{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T15:13:17Z","timestamp":1775229197699,"version":"3.50.1"},"reference-count":56,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"2","license":[{"start":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T00:00:00Z","timestamp":1706745600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T00:00:00Z","timestamp":1706745600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T00:00:00Z","timestamp":1706745600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation through the Project \u201cA Learning graPh-baSed framework FOr cybeR-physical sysTems (ALPSFORT)\u201d","doi-asserted-by":"publisher","award":["200021 172671"],"award-info":[{"award-number":["200021 172671"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Neural Netw. Learning Syst."],"published-print":{"date-parts":[[2024,2]]},"DOI":"10.1109\/tnnls.2022.3190922","type":"journal-article","created":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T19:28:20Z","timestamp":1658431700000},"page":"2708-2718","source":"Crossref","is-referenced-by-count":83,"title":["Understanding Pooling in Graph Neural Networks"],"prefix":"10.1109","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9506-037X","authenticated-orcid":false,"given":"Daniele","family":"Grattarola","sequence":"first","affiliation":[{"name":"Faculty of Informatics, Università della Svizzera italiana (USI), Lugano, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3722-9784","authenticated-orcid":false,"given":"Daniele","family":"Zambon","sequence":"additional","affiliation":[{"name":"Faculty of Informatics, Università della Svizzera italiana (USI), Lugano, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7145-3846","authenticated-orcid":false,"given":"Filippo Maria","family":"Bianchi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, UiT the Arctic University of Norway, Tromsø, Norway"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3819-0025","authenticated-orcid":false,"given":"Cesare","family":"Alippi","sequence":"additional","affiliation":[{"name":"Faculty of Informatics, Università della Svizzera italiana (USI), Lugano, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref1","article-title":"Neural message passing for quantum chemistry","author":"Gilmer","year":"2017","journal-title":"arXiv:1704.01212"},{"key":"ref2","article-title":"Relational inductive biases, deep learning, and graph networks","author":"Battaglia","year":"2018","journal-title":"arXiv:1806.01261"},{"key":"ref3","article-title":"Understanding attention and generalization in graph neural networks","author":"Knyazev","year":"2019","journal-title":"arXiv:1905.02850"},{"key":"ref4","first-page":"1","article-title":"Rethinking pooling in graph neural networks","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","volume":"33","author":"Mesquita"},{"key":"ref5","article-title":"Towards interpretable sparse graph representation learning with Laplacian pooling","author":"Noutahi","year":"2019","journal-title":"arXiv:1905.11577"},{"key":"ref6","first-page":"7090","article-title":"Universal invariant and equivariant graph neural networks","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Keriven"},{"key":"ref7","first-page":"4363","article-title":"On the universality of invariant networks","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Maron"},{"key":"ref8","article-title":"Fast graph representation learning with PyTorch geometric","author":"Fey","year":"2019","journal-title":"arXiv:1903.02428"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/MCI.2020.3039072"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2007.1115"},{"key":"ref11","first-page":"3844","article-title":"Convolutional neural networks on graphs with fast localized spectral filtering","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Defferrard"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2017.576"},{"key":"ref13","article-title":"CayleyNets: Graph convolutional neural networks with complex rational spectral filters","author":"Levie","year":"2017","journal-title":"arXiv:1705.07664"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2018.00097"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2017.11"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2017.701"},{"key":"ref17","first-page":"5099","article-title":"PointNet++: Deep hierarchical feature learning on point sets in a metric space","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Qi"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2019.00986"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/0146-664X(82)90104-6"},{"issue":"116","key":"ref20","first-page":"1","article-title":"Graph reduction with spectral and cut guarantees","volume":"20","author":"Loukas","year":"2019","journal-title":"J. Mach. Learn. Res."},{"key":"ref21","article-title":"A unifying framework for spectrum-preserving graph sparsification and coarsening","author":"Bravo-Hermsdorff","year":"2019","journal-title":"arXiv:1902.09702"},{"key":"ref22","article-title":"Graph coarsening with neural networks","author":"Cai","year":"2021","journal-title":"arXiv:2102.01350"},{"key":"ref23","first-page":"1","article-title":"Clique pooling for graph classification","volume-title":"Proc. Int. Conf. Learn. Represent. (ICLR)","author":"Luzhnica"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-35166-3_21"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1145\/3292500.3330982"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2020.105578"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2020.3044146"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2012.2215780"},{"key":"ref29","article-title":"Hierarchical graph representation learning with differentiable pooling","author":"Ying","year":"2018","journal-title":"arXiv:1806.08804"},{"key":"ref30","article-title":"Deep graph mapper: Seeing graphs through the neural lens","author":"Bodnar","year":"2020","journal-title":"arXiv:2002.03864"},{"key":"ref31","first-page":"91","article-title":"Topological methods for the analysis of high dimensional data sets and 3D object recognition","volume-title":"Proc. SPBG","author":"Singh"},{"key":"ref32","article-title":"The PageRank citation ranking: Bringing order to the web","author":"Page","year":"1999"},{"key":"ref33","first-page":"874","article-title":"Spectral clustering with graph neural networks for graph pooling","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Bianchi"},{"key":"ref34","article-title":"Towards sparse hierarchical graph classifiers","author":"Cangea","year":"2018","journal-title":"arXiv:1811.01287"},{"key":"ref35","first-page":"1","article-title":"Graph U-Net","volume-title":"Proc. ICLR","author":"Gao"},{"key":"ref36","article-title":"Self-attention graph pooling","author":"Lee","year":"2019","journal-title":"arXiv:1904.08082"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v34i04.5997"},{"key":"ref38","first-page":"1","article-title":"Towards graph pooling by edge contraction","volume-title":"Proc. ICML Workshop Learn. Reasoning Graph-Structured Represent.","author":"Diehl"},{"key":"ref39","article-title":"Edge contraction pooling for graph neural networks","author":"Diehl","year":"2019","journal-title":"arXiv:1905.10990"},{"key":"ref40","first-page":"1","article-title":"StructPool: Structured graph pooling via conditional random fields","volume-title":"Proc. Int. Conf. Learn. Represent.","author":"Yuan"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1109\/tkde.2021.3090664"},{"key":"ref42","first-page":"2528","article-title":"Selecting receptive fields in deep networks","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Coates"},{"key":"ref43","article-title":"Gated graph sequence neural networks","author":"Li","year":"2015","journal-title":"arXiv:1511.05493"},{"key":"ref44","article-title":"Order matters: Sequence to sequence for sets","author":"Vinyals","year":"2015","journal-title":"arXiv:1511.06391"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1109\/IJCNN.2019.8852103"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1145\/3292500.3330950"},{"key":"ref47","article-title":"Function space pooling for graph convolutional networks","author":"Corcoran","year":"2019","journal-title":"arXiv:1905.06259"},{"key":"ref48","first-page":"1993","article-title":"Diffusion-convolutional neural networks","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Atwood"},{"key":"ref49","article-title":"How powerful are graph neural networks?","author":"Xu","year":"2018","journal-title":"arXiv:1810.00826"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.24963\/ijcai.2019\/275"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v32i1.11782"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2008.2005605"},{"key":"ref53","article-title":"A survey on the expressive power of graph neural networks","author":"Sato","year":"2020","journal-title":"arXiv:2003.04078"},{"key":"ref54","volume-title":"PyGSP: Graph Signal Processing in Python","author":"Defferrard","year":"2022"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2015.7298801"},{"key":"ref56","article-title":"TUDataset: A collection of benchmark datasets for learning with graphs","author":"Morris","year":"2020","journal-title":"arXiv:2007.08663"}],"container-title":["IEEE Transactions on Neural Networks and Learning Systems"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/5962385\/10422842\/09836996.pdf?arnumber=9836996","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,11]],"date-time":"2024-12-11T01:44:45Z","timestamp":1733881485000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9836996\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2]]},"references-count":56,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.1109\/tnnls.2022.3190922","relation":{},"ISSN":["2162-237X","2162-2388"],"issn-type":[{"value":"2162-237X","type":"print"},{"value":"2162-2388","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2]]}}}