|Abstract: ||In medical imaging analysis and computer vision, there is a growing interest in analyzing various manifold-valued data including 3D rotations, planar shapes, oriented or directed directions, the Grassmann manifold, deformation field, symmetric positive definite (SPD) matrices and medial shape representations (m-rep) of subcortical structures. Particularly, the scientific interests of most population studies focus on establishing the associations between a set of covariates (e.g., diagnostic status, age, and gender) and manifold-valued data for characterizing brain structure and shape differences, thus requiring a statistical modeling framework for manifold-valued data. The aim of this talk is to introduce a series of statistical models for the analysis of manifold-valued data as responses in a Riemannian manifold and their associations with a set of covariates, such as age and gender, in Euclidean space. Because manifold-valued data do not form a vector space, directly applying classical multivariate regression may be inadequate in establishing the relationship between manifold-valued data and covariates of interest, such as age and gender, in real applications. We apply our methods to the detection of the difference in the morphological changes of the left and right hippocampi between schizophrenia patients and healthy controls using medial shape description.
Dr. Hongtu Zhu is a professor in the Department of Biostatistics at the University of Texas M.D. Anderson Cancer Center. He has a broad background in statistics, biostatistics, medical imaging, genetics and computational neuroscience, with specific training and expertise in neuroimaging data analysis and big data integration as well as secondary data analysis on neurodegenerative and neuropsychiatric diseases. His methodological research has been focused on the development of various models for the analysis of imaging, genetic, biochemical, behavioral, and clinical data and their integration. Such development requires novel methods that explicitly exploit special features, particularly the correlation, smoothness, and low-dimensional structure, of the data space and the model space.