{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T13:50:23Z","timestamp":1765547423772,"version":"3.41.0"},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:00:00Z","timestamp":1746057600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T00:00:00Z","timestamp":1746748800000},"content-version":"vor","delay-in-days":8,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62172451"],"award-info":[{"award-number":["62172451"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. King Saud Univ. Comput. Inf. Sci."],"published-print":{"date-parts":[[2025,5]]},"DOI":"10.1007\/s44443-025-00046-x","type":"journal-article","created":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T10:44:58Z","timestamp":1746787498000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Improving hierarchical graph pooling with information bottleneck"],"prefix":"10.1007","volume":"37","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0163-0007","authenticated-orcid":false,"given":"Jun","family":"Long","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-6285-8806","authenticated-orcid":false,"given":"Zidong","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tingxuan","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8319-0724","authenticated-orcid":false,"given":"Liu","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,9]]},"reference":[{"issue":"1","key":"46_CR1","first-page":"1947","volume":"19","author":"A Achille","year":"2018","unstructured":"Achille A, Soatto S (2018) Emergence of invariance and disentanglement in deep representations. J Mach Learn Res 19(1):1947\u20131980","journal-title":"J Mach Learn Res"},{"issue":"12","key":"46_CR2","doi-asserted-by":"publisher","first-page":"2897","DOI":"10.1109\/TPAMI.2017.2784440","volume":"40","author":"A Achille","year":"2018","unstructured":"Achille A, Soatto S (2018) Information dropout: learning optimal representations through noisy computation. IEEE Trans Pattern Anal Mach Intell 40(12):2897\u20132905","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"46_CR3","unstructured":"Ahmadi AHK, Hassani K, Moradi P, Lee L, Morris Q (2020) Memory-based graph networks. In: Proceedings of the 8th international conference on learning representations"},{"key":"46_CR4","unstructured":"Alemi AA, Fischer I, Dillon JV, Murphy K (2017) Deep variational information bottleneck. In: Proceedings of the 5th international conference on learning representations"},{"key":"46_CR5","unstructured":"Bianchi FM, Grattarola D, Alippi C (2020) Spectral clustering with graph neural networks for graph pooling. In: Proceedings of the 37th international conference on machine learning, pp 874\u2013883"},{"key":"46_CR6","doi-asserted-by":"publisher","first-page":"P10008","DOI":"10.1088\/1742-5468\/2008\/10\/P10008","volume":"10","author":"VD Blondel","year":"2008","unstructured":"Blondel VD, Guillaume J-L, Lambiotte R (2008) Lefebvre E (2008) Fast unfolding of communities in large networks. J Stat Mech Theory Exper 10:P10008","journal-title":"J Stat Mech Theory Exper"},{"key":"46_CR7","doi-asserted-by":"crossref","unstructured":"Borgwardt KM, Ong CS, Stefan SSVN, Vishwanathan AJ, Smola, Hans-Peter K (2005) Protein function prediction via graph kernels. Bioinformatics 21(1):47\u201356","DOI":"10.1093\/bioinformatics\/bti1007"},{"issue":"4","key":"46_CR8","doi-asserted-by":"publisher","first-page":"771","DOI":"10.1016\/S0022-2836(03)00628-4","volume":"330","author":"PD Dobson","year":"2003","unstructured":"Dobson PD, Doig AJ (2003) Distinguishing enzyme structures from non-enzymes without alignments. J Molecular Biology 330(4):771\u2013783","journal-title":"J Molecular Biology"},{"key":"46_CR9","unstructured":"Errica F, Podda M, Bacciu D, Micheli A (2020) A fair comparison of graph neural networks for graph classification. In: Proceedings of the 8th international conference on learning representations"},{"key":"46_CR10","doi-asserted-by":"crossref","unstructured":"Fey M, Lenssen JE, Weichert F, M\u00fcller H (2018) Splinecnn: fast geometric deep learning with continuous b-spline kernels. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 869\u2013877,","DOI":"10.1109\/CVPR.2018.00097"},{"issue":"9","key":"46_CR11","first-page":"4948","volume":"44","author":"H Gao","year":"2022","unstructured":"Gao H, Ji S (2022) Graph u-nets. IEEE Trans Pattern Anal Mach Intell 44(9):4948\u20134960","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"9","key":"46_CR12","doi-asserted-by":"publisher","first-page":"5032","DOI":"10.1109\/TNNLS.2021.3067441","volume":"33","author":"X Gao","year":"2021","unstructured":"Gao X, Dai W, Li C, Xiong H, Frossard P (2021) ipool\u2013information-based pooling in hierarchical graph neural networks. IEEE Trans Neural Netw Learn Syst 33(9):5032\u20135044","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"46_CR13","doi-asserted-by":"crossref","unstructured":"Gao H, Chen Y, Ji S (2019) Learning graph pooling and hybrid convolutional operations for text representations. In: Proceedings of the 28th international world wide web conference, pp 2743\u20132749","DOI":"10.1145\/3308558.3313395"},{"key":"46_CR14","unstructured":"Goyal A, Islam R, Strouse D, Ahmed Z, Botvinick M, Larochelle H, Bengio Y, Levine S (2019) Infobot: transfer and exploration via the information bottleneck. In: Proceedings of the 7th International conference on learning representations"},{"key":"46_CR15","doi-asserted-by":"crossref","unstructured":"Haddadian P, Booryaee R, Abedian R, Moeini A (2024) Multi-hop attention-based graph pooling: A personalized pagerank perspective. In: 2024 Third international conference on distributed computing and high performance computing, IEEE, pp 1\u20137","DOI":"10.1109\/DCHPC60845.2024.10454077"},{"key":"46_CR16","doi-asserted-by":"crossref","unstructured":"He K, Zhang X, Ren S, Sun J (2016) Deep residual learning for image recognition. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 770\u2013778","DOI":"10.1109\/CVPR.2016.90"},{"key":"46_CR17","unstructured":"Igl M, Ciosek K, Li Y, Tschiatschek S, Zhang C, Devlin S, Hofmann K (2019) Generalization in reinforcement learning with selective noise injection and information bottleneck. In: Proceedings of the 33rd international conference on neural information processing systems, pp 13979\u201313991"},{"key":"46_CR18","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1016\/j.neunet.2021.11.001","volume":"145","author":"TD Itoh","year":"2022","unstructured":"Itoh TD, Kubo T, Ikeda K (2022) Multi-level attention pooling for graph neural networks: unifying graph representations with multiple localities. Neural Netw 145:356\u2013373","journal-title":"Neural Netw"},{"key":"46_CR19","doi-asserted-by":"crossref","unstructured":"Jindong G (2021) Interpretable graph capsule networks for object recognition. In: Proceedings of the AAAI conference on artificial intelligence, pp 1469\u20131477,","DOI":"10.1609\/aaai.v35i2.16237"},{"key":"46_CR20","unstructured":"Junchi Y, Cao J, He R (2022) Improving subgraph recognition with variational graph information bottleneck. In: Proceedings of the IEEE\/CVF conference on computer vision and pattern recognition, pp 19396\u201319405"},{"key":"46_CR21","unstructured":"Junchi Y, Tingyang X, Rong Y, Bian Y, Huang J, He R (2021) Recognizing predictive substructures with subgraph information bottleneck. IEEE Trans Pattern Anal Mach Intell:1\u20131"},{"key":"46_CR22","unstructured":"Keyulu X, Weihua H, Leskovec J, Jegelka S (2018) How powerful are graph neural networks? In: Proceedings of the 6th international conference on learning representations"},{"key":"46_CR23","unstructured":"Kingma DP, Salimans T, Welling M (2015) Variational dropout and the local reparameterization trick. Advan Neural Inform Process Syst:2575\u20132583"},{"key":"46_CR24","unstructured":"Kingma DP, Welling M (2014) Auto-encoding variational bayes. In: Proceedings of the 2nd international conference on learning representations"},{"key":"46_CR25","unstructured":"Kipf TN, Welling M (2017) Semi-supervised classification with graph convolutional networks. In: Proceedings of the 5th international conference on learning representations"},{"key":"46_CR26","unstructured":"Lee J, Lee I, Kang J (2019) Self-attention graph pooling. In: Proceedings of the 36th international conference on machine learning, pp 6661\u20136670"},{"issue":"4","key":"46_CR27","doi-asserted-by":"publisher","first-page":"3952","DOI":"10.1109\/TKDE.2021.3133646","volume":"35","author":"N Liu","year":"2023","unstructured":"Liu N, Jian S, Li D, Zhang Y, Lai Z, Hongzuo X (2023) Hierarchical adaptive pooling by capturing high-order dependency for graph representation learning. IEEE Trans Knowl Data Eng 35(4):3952\u20133965","journal-title":"IEEE Trans Knowl Data Eng"},{"key":"46_CR28","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1016\/j.neunet.2023.08.046","volume":"167","author":"C Liu","year":"2023","unstructured":"Liu C, Zhan Y, Baosheng Y, Liu L, Bo D, Wenbin H, Liu T (2023) On exploring node-feature and graph-structure diversities for node drop graph pooling. Neural Netw 167:559\u2013571","journal-title":"Neural Netw"},{"key":"46_CR29","doi-asserted-by":"crossref","unstructured":"Liu C, Zhan Y, Li C, Bo D, Jia W, Wenbin H, Liu T, Tao D (2022) Graph pooling for graph neural networks: progress, challenges, and opportunities. arXiv:2204.07321","DOI":"10.24963\/ijcai.2023\/752"},{"key":"46_CR30","doi-asserted-by":"crossref","unstructured":"Luo Y, Liu P, Guan T, Junqing Y, Yang Y (2019) Significance-aware information bottleneck for domain adaptive semantic segmentation. In: 2019 IEEE\/CVF International Conference on Computer Vision (ICCV), pp 6777\u20136786","DOI":"10.1109\/ICCV.2019.00688"},{"key":"46_CR31","unstructured":"Ma X, Jia W, Xue S, Yang J, Zhou C, Sheng QZ, Xiong H, Akoglu L (2021) A comprehensive survey on graph anomaly detection with deep learning. IEEE Trans Knowl Data Eng:1\u20131"},{"key":"46_CR32","unstructured":"Peng XB, Kanazawa A, Toyer S, Abbeel P, Levine S (2019) Variational discriminator bottleneck: Improving imitation learning, inverse rl, and gans by constraining information flow. In: Proceedings of the 7th international conference on learning representations"},{"key":"46_CR33","unstructured":"Pinar Y, SVN V (2015) Deep graph kernels. In: Proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, pp 1365\u20131374"},{"key":"46_CR34","doi-asserted-by":"crossref","unstructured":"Ranjan E, Sanyal S, Talukdar P (2020) Asap: adaptive structure aware pooling for learning hierarchical graph representations. In: Proceedings of the AAAI conference on artificial intelligence, pp 5470\u20135477","DOI":"10.1609\/aaai.v34i04.5997"},{"key":"46_CR35","doi-asserted-by":"crossref","unstructured":"Roy KK, Amit RAKM, Mahbubur RM, Amin A, Ali AA (2021) Structure-aware hierarchical graph pooling using information bottleneck. In: 2021 International Joint Conference on Neural Networks (IJCNN), IEEE, pp 1\u20138","DOI":"10.1109\/IJCNN52387.2021.9533778"},{"key":"46_CR36","unstructured":"Rundong WX, He RY, Wei q, Bo A, Zinovi R (2020) Learning efficient multi-agent communication: an information bottleneck approach. In: Proceedings of the 37th international conference on machine learning, pp 9908\u20139918"},{"key":"46_CR37","doi-asserted-by":"crossref","unstructured":"Sun Q, Li J, Peng H, Jia W, Xingcheng F, Ji C, Yu PS (2022) Graph structure learning with variational information bottleneck. In: Proceedings of the AAAI conference on artificial intelligence, pp 4165\u20134174,","DOI":"10.1609\/aaai.v36i4.20335"},{"key":"46_CR38","unstructured":"Tailin W, Ren H, Li P, Leskovec J (2020) Graph information bottleneck. In: Proceedings of the 34th international conference on neural information processing systems, pp 20437\u201320448"},{"key":"46_CR39","unstructured":"Tishby N, Pereira FC, William B (2000) The information bottleneck method. arXiv preprint physics\/0004057"},{"key":"46_CR40","doi-asserted-by":"crossref","unstructured":"Tishby N, Zaslavsky N (2015) Deep learning and the information bottleneck principle. In: 2015 IEEE Information Theory Workshop (ITW), IEEE, pp 1\u20135","DOI":"10.1109\/ITW.2015.7133169"},{"key":"46_CR41","unstructured":"Vinyals O, Bengio S, Kudlur M (2016) Order matters: sequence to sequence for sets. In: Proceedings of the 4th international conference on learning representations"},{"key":"46_CR42","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1007\/s10115-007-0103-5","volume":"14","author":"N Wale","year":"2008","unstructured":"Wale N, Watson IA, Karypis G (2008) Comparison of descriptor spaces for chemical compound retrieval and classification. Knowl Inform Syst 14:347\u2013375","journal-title":"Knowl Inform Syst"},{"key":"46_CR43","unstructured":"Xiang LL, Jason E (2019) Specializing word embeddings (for parsing) by information bottleneck. In: Proceedings of the 2019 conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), pp 2744\u20132754"},{"key":"46_CR44","doi-asserted-by":"crossref","unstructured":"Yang L, Fan W, Zheng Z, Niu B, Junhua G, Wang C, Cao X, Guo Y (2021) Heterogeneous graph information bottleneck. In: Proceedings of the thirtieth international joint conference on artificial intelligence, pp 1638\u20131645","DOI":"10.24963\/ijcai.2021\/226"},{"key":"46_CR45","doi-asserted-by":"crossref","unstructured":"Yang J, Peilin ZY, Rong CY, Li C, Ma H, Huang J (2021) Hierarchical graph capsule network. In: Proceedings of the AAAI conference on artificial intelligence, pp 10603\u201310611","DOI":"10.1609\/aaai.v35i12.17268"},{"key":"46_CR46","doi-asserted-by":"crossref","unstructured":"Yi H-C, You Z-H, Huang D-S, Kwoh CK (2022) Graph representation learning in bioinformatics: trends, methods and applications. Briefings Bioinform 23(1)","DOI":"10.1093\/bib\/bbab340"},{"key":"46_CR47","unstructured":"Ying R, You J, Morris C, Ren X, Hamilton WL, Leskovec J (2018) Hierarchical graph representation learning with differentiable pooling. In: Proceedings of the 32nd international conference on neural information processing systems, pp 4805\u20134815"},{"key":"46_CR48","unstructured":"Yuan H, Ji S (2020) Structpool: structured graph pooling via conditional random fields. In: Proceedings of the 8th international conference on learning representations"},{"issue":"1","key":"46_CR49","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1109\/TBDATA.2018.2850013","volume":"6","author":"Daokun Zhang","year":"2020","unstructured":"Zhang Daokun, Yin Jie, Zhu Xingquan, Zhang Chengqi (2020) Network representation learning: a survey. IEEE Trans Big Data 6(1):3\u201328","journal-title":"IEEE Trans Big Data"},{"issue":"1","key":"46_CR50","first-page":"545","volume":"35","author":"Z Zhang","year":"2021","unstructured":"Zhang Z, Jiajun B, Ester M, Zhang J, Li Z, Yao C, Dai H, Zhi Y, Wang C (2021) Hierarchical multi-view graph pooling with structure learning. IEEE Trans Knowl Data Eng 35(1):545\u2013559","journal-title":"IEEE Trans Knowl Data Eng"},{"key":"46_CR51","doi-asserted-by":"crossref","unstructured":"Zhang M, Cui Z, Neumann M, Chen Y (2018) An end-to-end deep learning architecture for graph classification. In: Proceedings of the thirty-second aaai conference on artificial intelligence and thirtieth innovative applications of artificial intelligence conference and eighth AAAI symposium on educational advances in artificial intelligence, pp 4438\u20134445","DOI":"10.1609\/aaai.v32i1.11782"},{"key":"46_CR52","doi-asserted-by":"crossref","unstructured":"Zhang L, Wang X, Li H, Zhu G, Shen P, Li P, Xiaoyuan L, Shah SAA, Bennamoun M (2020) Structure-feature based graph self-adaptive pooling. In: Proceedings of the 29th international world wide web conference, pp 3098\u20133104","DOI":"10.1145\/3366423.3380083"},{"key":"46_CR53","doi-asserted-by":"publisher","first-page":"110089","DOI":"10.1016\/j.knosys.2022.110089","volume":"260","author":"Q Zhao","year":"2023","unstructured":"Zhao Q, Zhang H, He M, Li W, Kang C, Han M (2023) Graph pooling via dual-view multi-level infomax. Knowl-Based Syst 260:110089","journal-title":"Knowl-Based Syst"}],"container-title":["Journal of King Saud University Computer and Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44443-025-00046-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s44443-025-00046-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44443-025-00046-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T11:46:02Z","timestamp":1748605562000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s44443-025-00046-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5]]},"references-count":53,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,5]]}},"alternative-id":["46"],"URL":"https:\/\/doi.org\/10.1007\/s44443-025-00046-x","relation":{},"ISSN":["1319-1578","2213-1248"],"issn-type":[{"type":"print","value":"1319-1578"},{"type":"electronic","value":"2213-1248"}],"subject":[],"published":{"date-parts":[[2025,5]]},"assertion":[{"value":"11 February 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 April 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 May 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All authors have no conflicts of interest to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}],"article-number":"36"}}