.dokmanic[@]unibas.ch