Lopata Hall, Room 101
Statistical Machine Learning on Manifolds for Structured Data (Without the Pain)
Hyunwoo J. Kim
Department of Computer Sciences
University of Wisconsin-Madison
Manifold-valued data naturally occur in many disciplines. For example, directional data can be represented as points on the unit sphere. Diffusion tensors in magnetic resonance images form a quotient manifold GL(n)/O(n), which is a space of symmetric positive definite (SPD) matrices. Also, the Hilbert unit sphere can be used for the square-root representation of orientation distribution functions (ODFs) or probability density functions (PDFs). Their data spaces are known, a priori, to have a nice mathematical structure with well-studied properties. It makes sense that if algorithms make use of this additional information, even more efficient inference procedures can be developed. Motivated by this intuition, in this talk we study the relationship between statistical learning algorithms and the geometric structures of data spaces encountered in machine learning, computer vision and neuroimaging using mathematical tools (e.g. Riemannian geometry). As a result, this framework gives new insights into statistical inference methods for image analysis and enables developing new models for manifold-valued data (and potentially manifold-valued parameters) to improve statistical power
Hyunwoo J. Kim is a Ph.D. candidate in the Department of Computer Sciences at University of Wisconsin-Madison (Ph.D. minor: statistics). He earned a B.S. degree and an M.S. in computer science at Korea University and Seoul National University respectively. His research interests include statistical machine learning and manifold statistics for structured data with applications in computer vision and medical imaging. He is actively collaborating with the Wisconsin Alzheimer's Disease Research Center (ADRC) at UW-Madison.