Matrix Completion with Sparse Noisy Rows
This work addresses matrix completion for applications with row-wise noise, but it appears incremental as it modifies an existing noise model from columns to rows.
The paper tackles the problem of exact low-rank matrix completion under a non-degenerate noise model where noise is sparse and occurs in rows instead of columns, proposing an interactive algorithm that recovers the underlying matrix under specified conditions.
Exact matrix completion and low rank matrix estimation problems has been studied in different underlying conditions. In this work we study exact low-rank completion under non-degenerate noise model. Non-degenerate random noise model has been previously studied by many researchers under given condition that the noise is sparse and existing in some of the columns. In this paper, we assume that each row can receive random noise instead of columns and propose an interactive algorithm that is robust to this noise. We show that we use a parametrization technique to give a condition when the underlying matrix could be recoverable and suggest an algorithm which recovers the underlying matrix.