This is just a gentle reminder about today's seminar "From PDEs to
data science: an adventure with the graph Laplacian" by Martin Stoll
(TU-Chemnitz). Abstract below.
From PDEs to data science: an adventure with the graph Laplacian
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 over the last years
semi-supervised learning strategies could be implemented with these
PDEs at the core. 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 illustrate
the performance on several examples.
—
Francesco Tudisco
Assistant Professor
School of Mathematics
GSSI Gran Sasso Science Institute
Web: https://ftudisco.gitlab.io