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A Nonlinear Hierarchical Model for Longitudinal Data on Manifolds

  • Large longitudinal studies provide lots of valuable information, especially in medical applications. A problem which must be taken care of in order to utilize their full potential is that of correlation between intra-subject measurements taken at different times. For data in Euclidean space this can be done with hierarchical models, that is, models that consider intra-subject and between-subject variability in two different stages. Nevertheless, data from medical studies often takes values in nonlinear manifolds. Here, as a first step, geodesic hierarchical models have been developed that generalize the linear ansatz by assuming that time-induced intra-subject variations occur along a generalized straight line in the manifold. However, this is often not the case (e.g., periodic motion or processes with saturation). We propose a hierarchical model for manifold-valued data that extends this to include trends along higher-order curves, namely Bézier splines in the manifold. To this end, we present a principled way of comparing shape trends in terms of a functional-based Riemannian metric. Remarkably, this metric allows efficient, yet simple computations by virtue of a variational time discretization requiring only the solution of regression problems. We validate our model on longitudinal data from the osteoarthritis initiative, including classification of disease progression.

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Author:Martin HanikORCiD, Hans-Christian HegeORCiD, Christoph von TycowiczORCiD
Document Type:In Proceedings
Parent Title (English):2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI)
First Page:1
Last Page:5
Year of first publication:2022
ArXiv Id:http://arxiv.org/abs/2202.01180
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