LOW-RANK MATRIX COMPLETION WITH GEOMETRIC PERFORMANCE GUARANTEES
Compressed Sensing: Theory and Methods
Přednášející: Wei Dai, Autoři: Wei Dai, Ely Kerman, Olgica Milenkovic, University of Illinois Urbana-Champaign, United States
The low-rank matrix completion problem can be stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. There exist several low-complexity algorithms for low-rank matrix completion which focus on the minimization of the Frobenius norm of the matrix projection residue. This optimization framework has inherent difficulties: the objective function is not continuous and the solution set is not closed. To address this problem, we propose a geometric objective function to replace the Frobenius norm: the new objective function is continuous everywhere and the solution set is the closure of the solution set of the Frobenius metric. Furthermore, using the geometric objective function and a simple gradient descent procedure, we are able to preclude the existence of local minimizers, and hence establish strong performance guarantees for special completion scenarios, which do not require matrix incoherence or large matrix size.
Informace o přednášce
| Nahráno: | 2011-05-26 14:45 - 15:05, Club B |
|---|---|
| Přidáno: | 22. 6. 2011 03:53 |
| Počet zhlédnutí: | 90 |
| Rozlišení videa: | 1024x576 px, 512x288 px |
| Délka videa: | 0:20:15 |
| Audio stopa: | MP3 [6.85 MB], 0:20:15 |
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