Discrete Signature Varieties

This page contains auxiliary files and supplementary code to the following paper:
Carlo Bellingeri, Raul Penaguiao: Discrete Signature Varieties
ARXIV: https://arxiv.org/abs/2303.13377 CODE: https://github.com/raulpenaguiao/discrete_signature_varieties_macaulay2

ABSTRACT: Discrete signatures are invariants computed from time series corresponding to the discretised version of the signature of paths. We study the algebraic varieties arising from their images, the discrete signature varieties. We introduce them and compute their dimension in many cases. From a particular subclass of these varieties, we derive a partial solution to the Chen-Chow theorem for complex-valued time series.

Section 3

Project page created: 16/04/2025

Project contributors: Carlo Bellingeri, Raul Penaguiao

Corresponding author of this page: Raul Penaguiao, raul.penaguiao@proton.me

Software used: Macaulay2 (Version 1.13)

System setup used: MacBook Pro with macOS Monterey 12.0.1, Processor 2.7 GHz Intel Core i7, Memory 16 GB 2133 MHz LPDDR3