7 papers
Universal Varieties for Signatures of Membranes
Carlos Améndola, Gabriel Riffo, Leonard Schmitz
Membranes are sufficiently smooth vector-valued functions defined on the unit square, widely used in applications such as interpolation of image data. The signature of a membrane i…
SignatureTensors.jl: A Package for Signature Tensors in Julia
Gabriel Riffo, Leonard Schmitz
We introduce SignatureTensors.jl, a new package for computing signature tensors of paths in julia. We present its core functionality and demonstrate its use through illustrative ex…
Signature Varieties of Splines
Carlos Améndola, Felix Lotter, Leonard Schmitz
Splines are central objects for the interpolation of discrete data via piecewise smooth paths. Their iterated-integral signature is an infinite collection of tensors which characte…
An Efficient Algorithm for Path Recovery from Signature Tensors
Leonard Schmitz
We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this re…
Learning Barycenters from Signature Matrices
Carlos Améndola, Leonard Schmitz
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 Ka…
Signature matrices of membranes
Felix Lotter, Leonard Schmitz
The signature of a membrane is a sequence of tensors whose entries are iterated integrals. We study algebraic properties of membrane signatures, with a focus on signature matrices…
Free generators and Hoffman's isomorphism for the two-parameter shuffle algebra
Leonard Schmitz, Nikolas Tapia
Signature transforms have recently been extended to data indexed by two and more parameters. With free Lyndon generators, ideas from -algebras and a novel two-pa…