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Low Rank Matrix Completion through Semi-definite Programming with Facial Reduction
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 2016 |
| Abstract | The matrix completion problem is a hot problem in data science. In recent years, many theories and practices on efficiently recovering the partially observed matrix have been introduced. A good example is the Netflix Challenge [15], where the provided data set is a partially observed matrix with each row represents a user and each column represents a film. The winning team of this competition applied matrix completion algorithm to this challenge, and improved the success rate of rating system by 10%. In this report, We will show how to convert the original low rank matrix completion problem which is nonconvex to convex problem. Furthermore we will convert the convex optimization problem to a semi-definite programming problem. For the semi-definite programming problem, although Slater’s condition holds, the facial reduction method can still be applied to obtain a proper face containing the optimal set and so can dramatically shrink the size of original problem while guaranteeing a low-rank solution. We include numerical tests for both the case without noise and the case with noise. In all cases the target rank is pre-defined. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://uwaterloo.ca/computational-mathematics/sites/ca.computational-mathematics/files/uploads/files/xinghangthesis.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
