{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T15:38:52Z","timestamp":1780501132498,"version":"3.54.1"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T00:00:00Z","timestamp":1605225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Graph Neural Networks (GNNs) have received wide acclaim in recent times due to their performance on inference tasks for unstructured data. Typically, GNNs operate by exploiting local structural information in graphs and disregarding their global structure. This is influenced by assumptions of homophily and unbiased class distributions. As a result, this could impede model performance on noisy real-world graphs such as spatial graphs where these assumptions may not be sufficiently held. In this article, we study the problem of graph learning on spatial graphs. Particularly, we focus on transductive learning methods for the imbalanced case. Given the nature of these graphs, we hypothesize that taking the global structure of the graph into account when aggregating local information would be beneficial especially with respect to generalisability. Thus, we propose a novel approach to training GNNs for these type of graphs. We achieve this through a sampling technique: Structure-Aware Sampling (SAS), which leverages the intra-class and global-geodesic distances between nodes. We model the problem as a node classification one for street networks with high variance between class sizes. We evaluate our approach using large real-world graphs against state-of-the-art methods. In the majority of cases, our approach outperforms traditional methods by up to a mean F1-score of 20%.<\/jats:p>","DOI":"10.3390\/ijgi9110674","type":"journal-article","created":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T08:44:02Z","timestamp":1605257042000},"page":"674","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Improved Graph Neural Networks for Spatial Networks Using Structure-Aware Sampling"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8677-3159","authenticated-orcid":false,"given":"Chidubem","family":"Iddianozie","sequence":"first","affiliation":[{"name":"School of Computer Science, University College Dublin, Dublin 4, Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0613-546X","authenticated-orcid":false,"given":"Gavin","family":"McArdle","sequence":"additional","affiliation":[{"name":"School of Computer Science, University College Dublin, Dublin 4, Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,13]]},"reference":[{"key":"ref_1","unstructured":"Battaglia, P.W., Hamrick, J.B., Bapst, V., Sanchez-Gonzalez, A., Zambaldi, V., Malinowski, M., Tacchetti, A., Raposo, D., Santoro, A., and Faulkner, R. (2018). Relational inductive biases, deep learning, and graph networks. arXiv."},{"key":"ref_2","unstructured":"Li, J., Cai, D., and He, X. (2017). Learning graph-level representation for drug discovery. arXiv."},{"key":"ref_3","unstructured":"Tolstaya, E., Gama, F., Paulos, J., Pappas, G., Kumar, V., and Ribeiro, A. (2019). Learning decentralized controllers for robot swarms with graph neural networks. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Liu, Z., Chen, C., Yang, X., Zhou, J., Li, X., and Song, L. (2018, January 22\u201326). Heterogeneous graph neural networks for malicious account detection. Proceedings of the 27th ACM International Conference on Information and Knowledge Management, Turin, Italy.","DOI":"10.1145\/3269206.3272010"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Corcoran, P., Jilani, M., Mooney, P., and Bertolotto, M. (2015, January 3\u20136). Inferring semantics from geometry: The case of street networks. Proceedings of the 23rd SIGSPATIAL International Conference on Advances in Geographic Information Systems, Bellevue, WA, USA.","DOI":"10.1145\/2820783.2820822"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Iddianozie, C., and McArdle, G. (2019, January 8\u201312). A transfer learning paradigm for spatial networks. Proceedings of the 34th ACM\/SIGAPP Symposium on Applied Computing, Limassol, Cyprus.","DOI":"10.1145\/3297280.3297342"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"32258","DOI":"10.1109\/ACCESS.2020.2973885","article-title":"Exploring Budgeted Learning for Data-Driven Semantic Inference via Urban Functions","volume":"8","author":"Iddianozie","year":"2020","journal-title":"IEEE Access"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"He, S., Bastani, F., Jagwani, S., Park, E., Abbar, S., Alizadeh, M., Balakrishnan, H., Chawla, S., Madden, S., and Sadeghi, M.A. (2020, January 7\u201312). RoadTagger: Robust Road Attribute Inference with Graph Neural Networks. Proceedings of the Thirty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2020, New York, NY, USA.","DOI":"10.1609\/aaai.v34i07.6730"},{"key":"ref_9","first-page":"1995","article-title":"Convolutional networks for images, speech, and time series","volume":"3361","author":"LeCun","year":"1995","journal-title":"Handb. Brain Theory Neural Netw."},{"key":"ref_10","unstructured":"Karpathy, A., Johnson, J., and Fei-Fei, L. (2015). Visualizing and understanding recurrent networks. arXiv."},{"key":"ref_11","unstructured":"Kipf, T.N., and Welling, M. (2016). Semi-supervised classification with graph convolutional networks. arXiv."},{"key":"ref_12","unstructured":"Veli\u010dkovi\u0107, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., and Bengio, Y. (2017). Graph attention networks. arXiv."},{"key":"ref_13","unstructured":"Hamilton, W., Ying, Z., and Leskovec, J. (2017, January 4\u20139). Inductive representation learning on large graphs. Proceedings of the Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, Long Beach, CA, USA."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Jepsen, T.S., Jensen, C.S., and Nielsen, T.D. (2019, January 5\u20138). Graph convolutional networks for road networks. Proceedings of the 27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, Chicago, IL, USA.","DOI":"10.1145\/3347146.3359094"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Roth, C., Kang, S.M., Batty, M., and Barth\u00e9lemy, M. (2011). Structure of urban movements: Polycentric activity and entangled hierarchical flows. PLoS ONE, 6.","DOI":"10.1371\/journal.pone.0015923"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2010.11.002","article-title":"Spatial networks","volume":"499","year":"2011","journal-title":"Phys. Rep."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Li, Q., Han, Z., and Wu, X.M. (2018, January 2\u20137). Deeper insights into graph convolutional networks for semi-supervised learning. Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, Riverside, NO, USA.","DOI":"10.1609\/aaai.v32i1.11604"},{"key":"ref_18","unstructured":"Rong, Y., Huang, W., Xu, T., and Huang, J. (2019). Dropedge: Towards deep graph convolutional networks on node classification. arXiv."},{"key":"ref_19","unstructured":"Bruna, J., Zaremba, W., Szlam, A., and LeCun, Y. (2013). Spectral networks and locally connected networks on graphs. arXiv."},{"key":"ref_20","unstructured":"Duvenaud, D.K., Maclaurin, D., Iparraguirre, J., Bombarell, R., Hirzel, T., Aspuru-Guzik, A., and Adams, R.P. (2015, January 7\u201312). Convolutional networks on graphs for learning molecular fingerprints. Proceedings of the Advances in Neural Information Processing Systems 28: Annual Conference on Neural Information Processing Systems 2015, Montreal, QC, Canada."},{"key":"ref_21","unstructured":"Defferrard, M., Bresson, X., and Vandergheynst, P. (2016, January 5\u201310). Convolutional neural networks on graphs with fast localized spectral filtering. Proceedings of the Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems 2016, Barcelona, Spain."},{"key":"ref_22","unstructured":"Zhou, J., Cui, G., Zhang, Z., Yang, C., Liu, Z., Wang, L., Li, C., and Sun, M. (2018). Graph neural networks: A review of methods and applications. arXiv."},{"key":"ref_23","unstructured":"Diao, Z., Wang, X., Zhang, D., Liu, Y., Xie, K., and He, S. (February, January 27). Dynamic spatial-temporal graph convolutional neural networks for traffic forecasting. Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence, Honolulu, HI, USA."},{"key":"ref_24","unstructured":"Bonafilia, D., Gill, J., Basu, S., and Yang, D. (2019, January 16\u201317). Building High Resolution Maps for Humanitarian Aid and Development with Weakly-and Semi-Supervised Learning. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, Long Beach, CA, USA."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1347","DOI":"10.3390\/rs6021347","article-title":"Ontology-based classification of building types detected from airborne laser scanning data","volume":"6","author":"Belgiu","year":"2014","journal-title":"Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1111\/j.1538-4632.1992.tb00262.x","article-title":"Network autocorrelation in transport network and flow systems","volume":"24","author":"Black","year":"1992","journal-title":"Geogr. Anal."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Chen, J., Lai, C., Meng, X., Xu, J., and Hu, H. (2007). Clustering moving objects in spatial networks. International Conference on Database Systems for Advanced Applications, Springer.","DOI":"10.1007\/978-3-540-71703-4_52"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Kaul, M., Yang, B., and Jensen, C.S. (2013, January 3\u20136). Building accurate 3d spatial networks to enable next generation intelligent transportation systems. Proceedings of the 2013 IEEE 14th International Conference on Mobile Data Management, Milan, Italy.","DOI":"10.1109\/MDM.2013.24"},{"key":"ref_29","unstructured":"Gilmer, J., Schoenholz, S.S., Riley, P.F., Vinyals, O., and Dahl, G.E. (2017, January 6\u201311). Neural message passing for quantum chemistry. Proceedings of the 34th International Conference on Machine Learning, ICML 2017, Sydney, NSW, Australia."},{"key":"ref_30","first-page":"185","article-title":"On the pairing of the softmax activation and cross-entropy penalty functions and the derivation of the softmax activation function","volume":"Volume 181","author":"Dunne","year":"1997","journal-title":"Proceedings of the 8th Australia Conference on the Neural Networks 1997"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Oldham, S., Fulcher, B., Parkes, L., Arnatkeviciute, A., Suo, C., and Fornito, A. (2019). Consistency and differences between centrality measures across distinct classes of networks. PLoS ONE, 14.","DOI":"10.1371\/journal.pone.0220061"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0378-8733(78)90021-7","article-title":"Centrality in social networks conceptual clarification","volume":"1","author":"Freeman","year":"1978","journal-title":"Soc. Netw."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2303","DOI":"10.1142\/S0218127407018403","article-title":"Centrality estimation in large networks","volume":"17","author":"Brandes","year":"2007","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.compenvurbsys.2017.05.004","article-title":"OSMnx: New methods for acquiring, constructing, analyzing, and visualizing complex street networks","volume":"65","author":"Boeing","year":"2017","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1002\/widm.25","article-title":"Identifying Patterns in Spatial Information: A Survey of Methods","volume":"1","author":"Shekhar","year":"2011","journal-title":"Wiley Interdiscip. Rev. Data Min. Knowl. Discov."},{"key":"ref_36","unstructured":"Alexander, C. (2017). A City Is Not a Tree, Sustasis Press\/Off The Common Books."},{"key":"ref_37","unstructured":"Lowell, W.B., and Wilson, R.J. (1978). Line Graphs and Line Digraphs, Selected Topics in Graph Theory, The Academic Press."},{"key":"ref_38","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_39","unstructured":"Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., and Antiga, L. (2019, January 8\u201314). PyTorch: An Imperative Style, High-Performance Deep Learning Library. Proceedings of the Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, Vancouver, BC, Canada."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/9\/11\/674\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:32:52Z","timestamp":1760178772000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/9\/11\/674"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,13]]},"references-count":39,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["ijgi9110674"],"URL":"https:\/\/doi.org\/10.3390\/ijgi9110674","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,13]]}}}