Baba C. Vemuri
Wilson and Marie Collins Professor in Engineering
Department of Computer & Information Science and Engineering
University of Florida
Seminar: ManifoldNet: A Deep Neural Network for Manifold-valued Data with Applications
Abstract: Developing deep neural networks (DNNs) for manifold-valued data sets has gained significant interest of late in the deep learning research community. Manifold-valued data abound in the medical imaging and computer vision domains e.g., diffusion tensor images (DTI), shapes (landmarks), covariance matrices, and others. Vemuri will present a novel theoretical framework for DNNs tailored for manifold-valued data inputs, dubbed ManifoldNet. Analogous to vector spaces where convolutions are equivalent to computing weighted means, manifold valued data convolutions will be defined using the weighted Fr´echet Mean (wFM). To this end, a provably convergent recursive algorithm for computation of the wFM of the given data is presented, where the weights are to be learned. Further, the proposed wFM operator is provably equivariant to the natural group actions admitted by the data manifold and achieves a contraction mapping. A novel network architecture to realize the ManifoldNet will be detailed during the talk. Experiments showcasing the performance of the ManifoldNet on regression and classification problems in neuroimaging will be presented. Finally, if time permits, a generalization of the ManifoldNet to accommodate higher order manifold-valued convolutions with applications will be briefly discussed. This research was in part funded by the NSF grant IIS-1724174.
About the Speaker:Baba Vemuri received his PhD in Electrical and Computer Engineering from the University of Texas at Austin in 1987. He then joined the Department of Computer and Information Sciences at the University of Florida, Gainesville, where he currently holds the Wilson and Marie Collins Professorship in Engineering. His research interests include Geometric Deep Learning, Geometric Statistics, Medical Image Computing, Computer Vision, Machine Learning and Information Geometry. He has published over 200 refereed journal and conference articles in the aforementioned areas and received several best paper awards. He has served as a program chair and area chair of several IEEE sponsored conferences. He was an associate editor for several area journals and is currently an associate editor for the Journal of Medical Image Analysis (MedIA) and the International Journal of Computer Vision (IJCV). Professor Vemuri is a recipient of the IEEE Computer Society’s Technical Achievement Award and is a Fellow of the IEEE and ACM.
Tom Fletcher, associate professor of electrical and computer engineering and computer science
Miaomiao Zhang, assistant professor of electrical and computer engineering and computer science