Approximate Euclidean lengths and distances beyond Johnson-Lindenstrauss
Authors: Aleksandros Sobczyk, Mathieu Luisier
NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Proof-of-concept numerical experiments are presented to validate the theoretical analysis. |
| Researcher Affiliation | Collaboration | Aleksandros Sobczyk IBM Research and ETH Zürich Zürich, Switzerland obc@zurich.ibm.com Mathieu Luisier ETH Zürich Zürich, Switzerland mluisier@iis.ee.ethz.ch |
| Pseudocode | Yes | Algorithm 1 Adaptive Euclidean Norm Estimation |
| Open Source Code | No | No because the code is proprietary. |
| Open Datasets | No | The paper discusses generating 'synthetic matrices' and provides details on their construction but does not refer to any publicly available datasets or provide access information for the generated data. |
| Dataset Splits | No | The paper describes numerical experiments, but it does not specify any training/test/validation splits. It discusses generating synthetic matrices and running experiments, but no explicit data partitioning is mentioned. |
| Hardware Specification | No | Our small scale indicative experiments were ran on a small laptop. |
| Software Dependencies | No | Algorithm 1 was implemented in Python using Num Py. |
| Experiment Setup | Yes | Specifically, d d matrices A, with d = 5000, were created as follows. We drew a random orthogonal d d matrix Q. We then fixed a diagonal d d matrix Λ which defines the eigenvalues of the matrix. Each element Λi,i, i [d] is set to i c for a given c 0. The larger the c, the faster the spectral decay. We finally constructed the symmetric A = QΛQ which were used in the numerical experiments. Following [34], we applied four different decay factors, specifically c = {0.5, 1, 1.5, 2}. Therefore, we set G, S, and Q in Algorithm 1 to have size d m/4, so that both algorithms are tested with the same number of matrix-vector products. |