Manifold Fitting under Unbounded Noise
Authors: Zhigang Yao, Yuqing Xia
JMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical simulations are conducted as part of this new method to help validate our theoretical findings and demonstrate the advantages of our method over other relevant manifold fitting methods. Finally, our method is applied to real data examples. |
| Researcher Affiliation | Academia | Zhigang Yao EMAIL Department of Statistics and Data Science National University of Singapore 21 Lower Kent Ridge Road Singapore 117546 Yuqing Xia EMAIL School of Data Sciences Zhejiang University of Finance and Economics Hangzhou 310018, China |
| Pseudocode | Yes | Algorithm 1: Project x onto Mout |
| Open Source Code | Yes | Implementation: the MATLAB codes, together with all numerical examples used in this paper, are available at https://zhigang-yao.github.io/research.html which contains a Git Hub link under the code tap. |
| Open Datasets | Yes | The classical Coil20 dataset (Nene et al., 1996), which contains images of 20 objects, may be used as an example. This subsection considers a concrete case denoising facial images selected from the video database in Happy et al. (2012). |
| Dataset Splits | Yes | From the 1,000 facial images, we select 5 with different head orientations. The goal of this experiment is to denoise these five blurred images by projecting them to the manifold learnt by the remaining 995 blurred images, which are treated as the noisy samples. |
| Hardware Specification | No | No specific hardware details (like GPU models, CPU types, or memory amounts) are mentioned in the paper. |
| Software Dependencies | No | The paper mentions 'the MATLAB codes' but does not specify a version number for MATLAB or any other software dependencies. |
| Experiment Setup | Yes | In constructing αi(x), our method requires β 2. We take β = d + 2 in the simulation, as Fefferman et al. (2018) did. So we take r = λ σ in this simulation, where λ is tuned in a large range for each method and each σ. The dimension d of the latent manifold is tuned from {1, 5, 10, 15, 20, 50, 75, 100} for each method and we choose d = 10 because of its outperformance. |