Optimisation algorithms on the Stiefel manifold
👉 Link to full write up 👈This project started as an investigation into the efficiency of the Grand Tour algorithm to generate "good" 2D projections of a high dimensional dataset with multiple classifications. A classic example use of the Grand Tour would be an animation of a rotating 3D cube on a 2D screen. Below is an example of a video made by stitching together projections produced by the Grand Tour.
As the object rotates we can start to discern some of the structure of
the object as we look at the sequential frames of the 2D projections.
For the project we used this idea and applied it to abstract high
dimensional datasets, we then applied machine learning models to the
projected 2D dataset. The Grand Tour is not a quick or efficient way to
find the best 2D projection for a dataset so we decided to explore
better ways of doing this.
This is when we started exploring the Grassmannian and Stiefel manifold
spaces, and with this we looked at optimisation alogirthms on these
spaces. This eventually led us to develop a novel genetic algorithm on
the Stiefel manifold.