Online algorithms for robust subspace recovery

In this talk, I will mainly discuss a family of GRASTA like online algorithms for robust subspace recovery and its applications in computer vision. GRASTA (Grassmannian Robust Adaptive Subspace Tracking Algorithm), a robust counterpart of GROUSE, was originally proposed to tackle robust subspace tracking from incomplete and corrupted data samples. It uses a natural \ell_1 norm as the robust subspace fit loss function. When dealing with the subspace update, we found that a simple dual reformulation could be a powerful tool for casting the non-smooth norm minimization into the online Grassmannian optimization framework. This observation led us to explore a general GRASTA like algorithm that can incorporate other robust but non-smooth norms that promote more structural information beyond sparsity. On the other hand, for certain computer vision tasks, we show that the nonlinear geometric transformation can also be simultaneously estimated by another GRASTA extension, called t-GRASTA, even though the images are corrupted by occlusions. I will also introduce a multi-level version of adaptive step-size for stochastic gradient descent (SGD) on the Grassmannian, which exhibits nice convergence for our robust subspace recovery problem.
Jun He received his Ph.D in Instrument Science and Engineering from Southeast University in 2009. He received his M.S and B.S both in Computer Science from Nanjing Automation Research Institute and Zhengzhou University respectively. He was a postdoctoral research associate of the Department of Computer Science & Engineering, The Chinese University of Hong Kong, working in ANSR lab and supervised by professor John C.S. Lui. He also was a research fellow of the Institute for Pure and Applied Mathematics (IPAM), UCLA, while he participated the Internet Multi-Resolution Analysis program in 2008 fall. He is a member of IEEE.