Minimal Sample Subspace Learning: Theory and Algorithms
Authors: Zhenyue Zhang, Yuqing Xia
JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, we report our numerical results and compare our method with existing algorithms on both noiseless synthetic data and real-world data in Section 8. 8. Experiments We evaluate the performance of our algorithms on synthetic data sets without noise and two kinds of real-world data sets for face recognition and motion detection. |
| Researcher Affiliation | Academia | Zhenyue Zhang EMAIL School of Mathematics Science Zhejiang University, Yuquan Campus Hangzhou 310027, China Yuqing Xia EMAIL School of Mathematics Science Zhejiang University, Yuquan Campus Hangzhou 310027, China |
| Pseudocode | Yes | Algorithm 1 MSS using manifold conjugated gradients (MSS MCG) ... Algorithm 2 Construct active set Ω ... Algorithm 3 Minimal subspace segmentation via alternative optimization (MSS AO) ... Algorithm 4 Subspace correction for solving the pseudo-dual problem (41) ... Algorithm 5 Minimal subspace segmentation via hybrid optimization (MSS HO) ... Algorithm 6 Graph construction from C ... Algorithm 7 Minimal subspace segmentation via relaxed optimization (MSS RO) |
| Open Source Code | No | The reported results of these algorithms were obtained using the codes provided by algorithm owners or downloaded from open sources. (This sentence refers to other algorithms, not the code for the method described in this paper. There is no explicit statement or link for the authors' own code.) |
| Open Datasets | Yes | We use the benchmark databases Extended Yale B for face clustering (Georghiades et al., 2001) and Hopkin 155 for motion segmentation (Tron and Vidal, 2007) to evaluate the performance of Algorithm 7 (MSS RO) on noisy data. |
| Dataset Splits | No | The testing sets are chosen as follows. A total of 38 individuals are divided into 4 groups each of the first three groups contains 10 individuals and the last group contains the remaining 8 individuals. In each group, we choose K individuals and test the segmentation of all 64K images from the chosen individuals. (This describes how data was sampled for clustering tasks, but not explicit train/test/validation splits with percentages, counts, or methodology for supervised learning.) |
| Hardware Specification | No | No specific hardware details (like GPU models, CPU models, or cloud instances with specs) are mentioned in the paper. |
| Software Dependencies | No | The reported results of these algorithms were obtained using the codes provided by algorithm owners or downloaded from open sources. (This refers to external code and does not specify version numbers for any software used in their own implementation.) |
| Experiment Setup | Yes | We set the parameters λ = 5, α = 20 X 1 , and β = 5, where X 1 = maxj xj 1. The self-expressive error is measured by the ℓ1-norm φ = 1. ... we use φ = 2 F for measuring the self-expressive error, and set the parameters λ = 10n/K, α = 50n/K, β = 0.05n/K, (61) |