Leonard Schmitz

Abstract

The expected signature of a family of paths need not be a signature of a path itself. Motivated by this, we consider the notion of a Lie group barycenter introduced by Buser and Karcher to propose a barycenter on path signatures. We show that every element of the free nilpotent Lie group is a barycenter of a group sample, where all but one sample element can be fixed arbitrarily. In the case of piecewise linear paths, we study the problem of recovering an underlying path corresponding to the barycenter of signatures. We determine the minimal number of segments required to learn from signature matrices, providing explicit transformations to the associated congruence normal forms.
 

Our speaker

Leonard Schmitz is a member of the Algebraische und Geometrische Methoden in der Datenanalyse group led by Carlos Amendola at TU Berlin. Prior to this, he was part of Bernd Sturmfels’ Nonlinear Algebra group at the Max Planck Institute for Mathematics in the Sciences in Leipzig. He completed his PhD at the University of Greifswald under the supervision of Joscha Diehl.
 

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