Exploring Stickiness in CAT(κ) Spaces

The Fréchet mean is a natural generalization of the classical expectation to general metric spaces. In recent years, however, it was observed that the Fréchet mean’s behavior can be quite unusual in some spaces. One of these phenomena is called stickiness. In singular spaces, the sample Fréchet mean can be confined to lower-dimensional subsets for large sample sizes. At the same time, the Fréchet mean of these distributions also seems to be unusually robust. We are going to investigate the phenomenon of stickiness in the general framework of CAT(κ) spaces before discussing applications to Billera-Holmes-Vogtmann spaces of phylogenetic trees.