Speaker
Vahid Shahverdi, Umeå University
Abstract
The Euclidean distance degree (EDD) of an algebraic variety is an invariant which counts the number of complex critical points of the squared distance function from a generic data point. This number also bounds the number of real critical points of the closest point problem, although this bound is not necessarily sharp.
To remedy this, the notion of average EDD is introduced to count the average number of such real critical points when the data point is sampled from a fixed distribution. Using this notion, we prove that when the data distribution is Gaussian and the variance is large, this average count converges to another invariant known as total absolute curvature. We briefly explain this connection and provide several examples.
This is ongoing work with Andrea Rosana.