Intrinsic partial linear models for manifold-valued data

Di Xiong

doi:10.1016/j.ipm.2022.102954

Intrinsic partial linear models for manifold-valued data

2022-07-01

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DOI：10.1016/j.ipm.2022.102954

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Abstract

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This paper aims to propose an intrinsic partial linear modelling (IPLM) framework for characterizing the complex relationship between the response manifold-valued data and a set of explanatory variables such as age, education years, or gender. Such manifold value data are widespread in medical imaging, gesture recognition, computer vision, feature tracking, shape modeling, and others. Compared with most nonparametric and parametric models for manifold-valued data, our IPLM as a semi-parametric model contains both parametric and nonparametric components, leading to better adaptability, interpretation, fitting, and robustness. Furthermore, we propose an iterative estimation strategy to estimate unknown components in IPLM and use simulation experiments to display the performance of the proposed estimation methods. Finally, we apply the proposed IPLM to model the association between the brain subcortical region Corpus Callosum (CC) 2D shape and multiple covariates, such as age, gender, or disease diagnosis, show its wide application in estimating the continuous 2D shape trajectories and comparing the difference in different groups.

Keywords:

Functional data analysis

Partial linear model

Riemannian manifold

Semi-parametric regression

Intrinsic partial linear models for manifold-valued data

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