Subspace Tracking

Data in the real world often have a great deal of structure. One way to capture that structure is with principal components or singular vectors. If one is interested in the best k vectors to approximate a dataset, the top k singular vectors provide exactly that. These vectors span the best-fit subspace to the data. I study the estimation of these subspaces as well as algorithms to track subspaces that change over time. I’m interested in understanding the impact of singular value gaps, noise, and corruption on subspace estimation and tracking.

For code, see posts on GROUSE, an l2 subspace tracking algorithm, GRASTA, an l1 subspace tracking algorithm, its Open CV version GRASTAcam, and TGRASTA, an algorithm that estimates a subspace under non-linear transformations.