Simple Approximate Varieties for Sets of Empirical Points
arXiv:1008.02742 citationsh-index: 9
Originality Synthesis-oriented
AI Analysis
For researchers in data analysis and geometric modeling, this provides a way to fit algebraic varieties to noisy data with guaranteed error bounds.
The paper presents a symbolic-numeric method that, given a noisy point set and a tolerance, automatically finds a low-degree polynomial whose variety approximates all points within that tolerance.
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 $\varepsilon$.