{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T05:10:37Z","timestamp":1791954637462,"version":"4.3.4"},"reference-count":59,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T00:00:00Z","timestamp":1768953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Korea Agency for Infrastructure Technology Advance-826 ment","award":["RS-2022-827 00143804"],"award-info":[{"award-number":["RS-2022-827 00143804"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>In a situation where cities are increasingly being developed vertically and complexly, a novel approach for analyzing vertical urban functional patterns is proposed. For this purpose, a multi-dimensional GDC (Geo Data Cube) consisting of spatial and temporal data x, y, z, t, and f dimensions containing layer information was created. At this time, the size of the GDC cell (interval in x, y, z dimensions) is calculated by cell point data using the three-dimensional (3D) Moran\u2019s I index value calculated with the 3D Diversity Factor (DF) based on information entropy proposed to reduce the uncertainty of information for each cell. In other words, the cell with the smallest index value was chosen to minimize the influence of Modifiable Areal Unit Problem (MAUP) that occurs when mapping. The 3D land use index (3D LUI) is calculated as a linearly weighted sum of the spatial accessibility of uses between cells (3D KDF) and the enrichment of uses (3D EF), taking into account the first law of geography. Finally, the 3D LUI value for each use was calculated for each cell of the GDC, and the use with the highest value was determined as the urban function of the cell. As a result of applying this to Seocho-gu, Seoul, Republic of Korea (ROK) in June 2024 and visually evaluating it using the street view provided by Kakao Map, it was confirmed that commercial and residential functions were vertically separated in buildings with residential\u2013commercial complexes or shops on the ground floor. It was also confirmed that such characteristics did not appear in the two-dimensional (2D) urban functional patter analysis.<\/jats:p>","DOI":"10.3390\/ijgi15010047","type":"journal-article","created":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T11:11:17Z","timestamp":1768993877000},"page":"47","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Vertical Urban Functional Pattern Analysis Based on Multi-Dimensional Geo Data Cube"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3618-4924","authenticated-orcid":false,"given":"Jiyoung","family":"Kim","sequence":"first","affiliation":[{"name":"Social Eco Tech Institute, KonKuk University, Seoul 05029, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hyojoong","family":"Kim","sequence":"additional","affiliation":[{"name":"Social Eco Tech Institute, KonKuk University, Seoul 05029, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4827-242X","authenticated-orcid":false,"given":"Jonghyeon","family":"Yang","sequence":"additional","affiliation":[{"name":"Social Eco Tech Institute, KonKuk University, Seoul 05029, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"21","DOI":"10.17208\/jkpa.2016.12.51.7.21","article-title":"Empirical analysis of the relationship between land use mix and pedestrian volume in Seoul, Korea","volume":"51","author":"Im","year":"2016","journal-title":"J. Korea Plan. Assoc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"87","DOI":"10.17208\/jkpa.2021.12.56.7.87","article-title":"Analysis of urban vitality and its determinant factors Using POI Bigdata in Seoul, Korea","volume":"56","author":"Cao","year":"2021","journal-title":"J. Korea Plan. Assoc."},{"key":"ref_3","unstructured":"Yi, J. (2021). The Influence of Mixed Land-Use on Travel Behavior\u2014An Analysis on Horizontal and Vertical Mixed Land-Use. [Master\u2019s Thesis, Seoul National University]."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wang, Y., Gu, Y., Dou, M., and Qiao, M. (2018). Using spatial semantics and interactions to identify urban functional regions. ISPRS Int. J. Geo-Inf., 7.","DOI":"10.3390\/ijgi7040130"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"101442","DOI":"10.1016\/j.compenvurbsys.2019.101442","article-title":"A framework for extracting urban functional regions based on multiprototype word embeddings using points-of-interest data","volume":"80","author":"Hu","year":"2020","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"101651","DOI":"10.1016\/j.compenvurbsys.2021.101651","article-title":"Delineating urban functional use from points of interest data with neural network embedding: A case study in Greater London","volume":"88","author":"Niu","year":"2021","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Luo, G., Ye, J., Wang, J., and Wei, Y. (2023). Urban functional zone classification based on POI data and machine learning. Sustainability, 15.","DOI":"10.3390\/su15054631"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"103988","DOI":"10.1016\/j.cities.2022.103988","article-title":"The characteristic and transformation of 3D urban morphology in three Chinese mega-cities","volume":"131","author":"Cai","year":"2022","journal-title":"Cities"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1111\/tgis.13123","article-title":"A new hierarchical analysis framework of building heights: Towards a more intuitive understanding of 3D urban structure","volume":"28","author":"Yang","year":"2024","journal-title":"Trans. GIS"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"104683","DOI":"10.1016\/j.landurbplan.2023.104683","article-title":"Modeling multi-type urban landscape dynamics along the horizontal and vertical dimensions","volume":"233","author":"He","year":"2023","journal-title":"Landsc. Urban Plan."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"103424","DOI":"10.1016\/j.habitatint.2025.103424","article-title":"Optimizing vertical urban development: The role of a multidimensional assessment framework for balancing vertical growth and habitability","volume":"161","author":"Wang","year":"2025","journal-title":"Habitat Int."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"106516","DOI":"10.1016\/j.cities.2025.106516","article-title":"Vertical 15-min city: Modeling urban density and functional mix with multi-source geospatial data","volume":"169","author":"Chen","year":"2026","journal-title":"Cities"},{"key":"ref_13","unstructured":"(2024, November 23). OGC Geodatacube Standard Working Group Charter. Available online: http:\/\/www.opengeospatial.org\/legal\/."},{"key":"ref_14","first-page":"565","article-title":"Crisis management analysis of foot-and-mouth disease using multi-dimensional data cube","volume":"17","author":"Noh","year":"2017","journal-title":"J. Korea Content Assoc."},{"key":"ref_15","unstructured":"Strobl, P., Baumann, P., Lewis, A., Szantoi, Z., Killough, B., Purss, M., Craglia, M., Nativi, S., Held, A., and Dhu, T. (2017, January 28\u201330). The Six Faces of the Data Cube. Proceedings of the 2017 Conference on Big Data from Space (BIDS\u2019 2017), Toulouse, France."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ferreira, K.R., Queiroz, G.R., Vinhas, L., Marujo, R.F.B., Simoes, R.E.O., Picoli, M.C.A., Camara, G., Cartaxo, R., Gomes, V.C.F., and Santos, I.A. (2020). Earth observation data cubes for Brazil: Requirements, methodology and products. Remote Sens., 12.","DOI":"10.3390\/rs12244033"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Cheng, M.-C., Chiou, C.-R., Chen, B., Liu, C., Lin, H.-C., Shih, I.-L., Chung, C.-H., Lin, H.-Y., and Chou, C.-Y. (2019, January 1). Open Data Cube (ODC) in Taiwan: The Initiative and Protocol Development. Proceedings of the IGARSS 2019\u20132019 IEEE International Geoscience and Remote Sensing Symposium, Yokohama, Japan.","DOI":"10.1109\/IGARSS.2019.8898576"},{"key":"ref_18","first-page":"62","article-title":"Consideration points for application of KOMPSAT data to open data cube","volume":"22","author":"Lee","year":"2019","journal-title":"J. Korean Assoc. Geogr. Inf. Stud."},{"key":"ref_19","first-page":"1215","article-title":"A suggestion for surface reflectance ARD building of high-resolution satellite images and its application","volume":"37","author":"Lee","year":"2021","journal-title":"Korean J. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"617","DOI":"10.7848\/ksgpc.2023.41.6.617","article-title":"Method of hierarchical grid partition based on geo data cube model for extracting urban functional areas","volume":"41","author":"Kim","year":"2023","journal-title":"J. Korean Soc. Surv. Geod. Photogramm. Cartogr."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"358","DOI":"10.7470\/jkst.2022.40.3.358","article-title":"Urban structure-based factor analysis of two-wheeler accidents using data cube model","volume":"40","author":"Kim","year":"2022","journal-title":"J. Korean Soc. Transp."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1853","DOI":"10.1080\/13658816.2022.2087222","article-title":"A multi-source spatio-temporal data cube for large-scale geospatial analysis","volume":"36","author":"Gao","year":"2022","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Abad, L., Sudmanns, M., and H\u00f6lbling, D. (2024, January 4\u20137). Vector Data Cubes for Features Evolving in Space and Time. Proceedings of the AGILE Conference 2024: Geographic Information Science for a Sustainable Future, Glasgow, UK.","DOI":"10.5194\/agile-giss-5-16-2024"},{"key":"ref_24","unstructured":"(2024, November 23). MOLIT. Available online: https:\/\/www.law.go.kr\/%EB%B2%95%EB%A0%B9\/%EA%B1%B4%EC%B6%95%EB%B2%95%EC%8B%9C%ED%96%89%EB%A0%B9."},{"key":"ref_25","first-page":"49","article-title":"Spatial-temporal coupling characteristics of population urbanization and land urbanization in northeast China","volume":"35","author":"Guo","year":"2015","journal-title":"J. Econ. Geogr."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"102005","DOI":"10.1016\/j.compenvurbsys.2023.102005","article-title":"3-D multi-aspect mix degree index: A method for measuring land use mix at street block level","volume":"104","author":"Zhao","year":"2023","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2691","DOI":"10.1111\/tgis.12979","article-title":"A hierarchical spatial unit partitioning approach for fine-grained urban functional region identification","volume":"26","author":"Jing","year":"2022","journal-title":"Trans. GIS"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Luo, S., Liu, Y., Du, M., Gao, S., Wang, P., and Liu, X. (2021). The influence of spatial grid division on the layout analysis of urban functional areas. ISPRS Int. J. Geo-Inf., 10.","DOI":"10.3390\/ijgi10030189"},{"key":"ref_29","first-page":"757","article-title":"The delineation of function regions and modifiable areal unit problem","volume":"7","author":"Lee","year":"1999","journal-title":"J. Geogr. Environ. Educ."},{"key":"ref_30","unstructured":"Openshaw, S. (1984). The Modifiable Areal Unit Problem, GeoBooks."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Dong, X., Xu, Y., Huang, L., Liu, Z., Xu, Y., Zhang, K., Hu, Z., and Wu, G. (2020). Exploring impact of spatial unit on urban land use mapping with multisource data. Remote Sens., 12.","DOI":"10.3390\/rs12213597"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Deng, Y., and He, R. (2022). Refined urban functional zone mapping by integrating open-source data. ISPRS Int. J. Geo-Inf., 11.","DOI":"10.3390\/ijgi11080421"},{"key":"ref_33","unstructured":"(2024, November 23). MOLIT. Available online: https:\/\/www.law.go.kr\/%EB%B2%95%EB%A0%B9\/%EA%B1%B4%EC%B6%95%EB%B2%95."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"04020014","DOI":"10.1061\/JTEPBS.0000334","article-title":"Influence of different spatial aggregations on variables implemented in macroscopic road-safety modeling","volume":"146","author":"Gomes","year":"2020","journal-title":"J. Transp. Eng. A"},{"key":"ref_35","first-page":"329","article-title":"Comparing univariate spatial association statistics (I): Focusing on global Lee\u2019s s statistics","volume":"4","author":"Lee","year":"2015","journal-title":"J. Assoc. Korean Geogr."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"8288248","DOI":"10.1155\/2022\/8288248","article-title":"Understanding the modifiable areal unit problem and identifying appropriate spatial units while studying the influence of the built environment on the traffic system state","volume":"2022","author":"Li","year":"2022","journal-title":"J. Adv. Transp."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s10109-016-0231-0","article-title":"Spatial indices for measuring three-dimensional patterns in a voxel-based space","volume":"18","author":"Jjumba","year":"2016","journal-title":"J. Geogr. Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1016\/j.compenvurbsys.2010.08.001","article-title":"Detecting conjugate-point pairs for map alignment between two polygon datasets","volume":"35","author":"Huh","year":"2011","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"234","DOI":"10.2307\/143141","article-title":"A computer movie simulating urban growth in the Detroit region","volume":"46","author":"Tobler","year":"1970","journal-title":"Econ. Geogr."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Anselin, L. (1988). Spatial Econometrics: Methods and Models, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-015-7799-1"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1111\/j.1435-5597.1988.tb01155.x","article-title":"Do spatial effects really matter in regression analysis?","volume":"65","author":"Anselin","year":"1988","journal-title":"Pap. Reg. Sci."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Du, S., Wu, Y., Guo, L., Fan, D., and Sun, W. (2024). How does the 2D\/3D urban morphology affect the urban heat island across urban functional zones? A case study of Beijing, China. ISPRS Int. J. Geo-Inf., 13.","DOI":"10.3390\/ijgi13040120"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"8864","DOI":"10.1109\/JSTARS.2021.3107543","article-title":"Identifying urban building function by integrating remote sensing imagery and POI data","volume":"14","author":"Lin","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_44","unstructured":"Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis, Chapman & Hall."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.compenvurbsys.2018.11.008","article-title":"Beyond word2vec: An approach for urban functional region extraction and identification by combining place2vec and POIs","volume":"74","author":"Zhai","year":"2019","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Zhang, C., Xu, L., Yan, Z., and Wu, S. (2021). A GloVe-Based POI Type Embedding Model for Extracting and Identifying Urban Functional Regions. ISPRS Int. J. Geo-Inf., 10.","DOI":"10.3390\/ijgi10060372"},{"key":"ref_47","first-page":"3564835","article-title":"Effectiveness of entropy weight method in decision-making","volume":"2020","author":"Zhu","year":"2020","journal-title":"Math. Probl. Eng."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Shen, T., Zhou, W., Yuan, S., and Huo, L. (2024). Spatiotemporal characterization of the three-dimensional morphology of urban buildings based on Moran\u2019s I. Sustainability, 16.","DOI":"10.3390\/su16156540"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1080\/13658816.2018.1542699","article-title":"Uncertainty in the effects of the modifiable areal unit problem under different levels of spatial autocorrelation: A simulation study","volume":"33","author":"Lee","year":"2019","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Fischer, M.M., and Nijkamp, P. (2021). Scale, aggregation, and the modifiable areal unit problem. Handbook of Regional Science, Springer. [2nd ed.].","DOI":"10.1007\/978-3-662-60723-7"},{"key":"ref_51","unstructured":"(2024, November 23). Kakao Map. Available online: https:\/\/map.kakao.com\/."},{"key":"ref_52","unstructured":"(2025, September 17). Kakao Developers. Available online: https:\/\/developers.kakao.com\/docs\/latest\/ko\/local\/dev-guide#search-by-category."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"101552","DOI":"10.1016\/j.compenvurbsys.2020.101552","article-title":"Quantify city-level dynamic functions across China using social media and POIs data","volume":"85","author":"Qian","year":"2021","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_54","first-page":"1288","article-title":"Effects of locations, structures and neighbourhoods to housing price: An empirical study in Shanghai, China","volume":"22","author":"Tam","year":"2019","journal-title":"Int. J. Constr. Manag."},{"key":"ref_55","unstructured":"(2026, January 04). Public Data Portal. Available online: https:\/\/www.data.go.kr\/data\/3036455\/fileData.do."},{"key":"ref_56","unstructured":"(2026, January 04). VWorld. Available online: https:\/\/www.vworld.kr\/dtmk\/dtmk_ntads_s002.do?pageIndex=&searchDsNm=&svcCde=NA&dsId=8."},{"key":"ref_57","unstructured":"(2026, January 04). VWorld. Available online: https:\/\/www.vworld.kr\/dtmk\/dtmk_ntads_s002.do?svcCde=NA&dsId=7."},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Shen, T., Kong, F., Yuan, S., Wang, X., Sun, D., and Ren, Z. (2025). From 2D to 3D urban analysis: An adaptive urban zoning framework that takes building height into account. Buildings, 15.","DOI":"10.3390\/buildings15071182"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1038\/s41597-024-03719-w","article-title":"Global building heights for urban studies (UT-GLOBUS) for city- and street-scale urban simulations: Development and first applications","volume":"11","author":"Kamath","year":"2024","journal-title":"Sci. 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