Semi-relaxed Gromov-Wasserstein divergence and applications on graphs
Authors: Cédric Vincent-Cuaz, Rémi Flamary, Marco Corneli, Titouan Vayer, Nicolas Courty
ICLR 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5 NUMERICAL EXPERIMENTS This section illustrates the behavior of sr GW on graph partitioning (a.k.a. nodes clustering), clustering of graphs and graph completion. All the Python implementations in the experiments will be released on Github. For all experiments we provide e.g. validation grids, initializations and complementary metrics in the annex (see sections: partitioning 7.5.1,clustering 7.5.2, completion 7.5.3). |
| Researcher Affiliation | Academia | C edric Vincent-Cuaz 1, R emi Flamary 2, Marco Corneli 1,3, Titouan Vayer 4, Nicolas Courty 5 Univ. Cˆote d Azur, Inria, Maasai, CNRS, LJAD 1; IP Paris, CMAP, UMR 7641 2; MSI 3; Univ. Lyon, Inria, CNRS, ENS de Lyon, LIP UMR 5668 4; Univ. Bretagne-Suf, CNRS, IRISA 5. |
| Pseudocode | Yes | Algorithm 1 CG solver for sr GW |
| Open Source Code | Yes | All the Python implementations in the experiments will be released on Github. For all experiments we provide e.g. validation grids, initializations and complementary metrics in the annex (see sections: partitioning 7.5.1,clustering 7.5.2, completion 7.5.3).1code available at https://github.com/cedricvincentcuaz/srGW. |
| Open Datasets | Yes | For the directed graphs, we adopt the symmetrization procedure described in Chowdhury & Needham (2021). Our main competitors are the two GW based partitioning methods proposed by Xu et al. (2019b) and Chowdhury & Needham (2021). The former (GWL) relies on adjacency matrices, the latter (Spec GWL) adopts heat kernels on the graph normalized laplacians (Spec GWL). |
| Dataset Splits | Yes | Finally, we considered the same settings for the stochastic algorithm hyperparameters across all methods: learning rates are validated within {0.01, 0.001} while the batch size is validated within {16, 32}; We learn all models fixing a maximum number of epochs of 100 (over convergence requirements) and implemented an (unsupervised) early-stopping strategy which consists in computing the respective unmixings every 5 epochs and stop the learning process if the cumulated reconstruction error (Errt) does not improve anymore over 2 consecutive evaluations (i.e. Errt Errt+1 and Errt Errt+2). |
| Hardware Specification | Yes | Measures taken on Intel(R) Core(TM) i7-4510U CPU @ 2.00GHz. |
| Software Dependencies | No | The paper mentions 'Python implementations' and refers to 'POT’s implementation (Flamary et al., 2021)' and 'Adam optimizer (Kingma & Ba, 2015)', but it does not provide specific version numbers for these software components. |
| Experiment Setup | Yes | For datasets with attributes involving FGW, we validated 15 values of the trade-off parameter α via a logspace search in (0, 0.5) and symmetrically (0.5, 1). For DL based approaches, a first step consists into learning the atoms. sr GW dictionary sizes are tested in M {10, 20, 30, 40, 50}... For sr GWg, sr GWe+g and GDLλ, the coefficient of our respective sparsity promoting regularizers is validated within {0.001, 0.01, 0.1, 1.0}. Then for sr GWe, sr GWe+g, GWF-f and GWF-r, the entropic regularization coefficient is validated also within {0.001, 0.01, 0.1, 1.0}. Finally, we considered the same settings for the stochastic algorithm hyperparameters across all methods: learning rates are validated within {0.01, 0.001} while the batch size is validated within {16, 32}; We learn all models fixing a maximum number of epochs of 100 (over convergence requirements) and implemented an (unsupervised) early-stopping strategy... |