LCOT: Linear Circular Optimal Transport
Authors: Rocio P Diaz Martin, Ivan Vladimir Medri, Yikun Bai, Xinran Liu, Kangbai Yan, Gustavo Rohde, Soheil Kolouri
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Lastly, through a set of numerical experiments, we demonstrate the benefits of LCOT in learning representations of circular measures. and 4 EXPERIMENTS To better understand the geometry induced by the LCOT metric, we perform Multidimensional Scaling (MDS) (Kruskal, 1964) on a family of densities, where the discrepancy matrices are computed using LCOT, COT, OT (with a fixed cutting point), and the Euclidean distance. |
| Researcher Affiliation | Academia | Roc ıo D ıaz Mart ın 1, Ivan Medri 2, Yikun Bai 3, Xiran Liu3, Kangbai Yan1, Gustavo K. Rohde 4, Soheil Kolouri 3 1Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA. 2Department of Computer Science, Tennessee State University, Nashville, TN 37209, USA. 3Department of Computer Science, Vanderbilt University, Nashville, TN 37240, USA. 4Department of Biomedical Engineering, Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22908, USA. |
| Pseudocode | No | The paper describes algorithms in text, but does not include formal pseudocode or algorithm blocks. |
| Open Source Code | No | No explicit statement about releasing source code or providing a link to a code repository for the methodology. |
| Open Datasets | No | The paper mentions generating random discrete measures, families of circular densities, and using 100 flower images for a hue-based retrieval experiment, but does not provide any specific links, DOIs, or formal citations for public access to these datasets. |
| Dataset Splits | No | The paper mentions generating and sampling densities but does not provide specific details on training, validation, or test dataset splits (e.g., percentages, sample counts, or citations to predefined splits). |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., exact GPU/CPU models, processor types, or memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details, such as library or solver names with version numbers, needed to replicate the experiments. |
| Experiment Setup | Yes | We assign a von Mises distribution with a small spread (κ = 200) to each distribution s axis/axes to introduce random perturbations of these distributions. |