Low-Rank Matrix Recovery from Row-and-Column Affine Measurements
Authors: Or Zuk, Avishai Wagner
ICML 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In simulations, our row-and-column design and SVLS algorithm show improved speed, and comparable and in some cases better accuracy compared to standard measurements designs and algorithms. Our theoretical and experimental results suggest that the proposed row-and-column affine measurements scheme, together with our recovery algorithm, may provide a powerful framework for affine matrix reconstruction. |
| Researcher Affiliation | Academia | Avishai Wagner AVISHAI.WAGNER@MAIL.HUJI.AC.IL Or Zuk OR.ZUK@MAIL.HUJI.AC.IL Dept. of Statistics, The Hebrew University of Jerusalem, Mt. Scopus, Jerusalem, 91905, Israel |
| Pseudocode | Yes | Algorithm 1 ... Algorithm 2 SVLS |
| Open Source Code | Yes | All of our algorithms and simulations are implemented in a Matlab software package available at https://github.com/avishaiwa/SVLS. |
| Open Datasets | No | The paper uses simulated data for its experiments, rather than pre-existing public datasets. It describes the data generation process (e.g., 'sampled a random rank-r matrix X = UV T with U, V Rn r , U, V i.i.d. N(0, σ2)') but does not provide access information for a public dataset. |
| Dataset Splits | No | The paper describes generating random matrices for each simulation run ('sampled 50 matrices', 'simulated 5 random matrices'). As the data is simulated and regenerated per run, there are no fixed train/validation/test splits in the traditional sense of a static dataset. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used to run the experiments, such as CPU/GPU models, memory, or cloud computing resources. |
| Software Dependencies | No | The paper states that 'All of our algorithms and simulations are implemented in a Matlab software package,' but it does not specify the version number of Matlab or any other software dependencies with their versions. |
| Experiment Setup | Yes | For simplicity, we concentrated on square matrices with n1 = n2 = n and used an equal number of row and column measurements, k(R) = k(C) = k. ... In all simulations we sampled a random rank-r matrix X = UV T with U, V Rn r , U, V i.i.d. N(0, σ2). ... In Figure 1 we show results for n = 150, r = 3 and σ = 1. ... We sampled a matrix X with n = 100, r = 3, σ = 1 and noise level τ 2 = 0.252, and varied the number of row and column measurements k. ... In Figure 3 we take n = 100 and r = 2, and change the number of measurements d = 2nk... We added Gaussian noise Z(R), Z(C) with different noise levels τ. |