Overview
This project is part of my master thesis, realized with Dr. Nicolas Berkouk. In applied topology, there is a powerful data analysis tool called persistent homology. We consider a generalization of this tool called multi-parameter persistent homology and implement an associated metric that allows for better understanding complex data such as high-dimensional point-clound data. We provide a rich visualization of the method by investigating the case of digit image classification.
Approach
We implement the core neural network algorithms with TensorFlow. The clustering part ouputs a distance matrix, which we visualize with a UMAP embedding (Uniform Manifold Approximation and Projection for Dimension Reduction). We make use of PyVis and Plotly for everything related to visualisation purposes.