High Rank Matrix Completion via Grassmannian Proxy Fusion
This addresses the problem of high-rank matrix completion for applications like data imputation, offering improved performance in low-sampling scenarios, though it appears incremental as it builds on existing subspace clustering methods.
The paper tackles high-rank matrix completion by clustering incomplete vectors via proxy subspaces and minimizing distances on the Grassmannian, achieving performance comparable to leading methods at high sampling rates and significantly better at low sampling rates, narrowing the gap to the theoretical sampling limit.
This paper approaches high-rank matrix completion (HRMC) by filling missing entries in a data matrix where columns lie near a union of subspaces, clustering these columns, and identifying the underlying subspaces. Current methods often lack theoretical support, produce uninterpretable results, and require more samples than theoretically necessary. We propose clustering incomplete vectors by grouping proxy subspaces and minimizing two criteria over the Grassmannian: (a) the chordal distance between each point and its corresponding subspace and (b) the geodesic distances between subspaces of all data points. Experiments on synthetic and real datasets demonstrate that our method performs comparably to leading methods in high sampling rates and significantly better in low sampling rates, thus narrowing the gap to the theoretical sampling limit of HRMC.