Geometry-based manifold learning with a focus on biological shape data

Description

Manifold learning is a machine learning paradigm that is used for, amongst others, the analysis of data. Recently, manifold learning techniques emerged that use the geometrical properties of the space in which the data lies. Moreover, some techniques use the geometry of the object itself such as the shape of biological cells, which might contain interesting information about the cell.

In this light, I will first discuss the importance of manifold learning for the SEARCH project (https://sites.google.com/view/search-utwente/home). The goal of the SEARCH project is to gain more understanding of protoplast plant cells such as understanding their development over time, how their development can be influenced by applying stress, etc.

Subsequently, I briefly discuss an issue with current manifold learning approaches. In short, the issue is that due to a limited amount of training data, the learned manifold might not represent objects that are physically plausible interpolations between two objects in the learned manifold. To remedy this, manifold learning approaches should better take into account this prior knowledge on physically plausible intermediate values.

Finally, for the core of the presentation, I provide an in-depth treatment of the paper ‘RSA-INR: Riemannian Shape Autoencoding via 4D Implicit Neural Representations’, which deals with the earlier mentioned issue when the data consists of shapes of biological objects. This paper develops a manifold learning approach that:
- Connects to the literature that considers the geometry of biological objects by treating their geometry / shape.
- Resolves the issue by utilizing the Riemannian geometry properties of the biological shape space.

Period	9 Nov 2023
Event title	AIM PhD networking event 2023
Event type	Other
Organiser	AI & Mathematics (AIM)
Location	Utrecht, NetherlandsShow on map