Stochastic development regression on non-linear manifolds
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Stochastic development regression on non-linear manifolds. / Kühnel, Line; Sommer, Stefan Horst.
Information Processing in Medical Imaging: 25th International Conference, IPMI 2017, Boone, NC, USA, June 25-30, 2017, Proceedings. Springer, 2017. s. 53-64 (Lecture notes in computer science, Bind 10265).Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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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
Y2 - 25 June 2017 through 30 June 2017
ER -
ID: 184143799