Optimal Transport for structured data with application on graphs
Authors: Vayer Titouan, Nicolas Courty, Romain Tavenard, Chapel Laetitia, Rémi Flamary
ICML 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We now illustrate the behaviour of FGW on synthetic and real datasets. The algorithms presented in the previous section have been implemented using the Python Optimal Transport toolbox (Flamary & Courty, 2017) and will be released upon publication.4.2. Graph-structured data classificationTable 1. Average classification accuracy on the graph datasets with vector attributes. |
| Researcher Affiliation | Academia | 1Univ. Bretagne-Sud, CNRS, IRISA, F-56000 Vannes 2Univ. Cˆote d Azur, CNRS, OCA Lagrange, F-06000 Nice 3Univ. Rennes, CNRS, LETG, F-35000 Rennes. |
| Pseudocode | Yes | Algorithm 1 Conditional Gradient (CG) for FGWAlgorithm 2 Line-search for CG (q = 2) |
| Open Source Code | No | The algorithms presented in the previous section have been implemented using the Python Optimal Transport toolbox (Flamary & Courty, 2017) and will be released upon publication. |
| Open Datasets | Yes | BZR, COX2 (Sutherland et al., 2003), PROTEINS, ENZYMES (Borgwardt & Kriegel, 2005), CUNEIFORM (Kriege et al., 2018) and SYNTHETIC (Feragen et al., 2013) are vector attributed graphs. MUTAG (Debnath et al., 1991), PTC-MR (Kriege et al., 2016) and NCI1 (Wale et al., 2008) contain graphs with discrete attributes derived from small molecules. IMDB-B, IMDB-M (Yanardag & Vishwanathan, 2015) contain unlabeled graphs derived from social networks. All datas are available in (Kersting et al., 2016). |
| Dataset Splits | Yes | To provide compare between the methods, most papers about graph classification usually perform a nested cross validation (using 9 folds for training, 1 for testing, and reporting the average accuracy of this experiment repeated 10 times) and report accuracies of the other methods taken from the original papers. |
| Hardware Specification | Yes | We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan X GPU used for this research. |
| Software Dependencies | No | The algorithms presented in the previous section have been implemented using the Python Optimal Transport toolbox (Flamary & Courty, 2017) and will be released upon publication. |
| Experiment Setup | Yes | For all methods using SVM, we cross validate the parameter C {10^-7, 10^-6, ..., 10^7}. The range of the WL parameter H is {0, 1..., 10}, and we also compute this kernel with H fixed at 2, 4. The decay factor λ for RWK {10^-6, 10^-5..., 10^-2}, for the GK kernel we set the graphlet size κ = 3 and cross validate the precision level ϵ and the confidence δ as in the original paper (Shervashidze et al., 2009). The tmax parameter for PROPAK is chosen within {1, 3, 5, 8, 10, 15, 20}. For PSCN, we choose the normalized betweenness centrality as labeling procedure and cross validate the batch size in {10, 15, ..., 35} and number of epochs in {10, 20, ..., 100}. Finally for FGW, γ is cross validated within {2^-10, 2^-9, ..., 2^10} and α is cross validated via a logspace search in [0, 0.5] and symmetrically [0.5, 1] (15 values are drawn). |