Estimation via length-constrained generalized empirical principal curves under small noise

TL;DR

This paper introduces a method for constructing length-constrained generalized empirical principal curves that converge to a target curve in Hausdorff distance, improving curve estimation under small noise conditions.

Contribution

The paper presents a novel approach to estimate principal curves with length constraints, ensuring convergence in Hausdorff distance under small noise.

Findings

Convergence of estimated curves to the true curve in Hausdorff distance.

Effective estimation method under small noise conditions.

Theoretical guarantees for the proposed principal curve estimation.

Abstract

In this paper, we propose a method to build a sequence of generalized empirical principal curves, with selected length, so that, in Hausdor distance, the images of the estimating principal curves converge in probability to the image of g.