KoPA: Automated Kronecker Product Approximation
Authors: Chencheng Cai, Rong Chen, Han Xiao
JMLR 2022 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the superiority of Ko PA over the low rank approximations through numerical studies, and several benchmark image examples. In Section 6, we carry out extensive simulations to assess the performance of our method, and demonstrate its superiority over the SVD approach. We also present a detailed analysis of the cameraman s image. |
| Researcher Affiliation | Academia | Chencheng Cai EMAIL Department of Statistics, Operations and Data Science Fox School of Business, Temple University Philadelphia, PA 19122, USA Rong Chen EMAIL Department of Statistics Rutgers University Piscataway, NJ 08854, USA Han Xiao EMAIL Department of Statistics Rutgers University Piscataway, NJ 08854, USA |
| Pseudocode | No | The paper describes the proposed procedure and methods mathematically and descriptively, but does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about the release of open-source code for the methodology described, nor does it provide a link to a code repository. |
| Open Datasets | Yes | Here we use the cameraman s image, a benchmark in image analysis... The 10 test images printed in Figure 11 are collected from Image Processing Place1 and The Waterloo image Repository2. Each 1. http://www.imageprocessingplace.com/root _files_V3/image_databases.htm 2. http://links.uwaterloo.ca/Repository.html |
| Dataset Splits | No | The paper uses benchmark images like the cameraman image and other test images for analysis and denoising experiments, but it does not specify any training/test/validation dataset splits. The methodology is applied to the images as a whole or to images corrupted by additive noise. |
| Hardware Specification | No | The paper does not provide specific hardware details such as GPU/CPU models, processor types, or memory specifications used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details with version numbers (e.g., library or solver names with version numbers) needed to replicate the experiment. |
| Experiment Setup | Yes | The simulation is based on model (4). Two configurations are considered: (i) M = N = 9, m0 = 4, n0 = 4, and (ii) M = N = 10, m0 = 5, n0 = 4. Similar to Section 6.1.1, the noise level is fixed at σ = 1, so the signal-to-noise ratio is controlled by λ. To control the representation gap ψ2, we construct the matrices A and B as follows: ... In the experiment, five values of ϕ2 are considered: ϕ2 {0.1, 0.2, 0.3, 0.4, 0.5}. In this simulation, we fix the configurations to M = N = 9, (m0, n0) = (4, 4) and consider four different relative strengths of the second term λ2 2/λ2 1 {0.3, 0.4, 0.5, 0.6}. |