{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T19:08:02Z","timestamp":1754161682222,"version":"3.41.2"},"publisher-location":"Cham","reference-count":27,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031995644"},{"type":"electronic","value":"9783031995651"}],"license":[{"start":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T00:00:00Z","timestamp":1753833600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T00:00:00Z","timestamp":1753833600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-031-99565-1_30","type":"book-chapter","created":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T06:42:23Z","timestamp":1753771343000},"page":"391-402","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-Hop Pooling: Leveraging Transition Matrices for\u00a0Hierarchical Graph Representation Learning"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-8733-2072","authenticated-orcid":false,"given":"Ahmed","family":"Begga","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3238-4021","authenticated-orcid":false,"given":"Francisco","family":"Escolano","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4757-5587","authenticated-orcid":false,"given":"Miguel Angel","family":"Lozano","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,30]]},"reference":[{"key":"30_CR1","unstructured":"Abu-El-Haija, S., et al.: Mixhop: higher-order graph convolutional architectures via sparsified neighborhood mixing. In: Proceedings of the 36th International Conference on Machine Learning, ICML. Proceedings of Machine Learning Research, vol.\u00a097, pp. 21\u201329. PMLR (2019)"},{"key":"30_CR2","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/J.PATREC.2024.09.009","volume":"186","author":"W Ali","year":"2024","unstructured":"Ali, W., Vascon, S., Stadelmann, T., Pelillo, M.: Hierarchical glocal attention pooling for graph classification. Pattern Recognit. Lett. 186, 71\u201377 (2024). https:\/\/doi.org\/10.1016\/J.PATREC.2024.09.009","journal-title":"Pattern Recognit. Lett."},{"key":"30_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/J.NEUNET.2024.106830","volume":"181","author":"A Begga","year":"2025","unstructured":"Begga, A., Escolano, F., Lozano, M.A.: Node classification in the heterophilic regime via diffusion-jump GNNS. Neural Netw. 181, 106830 (2025). https:\/\/doi.org\/10.1016\/J.NEUNET.2024.106830","journal-title":"Neural Netw."},{"key":"30_CR4","unstructured":"Chung, F.: Spectral Graph Theory. American Mathematical Society, Providence (1997)"},{"key":"30_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/J.PATCOG.2024.110606","volume":"154","author":"S Deng","year":"2024","unstructured":"Deng, S., et al.: Module-based graph pooling for graph classification. Pattern Recognit. 154, 110606 (2024). https:\/\/doi.org\/10.1016\/J.PATCOG.2024.110606","journal-title":"Pattern Recognit."},{"key":"30_CR6","doi-asserted-by":"publisher","unstructured":"Du, J., Wang, S., Miao, H., Zhang, J.: Multi-channel pooling graph neural networks. In: Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI 2021, pp. 1442\u20131448. IJCAI. org (2021). https:\/\/doi.org\/10.24963\/IJCAI.2021\/199","DOI":"10.24963\/IJCAI.2021\/199"},{"key":"30_CR7","unstructured":"Duvenaud, D., et al.: Convolutional networks on graphs for learning molecular fingerprints. CoRR abs\/1509.09292 (2015)"},{"key":"30_CR8","unstructured":"Feng, J., Chen, Y., Li, F., Sarkar, A., Zhang, M.: How powerful are k-hop message passing graph neural networks. In: Advances in Neural Information Processing Systems 35: Annual Conference on Neural Information Processing Systems 2022, NeurIPS 2022 (2022)"},{"issue":"9","key":"30_CR9","doi-asserted-by":"publisher","first-page":"4948","DOI":"10.1109\/TPAMI.2021.3081010","volume":"44","author":"H Gao","year":"2022","unstructured":"Gao, H., Ji, S.: Graph u-nets. IEEE Trans. Pattern Anal. Mach. Intell. 44(9), 4948\u20134960 (2022). https:\/\/doi.org\/10.1109\/TPAMI.2021.3081010","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"30_CR10","unstructured":"Gilmer, J., Schoenholz, S.S., Riley, P.F., Vinyals, O., Dahl, G.E.: Neural message passing for quantum chemistry. Paper presented at ICML 2017, Sydney, Australia, 6\u201311 Aug 2017"},{"key":"30_CR11","unstructured":"Hamilton, W.L., Ying, Z., Leskovec, J.: Inductive representation learning on large graphs. In: Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, pp. 1024\u20131034 (2017)"},{"key":"30_CR12","unstructured":"Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. Paper Presented at ICLR 2017, Toulon, France, 24\u201326 Apr 2017"},{"key":"30_CR13","unstructured":"Lee, J., Lee, I., Kang, J.: Self-attention graph pooling. In: Proceedings of the 36th International Conference on Machine Learning, ICML 2019. Proceedings of Machine Learning Research, vol.\u00a097, pp. 3734\u20133743. PMLR (2019)"},{"issue":"2","key":"30_CR14","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/S10462-024-10949-2","volume":"58","author":"Z Li","year":"2025","unstructured":"Li, Z., et al.: Graph pooling for graph-level representation learning: a survey. Artif. Intell. Rev. 58(2), 45 (2025). https:\/\/doi.org\/10.1007\/S10462-024-10949-2","journal-title":"Artif. Intell. Rev."},{"key":"30_CR15","doi-asserted-by":"publisher","unstructured":"Liu, C., et al.: Graph pooling for graph neural networks: Progress, challenges, and opportunities. CoRR abs\/2204.07321 (2022). https:\/\/doi.org\/10.48550\/ARXIV.2204.07321","DOI":"10.48550\/ARXIV.2204.07321"},{"issue":"4","key":"30_CR16","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/S11222-007-9033-Z","volume":"17","author":"U von Luxburg","year":"2007","unstructured":"von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395\u2013416 (2007). https:\/\/doi.org\/10.1007\/S11222-007-9033-Z","journal-title":"Stat. Comput."},{"key":"30_CR17","unstructured":"Luzhnica, E., Day, B., Li\u00f2, P.: Clique pooling for graph classification. CoRR abs\/1904.00374 (2019)"},{"key":"30_CR18","unstructured":"Morris, C., Kriege, N.M., Bause, F., Kersting, K., Mutzel, P., Neumann, M.: Tudataset: a collection of benchmark datasets for learning with graphs. arXiv preprint arXiv:2007.08663 (2020)"},{"key":"30_CR19","unstructured":"Ranjan, E., Sanyal, S., Talukdar, P.P.: ASAP: adaptive structure aware pooling for learning hierarchical graph representations. CoRR abs\/1911.07979 (2019)"},{"issue":"8","key":"30_CR20","doi-asserted-by":"publisher","first-page":"888","DOI":"10.1109\/34.868688","volume":"22","author":"J Shi","year":"2000","unstructured":"Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888\u2013905 (2000). https:\/\/doi.org\/10.1109\/34.868688","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"30_CR21","unstructured":"Velickovic, P., Cucurull, G., Casanova, A., Romero, A., Li\u00f2, P., Bengio, Y.: Graph attention networks. Paper Presented at ICLR 2018"},{"key":"30_CR22","unstructured":"Vinyals, O., Bengio, S., Kudlur, M.: Order matters: sequence to sequence for sets. In: 4th International Conference on Learning Representations, ICLR 2016, San Juan, Puerto Rico, May 2-4, 2016, Conference Track Proceedings (2016)"},{"key":"30_CR23","unstructured":"Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., Yu, P.S.: A comprehensive survey on graph neural networks. CoRR abs\/1901.00596 (2019)"},{"key":"30_CR24","unstructured":"Xu, K., Hu, W., Leskovec, J., Jegelka, S.: How powerful are graph neural networks? In: 7th International Conference on Learning Representations, ICLR 2019. OpenReview.net (2019)"},{"issue":"2","key":"30_CR25","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1109\/TCSS.2022.3169219","volume":"10","author":"Y Xu","year":"2023","unstructured":"Xu, Y., Wang, J., Guang, M., Yan, C., Jiang, C.: Multistructure graph classification method with attention-based pooling. IEEE Trans. Comput. Soc. Syst. 10(2), 602\u2013613 (2023). https:\/\/doi.org\/10.1109\/TCSS.2022.3169219","journal-title":"IEEE Trans. Comput. Soc. Syst."},{"key":"30_CR26","unstructured":"Ying, Z., You, J., Morris, C., Ren, X., Hamilton, W.L., Leskovec, J.: Hierarchical graph representation learning with differentiable pooling. In: Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, pp. 4805\u20134815 (2018)"},{"key":"30_CR27","doi-asserted-by":"publisher","unstructured":"Zhang, M., Cui, Z., Neumann, M., Chen, Y.: An end-to-end deep learning architecture for graph classification. In: Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, pp. 4438\u20134445. AAAI Press (2018). https:\/\/doi.org\/10.1609\/AAAI.V32I1.11782","DOI":"10.1609\/AAAI.V32I1.11782"}],"container-title":["Lecture Notes in Computer Science","Pattern Recognition and Image Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-99565-1_30","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T06:42:34Z","timestamp":1753771354000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-99565-1_30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,30]]},"ISBN":["9783031995644","9783031995651"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-99565-1_30","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2025,7,30]]},"assertion":[{"value":"30 July 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"IbPRIA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Iberian Conference on Pattern Recognition and Image Analysis","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Coimbra","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Portugal","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 July 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4 July 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ibpria2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.ibpria.org\/2025\/?page=home","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}