Subspace Estimation and Tracking when Data are Missing and Corrupted

Low-dimensional linear subspace approximations to high-dimensional data are powerful enough to capture a great deal of structure in many signals, and yet they also offer simplicity and ease of analysis. Because of this they have provided a powerful tool to many areas of engineering and science: problems of estimation, detection and prediction, with applications such as network monitoring, collaborative filtering, object tracking in computer vision, and environmental sensing. Corrupt and missing data are the norm in many massive datasets, not only because of errors and failures in data collection, but because it may be impossible to collect and process all the desired measurements.

In this talk, I will describe my recent results on estimating subspace projections from incomplete data and a fundamental theorem that provides a powerful tool for developing algorithms for subspace estimation and tracking with incomplete data. I will focus on the algorithm GROUSE (Grassmannian Rank-One Update Subspace Estimation), a subspace tracking algorithm that performs gradient descent on the Grassmannian (the manifold of all fixed-dimensional subspaces); I will describe its guarantees and its application to the matrix completion problem. I will also discuss the robust version, GRASTA (Grassmannian Robust Adaptive Subspace Tracking Algorithm), which is based on the analogous l1 cost function and has been applied very successfully to realtime separation of background and foreground in video.
Laura Balzano is an assistant professor in Electrical Engineering and Computer Science at the University of Michigan.

Laura received her BS, MS, and Ph.D. in Electrical Engineering from Rice University, the University of California in Los Angeles, and the University of Wisconsin, respectively. She received the Outstanding MS Degree of the year award from the UCLA EE Department, and the Best Dissertation award from the University of Wisconsin ECE Department. She has worked as a software engineer at Applied Signal Technology, Inc. Her PhD was supported by a 3M fellowship. Her main research focus is on statistical signal processing, estimation, and modeling with highly incomplete or corrupted data, and its applications in network monitoring, sensor networks, and collaborative filtering.