Joint Curve Registration and Classification with Two-level Functional Models

TL;DR

This paper introduces a joint model for simultaneous curve registration and classification, improving accuracy by addressing misalignment issues in functional data using EM algorithms and functional logistic regression.

Contribution

It proposes a novel data registration and classification framework that integrates curve alignment with functional logistic regression, with proven identifiability and asymptotic properties.

Findings

Effective in aligning curves and classifying data in simulations

Demonstrates improved classification accuracy on stroke patient data

Provides theoretical guarantees for model identifiability and estimation consistency

Abstract

Many classification techniques when the data are curves or functions have been recently proposed. However, the presence of misaligned problems in the curves can influence the performance of most of them. In this paper, we propose a model-based approach for simultaneous curve registration and classification. The method is proposed to perform curve classification based on a functional logistic regression model that relies on both scalar variables and functional variables, and to align curves simultaneously via a data registration model. EM-based algorithms are developed to perform maximum likelihood inference of the proposed models. We establish the identifiability results for curve registration model and investigate the asymptotic properties of the proposed estimation procedures. Simulation studies are conducted to demonstrate the finite sample performance of the proposed models. An application of the hyoid bone movement data from stroke patients reveals the effectiveness of the new models.