Dual Smoothing and Level Set Techniques for Variational Matrix Decomposition
This work addresses RPCA, a problem in machine learning for data analysis, but appears incremental as it reviews existing methods and applies known optimization techniques.
The paper tackles the robust principal component analysis (RPCA) problem by reviewing convex formulations and applying dual smoothing and level set techniques, presenting novel theoretical results and numerical experiments on simulated and real-world data.
We focus on the robust principal component analysis (RPCA) problem, and review a range of old and new convex formulations for the problem and its variants. We then review dual smoothing and level set techniques in convex optimization, present several novel theoretical results, and apply the techniques on the RPCA problem. In the final sections, we show a range of numerical experiments for simulated and real-world problems.