Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Dual Principal Component Pursuit
Authors: Manolis C. Tsakiris, René Vidal
JMLR 2018 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments on synthetic data show that the proposed methods are able to handle more outliers and higher relative dimensions than current state-of-the-art methods, while experiments in the context of the three-view geometry problem in computer vision suggest that the proposed methods can be a useful or even superior alternative to traditional RANSAC-based approaches for computer vision and other applications. (Abstract) ... In this section we evaluate the proposed algorithms experimentally. In 7.1 we investigate numerically the theoretical regime of success of recursion (10) predicted by Theorems 11 and 12. We also show that even when these sufficient conditions are violated, (10) can still converge to a normal vector to the subspace if initialized properly. Finally, in 7.2 we compare DPCP variants with state-of-the-art robust PCA algorithms for the purpose of outlier detection using synthetic data, and similarly in 7.3 using real images. (Section 7. Experiments) |
| Researcher Affiliation | Academia | Manolis C. Tsakiris EMAIL SCHOOL OF INFORMATION SCIENCE AND TECHNOLOGY SHANGHAITECH UNIVERSITY PUDONG, SHANGHAI, CHINA; Rene Vidal EMAIL MATHEMATICAL INSTITUTE FOR DATA SCIENCE JOHNS HOPKINS UNIVERSITY BALTIMORE, MD, 21218, USA |
| Pseudocode | Yes | Algorithm 1 Dual Principal Component Pursuit via Linear Programming ... Algorithm 2 Dual Principal Component Pursuit via Iteratively Reweighted Least Squares ... Algorithm 3 Denoised Dual Principal Component Pursuit |
| Open Source Code | No | The paper does not provide concrete access to source code for the methodology described in this paper. It mentions that "Co P is implemented using the code provided by its authors", referring to a third-party tool, but not their own implementation. |
| Open Datasets | Yes | Data. We use the first three views of the datasets Model House, Corridor and Merton College III, provided by the Visual Geometry Group at Oxford University. |
| Dataset Splits | No | The paper describes how the experimental datasets were constructed with varying percentages of inliers and outliers (e.g., "randomly pick N = 125 inlier correspondences... We further generate 100 M /(N + M )% = 30%, 40%, 50% outlier correspondences..."). However, it does not specify explicit training/test/validation splits for model training or evaluation in the traditional sense, as the experiments are primarily focused on outlier detection performance on these composite datasets, not on learning a model with distinct data partitioning phases. |
| Hardware Specification | Yes | The experiment is run in MATLAB on a standard Macbook-Pro with a dual core 2.5GHz Processor and a total of 4GB Cache memory. |
| Software Dependencies | Yes | Finally, the linear programs in DPCP-LP are solved via the generic LP solver Gurobi (Gurobi Optimization, 2015) |
| Experiment Setup | Yes | The convergence accuracy of all methods is set to 10-3. For REAPER we set the regularization parameter as δ = 10-6 and the maximum number of iterations equal to 100. For DPCP-d we set τ = 1/√(N + M) as suggested in Qu et al. (2014) and the maximum number of iterations to 1000. For RANSAC we set its thresholding parameter to 10-3... Both SE-RPCA and ℓ21-RPCA are implemented with ADMM, with augmented Lagrange parameters 1000 and 100 respectively. For ℓ21-RPCA λ is set to 3/(7√M), as suggested in Xu et al. (2012). DPCP variants are initialized via the SVD of the data as in Algorithm 1. Co P is implemented using the code provided by its authors, and selects 3d points upon classic PCA gives the subspace estimate. Finally, ... the maximum number of iterations for DPCP-LP is set to Tmax = 10. |