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.