Optimal Bounds for Johnson-Lindenstrauss Transformations
Authors: Michael Burr, Shuhong Gao, Fiona Knoll
JMLR 2018 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we provide a precise asymptotic threshold for the dimension of the image, above which, there exists a projection preserving the Euclidean distance, but, below which, there does not exist such a projection. The main result of this paper is captured in the following theorem: Theorem 2 For ϵ and δ sufficiently small, k0 4ϵ 2 log(1/δ). More precisely, lim ϵ,δ 0 k0(ϵ, δ) 4ϵ 2 log(1/δ) = 1. |
| Researcher Affiliation | Academia | Michael Burr EMAIL Shuhong Gao EMAIL Department of Mathematical Sciences Clemson University, Clemson SC 29634, USA Fiona Knoll EMAIL Department of Mathematical Sciences University of Cincinnati, Cincinnati, OH 45221, USA |
| Pseudocode | No | The paper describes mathematical proofs, theorems, and derivations. There are no explicitly labeled pseudocode blocks or algorithms, nor any structured code-like procedures presented. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide links to any code repositories or mention code in supplementary materials for the methodology described. |
| Open Datasets | No | This paper is theoretical, focusing on mathematical proofs and bounds for Johnson-Lindenstrauss transformations. It does not use or reference any specific datasets, thus there is no mention of publicly available datasets. |
| Dataset Splits | No | This paper is theoretical and does not involve the use of datasets for experiments, therefore, there is no information provided regarding dataset splits. |
| Hardware Specification | No | The paper is theoretical and focuses on mathematical proofs and derivations, not empirical experiments. Therefore, it does not describe any specific hardware used for running experiments. |
| Software Dependencies | No | The paper is theoretical and focuses on mathematical proofs, not software implementation or experiments. Consequently, it does not provide any specific software dependencies or version numbers. |
| Experiment Setup | No | As a theoretical paper primarily focused on mathematical proofs and derivations, it does not describe an experimental setup, hyperparameters, or training configurations. |