Simple Approximate Varieties for Sets of Empirical Points

TL;DR

This paper introduces a symbolic-numeric method to find low-degree polynomials that approximate a set of noisy data points within a specified tolerance, aiding in data analysis and modeling.

Contribution

It presents a novel approach combining symbolic and numeric techniques to identify approximate algebraic varieties fitting noisy data sets.

Findings

Successfully computes low-degree polynomials close to data points within tolerance

Automates the process of identifying approximate algebraic structures in noisy data

Enhances data analysis by providing symbolic-numeric tools for polynomial approximation

Abstract

We present a symbolic-numeric approach for the analysis of a given set of noisy data, represented as a finite set $\X$ of limited precision points. Starting from $\X$ and a permitted tolerance $\varepsilon$ on its coordinates, our method automatically determines a low degree monic polynomial whose associated variety passes close to each point of $\X$ by less than the given tolerance $\varepsilon$.