Abstract
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.
Wang’s research was partially supported by a grant from International Science & Technology Cooperation Program (20163400042410001).
Styner’s work was partially supported by grants R01-HD055741, R01-HD059854 and U54-HD079124.
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.
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Pan, W., Wang, X., Wen, C., Styner, M., Zhu, H. (2017). Conditional Local Distance Correlation for Manifold-Valued Data. In: Niethammer, M., et al. Information Processing in Medical Imaging. IPMI 2017. Lecture Notes in Computer Science(), vol 10265. Springer, Cham. https://doi.org/10.1007/978-3-319-59050-9_4
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