Stochastic development regression on non-linear manifolds

TY - GEN

T1 - Stochastic development regression on non-linear manifolds

AU - Kühnel, Line

AU - Sommer, Stefan Horst

N1 - Conference code: 25

PY - 2017

Y1 - 2017

N2 - We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes.

AB - We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes.

KW - Frame bundle

KW - Non-linear statistics

KW - Regression

KW - Statistics on manifolds

KW - Stochastic development

UR - http://www.scopus.com/inward/record.url?scp=85020493829&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-59050-9_5

DO - 10.1007/978-3-319-59050-9_5

M3 - Article in proceedings

AN - SCOPUS:85020493829

SN - 978-3-319-59049-3

T3 - Lecture notes in computer science

SP - 53

EP - 64

BT - Information Processing in Medical Imaging

PB - Springer

T2 - 25th International Conference on Information Processing in Medical Imaging

Y2 - 25 June 2017 through 30 June 2017

ER -