Michiel Hochstenbach (TU Eindhoven): Some recent trends in the Mathematics of Data Science

We will review some recent developments in some intriguing problems and methods, with lots of applications in Math and Data Science:

• How to select the most relevant features and data points from a data matrix? We will review various matrix decompositions, ranging from SVD/PCA to the CUR decomposition, where approximations are in terms of data points.

• How can we effectively reduce the dimension when our data points are labeled? We will review linear discriminant analysis and the trace ratio method.

• Gradient methods for high-dimensional nonlinear optimization. In many problems we have to minimize a difficult loss function. How can we choose the stepsize in gradient methods effectively?

This is joint work with PhD students Giulia Ferrandi and Perfect Gidisu.