TY - GEN
T1 - Conditional local distance correlation for manifold-valued data
AU - Pan, Wenliang
AU - Wang, Xueqin
AU - Wen, Canhong
AU - Styner, Martin
AU - Zhu, Hongtu
N1 - Funding Information:
Zhu’s work was partially supported by the US National Institutes of Health (grants MH086633, EB021391-01A1), the National Science Foundation (grants SES-1357666 and DMS-1407655), and a senior investigator grant from the Cancer Prevention Research Institute of Texas.
Funding Information:
Wang’s research was partially supported by a grant from International Science & Technology Cooperation Program (20163400042410001).
Publisher Copyright:
© Springer International Publishing AG 2017.
PY - 2017
Y1 - 2017
N2 - Manifold-valued data arises frequently in medical imaging, surface modeling, computational biology, and computer vision, among many others. The aim of this paper is to introduce a conditional local distance correlation measure for characterizing a nonlinear association between manifold-valued data, denoted by X, and a set of variables (e.g., diagnosis), denoted by Y , conditional on the other set of variables (e.g., gender and age), denoted by Z. Our nonlinear association measure is solely based on the distance of the space that X, Y , and Z are resided, avoiding both specifying any parametric distribution and link function and projecting data to local tangent planes. It can be easily extended to the case when both X and Y are manifold-valued data. We develop a computationally fast estimation procedure to calculate such nonlinear association measure. Moreover, we use a bootstrap method to determine its asymptotic distribution and p-value in order to test a key hypothesis of conditional independence. Simulation studies and a real data analysis are used to evaluate the finite sample properties of our methods.
AB - Manifold-valued data arises frequently in medical imaging, surface modeling, computational biology, and computer vision, among many others. The aim of this paper is to introduce a conditional local distance correlation measure for characterizing a nonlinear association between manifold-valued data, denoted by X, and a set of variables (e.g., diagnosis), denoted by Y , conditional on the other set of variables (e.g., gender and age), denoted by Z. Our nonlinear association measure is solely based on the distance of the space that X, Y , and Z are resided, avoiding both specifying any parametric distribution and link function and projecting data to local tangent planes. It can be easily extended to the case when both X and Y are manifold-valued data. We develop a computationally fast estimation procedure to calculate such nonlinear association measure. Moreover, we use a bootstrap method to determine its asymptotic distribution and p-value in order to test a key hypothesis of conditional independence. Simulation studies and a real data analysis are used to evaluate the finite sample properties of our methods.
KW - Local distance correlation
KW - Manifold-valued
KW - Shape statistics
UR - http://www.scopus.com/inward/record.url?scp=85020493550&partnerID=8YFLogxK
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U2 - 10.1007/978-3-319-59050-9_4
DO - 10.1007/978-3-319-59050-9_4
M3 - Conference contribution
C2 - 28943730
AN - SCOPUS:85020493550
SN - 9783319590493
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 41
EP - 52
BT - Information Processing in Medical Imaging - 25th International Conference, IPMI 2017, Proceedings
A2 - Zhu, Hongtu
A2 - Niethammer, Marc
A2 - Styner, Martin
A2 - Zhu, Hongtu
A2 - Shen, Dinggang
A2 - Yap, Pew-Thian
A2 - Aylward, Stephen
A2 - Oguz, Ipek
PB - Springer Verlag
T2 - 25th International Conference on Information Processing in Medical Imaging, IPMI 2017
Y2 - 25 June 2017 through 30 June 2017
ER -