Applied Mathematics and Analysis Seminar
As part of the Duke University
Department of Mathematics, the Program in Applied Mathematics
hosts this ongoing series of seminars. The presentations cover a broad range of topics including numerical analysis, ordinary and partial differential equations, nonlinear systems, scientific computing, dynamical systems theory, mathematical biology, pattern formation, and complex physical systems.
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As a convenience, some selected seminars and presentations can be viewed live via the web. Further, we have video archives of past talks, which are also publicly available for you to view at any time.
- Wednesday, April 25, 2018, 12:00pm, Physics 119, Applied Math And Analysis Seminar
Understanding Manifold-structured Data via Geometric Modeling and Learning
Rongjie Lai (Rensselaer Polytechnic Institute)
- Analyzing and inferring the underlying global intrinsic structures of data from its local information are critical in many fields. In practice, coherent structures of data allow us to model data as low dimensional manifolds, represented as point clouds, in a possible high dimensional space. Different from image and signal processing which handle functions on flat domains with well-developed tools for processing and learning, manifold-structured data sets are far more challenging due to their complicated geometry. For example, the same geometric object can take very different coordinate representations due to the variety of embeddings, transformations or representations (imagine the same human body shape can have different poses as its nearly isometric embedding ambiguities). These ambiguities form an infinite dimensional isometric group and make higher-level tasks in manifold-structured data analysis and understanding even more challenging. To overcome these ambiguities, I will first discuss modeling based methods. This approach uses geometric PDEs to adapt the intrinsic manifolds structure of data and extracts various invariant descriptors to characterize and understand data through solutions of differential equations on manifolds. Inspired by recent developments of deep learning, I will also discuss our recent work of a new way of defining convolution on manifolds and demonstrate its potential to conduct geometric deep learning on manifolds. This geometric way of defining convolution provides a natural combination of modeling and learning on manifolds. It enables further applications of comparing, classifying and understanding manifold-structured data by combing with recent advances in deep learning.
All seminars take place on Mondays at 4:30 pm in Room 119 Physics Building unless otherwise noted.
Tea and refreshments are served before the seminars at 4:00 pm in Physics 101.
Past speakers in the Duke Applied Mathematics seminars
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