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Conditional Local Distance Correlation for Manifold-Valued Data

  • Wenliang Pan
  • Xueqin Wang
  • Canhong Wen
  • Martin Styner
  • Hongtu ZhuEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10265)

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.

Keywords

Manifold-valued Local distance correlation Shape statistics 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Wenliang Pan
    • 1
    • 2
  • Xueqin Wang
    • 1
    • 2
  • Canhong Wen
    • 1
    • 2
  • Martin Styner
    • 3
  • Hongtu Zhu
    • 4
    Email author
  1. 1.Department of Statistical ScienceSun Yat-sen UniversityGuangzhouChina
  2. 2.Southern China Research Center of Statistical ScienceSun Yat-sen UniversityGuangzhouChina
  3. 3.University of North Carolina at Chapel HillChapel HillUSA
  4. 4.University of Texas MD Anderson Cancer CenterHoustonUSA

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