There is a growing empirical evidence that the spherical $k$-means clustering performs remarkably well in identification of groups of concomitant extremes in high dimensions, thereby leading to sparse models.
In our talk, we will provide first theoretical results supporting this approach, but also identify some pitfalls. Furthermore, we will develop a novel spherical $k$-principal-components clustering algorithm which is more appropriate for identification of concomitant extremes. Our main result establishes a broadly satisfied sufficient condition guaranteeing the success of this method. Finally, we will illustrate in simulations that $k$-principal-components outperforms $k$-means in the difficult case of weak asymptotic dependence within the groups.
The talk is based on joint work with Jevgenijs Ivanovs.