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.
CITATION STYLE
Pan, W., Wang, X., Wen, C., Styner, M., & Zhu, H. (2017). Conditional local distance correlation for manifold-valued data. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10265 LNCS, pp. 41–52). Springer Verlag. https://doi.org/10.1007/978-3-319-59050-9_4
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