Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Partial Gromov-Wasserstein Metric
Authors: Yikun Bai, Rocio Diaz Martin, Abihith Kothapalli, Hengrong Du, Xinran Liu, Soheil Kolouri
ICLR 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments. We demonstrate the performance of our proposed algorithms in terms of computation time and efficacy on a series of tasks: shapematching with outliers between 2D and 3D objects, shape retrieval between 2D shapes, and shape interpolation using the concept of PGW barycenters. We compare the performance of our proposed algorithms against existing baselines for each task. |
| Researcher Affiliation | Academia | Yikun Bai1, Rocio Diaz Martin*2, Abihith Kothapalli*1, Hengrong Du3, Xinran Liu1, and Soheil Kolouri1 1Department of Computer Science, Vanderbilt University 2Department of Mathematics, Tufts University 3Department of Mathematics, University of California, Irvine |
| Pseudocode | Yes | Algorithm 1: Frank-Wolfe Algorithm for PGW, ver 1 Algorithm 2: Frank-Wolfe Algorithm for partial GW, ver 2 Algorithm 3: Partial Gromov-Wasserstein Barycenter Algorithm 4: Mass-Constrained Partial Gromov-Wasserstein Barycenter |
| Open Source Code | Yes | Our code is available at https://github.com/mint-vu/PGW_Metric. |
| Open Datasets | Yes | We test two datasets in this experiment, which we refer to as Dataset I and Dataset II. We construct Dataset I by adapting the 2D shape dataset given in (Beier et al., 2022).... For Dataset II, we generate 20 shapes for each of the classes: rectangle, house, arrow, double arrow, semicircle, and circle. We apply the dataset in (Peyré et al., 2016) with download link. The datasets include MNIST, EMNIST, and the following three domains of Caltech Office: Amazon (A), Webcam (W), and DSLR (D) (Saenko et al., 2010). |
| Dataset Splits | Yes | Finally, using the approach given by (Beier et al., 2022; Titouan et al., 2019b), we combine each distance with a support vector machine (SVM), applying stratified 10-fold cross-validation. For the MNIST and EMNIST datasets, we set n = 1000 and m = 5000. In the Surf(A) and Decaf(A) datasets, each class contained an average of 100 samples. To ensure the SCAR assumption, we set n = 1/2 * 100 = 50 and m = 250. Similarly, for the Surf(D) and Decaf(D) datasets, we set n = 15 and m = 75. Finally, for Surf(W) and Decaf(W), we used n = 20 and m = 100. |
| Hardware Specification | Yes | All experiments presented in this paper are conducted on a computational machine with an AMD EPYC 7713 64-Core Processor, 8 * 32GB DIMM DDR4, 3200 MHz, and an NVIDIA RTX A6000 GPU. |
| Software Dependencies | No | Regarding the acceleration technique, for the POT problem in step 1, our algorithms and the MPGW algorithm apply the linear programming solver provided by Python OT package (Flamary et al., 2021), which is written in C++. |
| Experiment Setup | Yes | For the SVM experiments, we use exp(σD) as the kernel for the SVM model. Here, we normalize the matrix D and choose the best σ {0.001, 0.01, 0.1, 1, 10, 100, 1000, 10000} for each method used in order to facilitate a fair comparison of the resulting performances. In computing the pairwise distances, for the PGW method, we set λ such that λ λmax = maxi (|Ci|2). In particular, we compute λmax for each dataset and use λ = 1/5λmax for each experiment. For UGW, we use ε = 10-1 and ρ1 = ρ2 = 1 for both experiments. Finally, for MPGW, we set the mass-constrained term to be ρ = min(|µi|, |µj|) when computing the similarity between shape Xi and Xj. In both GW and PGW barycenter algorithms, we set the largest number of iterations to 100. The threshold for convergence is set to be 1e-5. For the convergence criteria, we set the tolerance term for Frank-Wolfe convergence and the main loop in the UGW algorithm to be 1e-5. Additionally, the tolerance for Sinkhorn convergence in UGW was set to 1e-6. The maximum number of iterations for the POT solver in PGW and MPGW was set to 500n. |