There is growing empirical evidence that spherical k-means clustering performs well in identification of groups of concomitant extremes in high dimensions, thereby leading to sparse models.

We provide first theoretical results supporting this approach, but also identify some pitfalls. Furthermore, we show that an alternative cost function may be more appropriate for identification of concomitant extremes, and it results in a novel spherical k-principal components clustering algorithm. Our main result establishes a broadly satisfied sufficient condition guaranteeing the success of this method.

Finally, we 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.