Typical and Generic Ranks in Low Rank Matrix Completion

Research Horizons Seminar
Wednesday, January 31, 2018 - 12:10
1 hour (actually 50 minutes)
Skiles 006
GA Tech
In recent years the problem of low-rank matrix completion received a tremendous amount of attention. I will consider the problem of exact low-rank matrix completion for generic data. Concretely, we start with a partially-filled matrix M, with real or complex entries, with the goal of finding the unspecified entries (completing M) in such a way that the completed matrix has the lowest possible rank, called the completion rank of M. We will be interested in how this minimal completion rank depends on the known entries, while keeping the locations of specified and unspecified entries fixed. Generic data means that we only consider partial fillings of M where a small perturbation of the entries does not change the completion rank of M.