Non-convex Robust PCA
Authors: Praneeth Netrapalli, Niranjan U N, Sujay Sanghavi, Animashree Anandkumar, Prateek Jain
NeurIPS 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments on both synthetic and real data establishes the improved speed and accuracy of our method over existing convex implementations.We now present an empirical study of our Alt Proj method. The goal of this study is two-fold: a) establish that our method indeed recovers the low-rank and sparse part exactly, without significant parameter tuning, b) demonstrate that Alt Proj is significantly faster than Conv-RPCA (see (1)); we solve Conv-RPCA using the IALM method [CLMW11], a state-of-the-art solver [LCM10]. We implemented our method in Matlab and used a Matlab implementation of the IALM method by [LCM10]. |
| Researcher Affiliation | Collaboration | 1Microsoft Research, Cambridge MA. 2The University of California at Irvine. 3The University of Texas at Austin. 4Microsoft Research, India. |
| Pseudocode | Yes | Algorithm 1 (b L, b S) = Alt Proj(M, ϵ, r, β): Non-convex Alternating Projections based Robust PCA |
| Open Source Code | No | The paper does not provide a specific repository link, explicit code release statement, or indicate code availability in supplementary materials for the described methodology. |
| Open Datasets | Yes | We consider both synthetic experiments and experiments on real data involving the problem of foreground-background separation in a video.Here, we used two benchmark datasets named Escalator and Restaurant dataset. |
| Dataset Splits | No | The paper does not provide specific dataset split information (exact percentages, sample counts, citations to predefined splits, or detailed splitting methodology) needed to reproduce the data partitioning. |
| Hardware Specification | No | The paper does not provide specific hardware details (exact GPU/CPU models, processor types with speeds, memory amounts, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | The paper states 'We implemented our method in Matlab and used a Matlab implementation of the IALM method by [LCM10]', but it does not specify version numbers for Matlab or any other software dependencies. |
| Experiment Setup | Yes | Parameter Setting: Our pseudo-code (Algorithm 1) prescribes the threshold ζ in Step 4, which depends on the knowledge of the singular values of the low rank component L . Instead, in the experiments, we set the threshold at the (t + 1)-th step of k-th stage as ζ = µσk+1(M S(t)) n . For synthetic experiments, we employ the µ used for data generation, and for real-world datasets, we tune µ through cross-validation. We found that the above thresholding provides exact recovery while speeding up the computation significantly. We would also like to note that [CLMW11] sets the regularization parameter λ in Conv-RPCA (1) as 1/ n (assuming m n). However, we found that that for problems with large incoherence such a parameter setting does not provide exact recovery. Instead, we set λ = µ/ n in our experiments. |