Local reconstruction of low-rank matrices and subspaces

AbstractWe study the problem of reconstructing a low-rank matrix, where the input is an n×m matrix M over a field F and the goal is to reconstruct a near-optimal matrix M' that is low-rank and close to M under some distance function Δ. Furthermore, the reconstruction must be local, i.e., provides access to any desired entry of M' by reading only a few entries of the input M ideally, independent of the matrix dimensions n and m. Our formulation of this problem is inspired by the local reconstruction framework of Saks and Seshadhri SICOMP, 2010.