Subspaces lie at the heart of data analysis. As soon as we get our hands on some data, finding a subspace that explains it is one of the first things we try, for example, using Principal Component Analysis (PCA) or linear regression.
Many applications have missing data and gross errors. For example, in computer vision, occlusions produce missing data; in surveys and recommender systems, subjects do not know or do not want to provide all information.
The main focus of my research is learning subspaces from highly incomplete and corrupted data. This has numerous applications in networks, computer vision, drug-discovery, rigidity theory, recommender systems, surveys, and pretty much anywhere there are subspaces and incomplete or corrupted data.
My research interests include signal processing, machine learning, optimization, statistics, and algebraic geometry.