Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings.  studies deterministic conditions for completion. An incomplete d × N matrix is finitely rank-r completable if there are at most finitely many rank-r matrices that agree with all its observed entries. Finite completability is the tipping point in LRMC, as a few additional samples of a finitely completable matrix guarantee its unique completability. The main contribution of this paper is a characterization of finitely completable observation sets.  use this characterization to derive sufficient deterministic sampling conditions for unique completability.  also show that under uniform random sampling schemes, these conditions are satisfied with high probability if O(max{r; log d}) entries per column are observed.
['Daniel L. Pimentel-Alarcon', 'Nigel Boston', 'Robert D. Nowak']
I am writing a research paper on a idea A characterization of deterministic sampling patterns for low-rank matrix completion
[{"from": "human", "value": "I am writing a research paper on a idea A characterization of deterministic sampling patterns for low-rank matrix completion"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings.  studies deterministic conditions for completion. An incomplete d \u00d7 N matrix is finitely rank-r completable if there are at most finitely many rank-r matrices that agree with all its observed entries. Finite completability is the tipping point in LRMC, as a few additional samples of a finitely completable matrix guarantee its unique completability. The main contribution of this paper is a characterization of finitely completable observation sets.  use this characterization to derive sufficient deterministic sampling conditions for unique completability.  also show that under uniform random sampling schemes, these conditions are satisfied with high probability if O(max{r; log d}) entries per column are observed."}]