Learning with the graph Laplacian: from PDEs to data science

• Date: 22. 4. 2021
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: Online via Zoom
• Speaker: Martin Stoll (TU Chemnitz)

In this talk we briefly review some basic PDE models that are used to model phase separation in materials science. They have since become important tools in image processing and semi-supervised learning. The main ingredient is the graph Laplacian that stems from a graph representation of the data. This matrix is large and typically dense. We illustrate some of its crucial features and show how to efficiently work with the graph Laplacian. In particular, we need some of its eigenvectors and for this the Lanczos process needs to be implemented efficiently. Here, we suggest the use of the NFFT method for evaluating the matrix vector products without even fully constructing the matrix. We have recently applied this technique in combination with a multilayer graph or time-series classification.