Matrix Completion With Selective Sampling
This work addresses matrix completion for data scientists by introducing a more efficient sampling approach, though it appears incremental as it builds on existing nuclear norm minimization methods.
The paper tackles the matrix completion problem by proposing selective sampling methods when prior knowledge about the matrix structure is available, allowing for designed observation sets instead of uniform sampling.
Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization problem. Almost all previous work assumes no explicit structure of the matrix and uses uniform sampling to decide the observed entries. We suggest methods for selective sampling in the case where we have some knowledge about the structure of the matrix and are allowed to design the observation set.