A robust algorithm for template curve estimation based on manifold embedding

TL;DR

This paper introduces a robust, parameter-free algorithm based on a modified Isomap technique to estimate a representative template function for curve data lying on a low-dimensional manifold, outperforming existing methods.

Contribution

A novel, parameter-free algorithm utilizing a robust isometric embedding approach for template curve estimation on manifolds.

Findings

The algorithm accurately estimates template functions in simulated data.

It outperforms existing methods on real datasets.

The method is robust and easier to use due to its parameter-free nature.

Abstract

This paper considers the problem of finding a meaningful template function that represents the common pattern of a sample of curves. To address this issue, a novel algorithm based on a robust version of the isometric featuring mapping (Isomap) algorithm is developed. Assuming that the functional data lie on an intrinsically low-dimensional smooth manifold with unknown underlying structure, we propose an approximation of the geodesic distance. This approximation is used to compute the corresponding empirical Fr\'echet median function, which provides an intrinsic estimator of the template function. Unlike the Isomap method, the algorithm has the advantage of being parameter free and easier to use. Comparisons with other methods, with both simulated and real datasets, show that the algorithm works well and outperforms these methods.