Weisfeiler and Leman Go Walking: Random Walk Kernels Revisited

Authors: Nils M. Kriege

NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We verify experimentally that walk-based kernels reach or even surpass the accuracy of Weisfeiler-Leman kernels in real-world classification tasks. 5 Experimental evaluation We experimentally verify the hypotheses that have originated from our theoretical results.
Researcher Affiliation Academia Nils M. Kriege Faculty of Computer Science, University of Vienna, Währinger Straße 29, 1090 Vienna, Austria Research Network Data Science @ Uni Vienna, Kolingasse 14 16, 1090 Vienna, Austria nils.kriege@univie.ac.at
Pseudocode Yes Algorithm 1: Generalized ℓ-walk node kernel Input: Graph G = (V, E), parameters ℓand α. Output: Kernel matrices K(i) and ˆ K(i) storing ki and ˆk+WL i for i ℓ, respectively. 1 A adjacency matrix of G G 2 w 1; w+ w 3 for i 1 to ℓdo 4 w Aw 5 w+ w+ + w 6 forall (u, v) V (G G) do 7 K(i) uv wuv 8 ˆK(i) uv e α(w+ uu+w+ vv 2w+ uv) Eq. (3) 9 wuv ˆK(i) uv (WL expressiveness)
Open Source Code Yes Our code is publicly available at https://github.com/nlskrg/node_centric_walk_kernels.
Open Datasets Yes We tested on widely-used graph classification benchmarks datasets of the TUDATASETS repository [32] representing graphs from different domains. MUTAG, NCI1, NCI109 and PTC-FM represent small molecules, ENZYMES and PROTEINS are derived from macromolecules, and COLLAB and IMDBBIN are social networks. All used datasets are publicly available.
Dataset Splits Yes We report mean prediction accuracies and standard deviations obtained by 10-fold nested cross-validation repeated 10 times with random fold assignment. Within each fold all necessary parameters were selected by cross-validation based on the training set.
Hardware Specification Yes All experiments were performed on an Intel Xeon E5-2690v4 machine at 2.6GHz with 384 GB of RAM.
Software Dependencies No We implemented the node-centric ℓ-walk graph kernel as well as all baselines in Java. We performed classification experiments with the C-SVM implementation LIBSVM [6]. However, specific version numbers for Java or LIBSVM are not provided.
Experiment Setup Yes For the Weisfeiler-Leman subtree kernel (WL), the ℓ-step random walk kernel (RW) as well as NCW and NCWWL we chose the iteration number and walk length from {0, . . . , 5} by cross-validation. For RW, λi = 1 for i {0, . . . , ℓ} was used. For NCW and NCWWL, we selected α from {0.01, 0.1, 1, 1000} and β from {0, 0.5, 1}.