Feature Sensitive Curve Registration by Kernel Matching

TL;DR

This paper introduces a kernel-matched registration method for aligning functional data with sharp features, outperforming existing methods by effectively matching landmarks without manual intervention.

Contribution

The paper presents a novel kernel-based registration technique that handles sharp features and landmarks automatically, with proven consistency and superior performance.

Findings

Outperforms existing registration methods in simulations

Successfully matches sharp landmarks without manual identification

Proven to be consistent under general conditions

Abstract

In this paper, we argue that the problem of registering two sets of functional data, where the underlying mean function has sharp features, is not properly addressed by methods designed to align a bunch of growth curves data. We provide a new method, which is able to pool local information without smoothing and to match sharp landmarks without manual identification. This method, which we refer to as kernel-matched registration, is based on maximizing a kernel-based measure of alignment. We prove that the proposed method is consistent under fairly general conditions. Simulation results show superiority of the performance of the proposed method over two existing methods. The proposed method is illustrated through the analysis of three sets of paleoclimatic data.