LectureParallel Transport Convolutional Neural Networks on Manifolds
Convolution has played a prominent role in various applications in science and engineering for many years. It is also the most important operation in convolutional neural networks (CNNs). There has been a recent growth of interests of research in generalizing CNNs on 3D objects, often represented as compact manifolds. However, existing approaches cannot preserve all the desirable properties of Euclidean convolutions, namely compactly supported filters, directionality, transferability across different manifolds. In this talk, I will discuss our recent work on a new way of defining convolution on manifolds via parallel transport. This geometric way of defining parallel transport convolution (PTC) provides a natural combination of modeling and learning on manifolds. PTC allows for the construction of compactly supported filters and is also robust to manifold deformations. I will demonstrate its applications to shape analysis using deep neural networks based on parallel transportation convolutional networks (PTC-net).
Dr. Rongjie Lai received his Ph.D. degree in applied mathematics from the University of California, Los Angeles, He is currently an assistant professor at the Rensselaer polytechnic Institute. Dr. Lais research interests are mainly in modern scientific computing including developing mathematical and computational tools for analyzing and processing signals, images as well as unorganized data using methods of variational partial differential equations, computational differential geometry and learning. In 2018, Dr. Lai was granted an NSF CAREER award for his research in geometry and learning for manifold-structured data in 3D and higher dimension.