Convergence Analysis of Gradient Descent for Eigenvector Computation
Authors: Zhiqiang Xu, Xin Cao, Xin Gao
IJCAI 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Theoretical properties are verified in experiments. |
| Researcher Affiliation | Academia | 1 KAUST, Saudi Arabia 2 UNSW, Australia zhiqiang.xu@kaust.edu.sa, xin.cao@unsw.edu.au, xin.gao@kaust.edu.sa |
| Pseudocode | No | The paper contains mathematical equations and derivations but does not include any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any specific links to open-source code or explicitly state that the code for the described methodology is publicly available. |
| Open Datasets | No | For synthetic data, the paper describes how it is generated (e.g., "follow [Shamir, 2015] to generate data") but does not provide a direct link to a publicly available dataset or a citation with author names and year for the specific dataset used. For real data, it mentions "Schenk1" and provides a URL "www.cise.ufl.edu/research/sparse/matrices/" but this is a general collection and not a direct link/citation to a specific dataset or file used within the context of this paper. |
| Dataset Splits | No | The paper does not provide specific details on training, validation, or test dataset splits (e.g., percentages or sample counts). |
| Hardware Specification | No | The paper does not specify any hardware details (e.g., CPU, GPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper mentions 'matlab s eigs function' but does not specify any software dependencies with version numbers. |
| Experiment Setup | Yes | If the initial x0 = y y 2 where entries of y are i.i.d. standard normal samples, i.e., yi N(0, 1)... The solver with constant step-sizes α < p 2λ2 1(1+α p) will converge... the solver with diminishing step-sizes αt = c τ+t for sufficiently large constants c, τ > 0 will converge... We set n = 1000 and follow [Shamir, 2015] to generate data using the full eigenvalue decomposition A = UΣU . Σ = diag(Σ1, Σ2), where Σ2 = diag( |g1| / n , ..., |gn r| / n ) with gi N(0, 1) and r being the order of Σ1. In addition, the following two settings are considered: p = 1: Σ1 = diag(1, 1 η, 1 1.1η, 1 1.2η, 1 1.3η, 1 1.4η), and then p / λ1 = η > 0, where η {0.2, 0.5, 0.8}. p = 3: Σ1 = diag(1, 1, 1), and then p / λ1 = 1 |g1| / n . (Figure 1 labels: c=12.87, τ=10; c=14.48, τ=10; c=16.09, τ=10). |