Fast methods for estimating the Numerical rank of large matrices
Authors: Shashanka Ubaru, Yousef Saad
ICML 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we illustrate the performance of the rank estimation techniques on matrices from various typical applications. In the first experiment, we use a 5, 981 5, 981 matrix named ukerbe1 from the AG-Monien group (the matrix is a Laplacian of an undirected graph), available in the University of Florida Sparse Matrix Collection (Davis & Hu, 2011) database. The performances of the Chebyshev Polynomial filter method and the extended Mc Weeny filter method for estimating the numerical rank of this matrix2 are shown in figure 3. |
| Researcher Affiliation | Academia | Shashanka Ubaru UBARU001@UMN.EDU Yousef Saad SAAD@CS.UMN.EDU Department of Computer Science and Engineering, University of Minnesota, Twin Cities, MN USA |
| Pseudocode | Yes | Algorithm 1 describes our approach for estimating the approximate rank rε by the two polynomial filtering methods discussed earlier. |
| Open Source Code | Yes | Matlab codes are available at http://www-users.cs. umn.edu/ ubaru/codes/rank_estimation.zip |
| Open Datasets | Yes | In the first experiment, we use a 5, 981 5, 981 matrix named ukerbe1 from the AG-Monien group (the matrix is a Laplacian of an undirected graph), available in the University of Florida Sparse Matrix Collection (Davis & Hu, 2011) database. |
| Dataset Splits | No | No explicit train/test/validation splits are mentioned for the datasets used in the experiments. The paper uses existing matrices from databases or image datasets for evaluation. |
| Hardware Specification | Yes | The estimation of its rank by the Chebyshev filter method took only 7.18 secs on average (over 10 trials) on a standard 3.3GHz Intel-i5 machine. |
| Software Dependencies | No | No specific software versions are mentioned. The paper only states 'Matlab codes are available...'. |
| Experiment Setup | No | No specific experimental setup details such as hyperparameters, learning rates, or optimizer settings are provided. The paper describes the general methods and their application to matrices. |