{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:13:52Z","timestamp":1760242432561,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,7,13]],"date-time":"2017-07-13T00:00:00Z","timestamp":1499904000000},"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>With the rapid explosion of information based on location, spatial clustering plays an increasingly significant role in this day and age as an important technique in geographical data analysis. Most existing spatial clustering algorithms are limited by complicated spatial patterns, which have difficulty in discovering clusters with arbitrary shapes and uneven density. In order to overcome such limitations, we propose a novel clustering method called Spatial Clustering with Multiple Density-Ordered Trees (SCMDOT). Motivated by the idea of the Density-Ordered Tree (DOT), we firstly represent the original dataset by the means of constructing Multiple Density-Ordered Trees (MDOT). In the constructing process, we impose additional constraints to control the growth of each Density-Ordered Tree, ensuring that they all have high spatial similarity. Furthermore, a series of MDOT can be successively generated from regions of sparse areas to the dense areas, where each Density-Ordered Tree, also treated as a sub-tree, represents a cluster. In the merging process, the final clusters are obtained by repeatedly merging a suitable pair of clusters until they satisfy the expected clustering result. In addition, a heuristic strategy is applied during the process of our algorithm for suitability for special applications. The experiments on synthetic and real-world spatial databases are utilised to demonstrate the performance of our proposed method.<\/jats:p>","DOI":"10.3390\/ijgi6070217","type":"journal-article","created":{"date-parts":[[2017,7,13]],"date-time":"2017-07-13T10:31:57Z","timestamp":1499941917000},"page":"217","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["SCMDOT: Spatial Clustering with Multiple Density-Ordered Trees"],"prefix":"10.3390","volume":"6","author":[{"given":"Xiaozhu","family":"Wu","sequence":"first","affiliation":[{"name":"Key Laboratory of Spatial Data Mining &amp; Information Sharing, Ministry of Education, Fuzhou University, Fuzhou 350002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong","family":"Jiang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Spatial Data Mining &amp; Information Sharing, Ministry of Education, Fuzhou University, Fuzhou 350002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chongcheng","family":"Chen","sequence":"additional","affiliation":[{"name":"Key Laboratory of Spatial Data Mining &amp; Information Sharing, Ministry of Education, Fuzhou University, Fuzhou 350002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.1002\/2013JD020762","article-title":"Urban signatures in the spatial clustering of summer heavy rainfall events over the Beijing metropolitan region","volume":"119","author":"Yang","year":"2014","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1023\/A:1015279009755","article-title":"Multi-level clustering and its visualization for exploratory spatial analysis","volume":"6","author":"Lee","year":"2002","journal-title":"GeoInformatica"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1186\/1475-2875-13-387","article-title":"Spatial clustering and risk factors of malaria infections in ratanakiri province, cambodia","volume":"13","author":"Sluydts","year":"2014","journal-title":"Malar. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1029\/2009JB006974","article-title":"A mechanism for spatial and temporal earthquake clustering","volume":"115","author":"Jagla","year":"2010","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/j.compenvurbsys.2011.02.003","article-title":"An adaptive spatial clustering algorithm based on delaunay triangulation","volume":"35","author":"Deng","year":"2011","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1145\/331499.331504","article-title":"Data clustering: A review","volume":"31","author":"Jain","year":"1999","journal-title":"ACM Comput. Surv."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1109\/TNN.2005.845141","article-title":"Survey of clustering algorithms","volume":"16","author":"Xu","year":"2005","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_8","unstructured":"MacQueen, J. (July, January 21). Some Methods for Classification and Analysis of Multivariate Observations. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA, USA."},{"key":"ref_9","unstructured":"Ester, M., Kriegel, H.-P., Sander, J., and Xu, X. (1996, January 2\u20134). A density-based algorithm for discovering clusters in large spatial databases with noise. Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD-96), Portland, OR, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1126\/science.1136800","article-title":"Clustering by passing messages between data points","volume":"315","author":"Frey","year":"2007","journal-title":"Science"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.physa.2016.05.041","article-title":"Spatial clustering with density-ordered tree","volume":"460","author":"Cheng","year":"2016","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1492","DOI":"10.1126\/science.1242072","article-title":"Clustering by fast search and find of density peaks","volume":"344","author":"Rodriguez","year":"2014","journal-title":"Science"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.neucom.2016.01.102","article-title":"Clustering by fast search and find of density peaks via heat diffusion","volume":"208","author":"Mehmood","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.ins.2016.08.086","article-title":"DenPEHC: Density peak based efficient hierarchical clustering","volume":"373","author":"Xu","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.cosrev.2007.05.001","article-title":"Graph clustering","volume":"1","author":"Schaeffer","year":"2007","journal-title":"Comput. Sci. Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1109\/2.781637","article-title":"Chameleon: A hierarchical clustering algorithm using dynamic modeling","volume":"32","author":"Karypis","year":"1999","journal-title":"Computer"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1109\/T-C.1971.223083","article-title":"Graph-theoretical methods for detecting and describing gestalt clusters","volume":"C-20","author":"Zahn","year":"1971","journal-title":"IEEE Trans. Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1016\/j.patcog.2009.07.010","article-title":"A graph-theoretical clustering method based on two rounds of minimum spanning trees","volume":"43","author":"Zhong","year":"2010","journal-title":"Pattern Recognit."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3397","DOI":"10.1016\/j.ins.2011.04.013","article-title":"Minimum spanning tree based split-and-merge: A hierarchical clustering method","volume":"181","author":"Zhong","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1111\/j.1467-9671.2011.01269.x","article-title":"Automatic region building for spatial analysis","volume":"15","author":"Guo","year":"2011","journal-title":"Trans. GIS"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Guha, S., Rastogi, R., and Shim, K. (1998, January 1\u20134). CURE: An Efficient Clustering Algorithm for large Databases. Proceedings of the ACM-SIGMOD International Conference on Management of Data, Seattle, WA, USA.","DOI":"10.1145\/276304.276312"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/S0306-4379(00)00022-3","article-title":"ROCK: A robust clustering algorithm for categorical attributes","volume":"25","author":"Guha","year":"2000","journal-title":"Inf. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.ins.2012.12.033","article-title":"A meta-learning approach for determining the number of clusters with consideration of nearest neighbors","volume":"232","author":"Lee","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1016\/j.ins.2010.10.028","article-title":"Data clustering by minimizing disconnectivity","volume":"181","author":"Lee","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1145\/361002.361007","article-title":"Multidimensional binary search trees used for associative searching","volume":"18","author":"Bentley","year":"1975","journal-title":"Commun. ACM"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Fu, L., and Medico, E. (2007). Flame, a novel fuzzy clustering method for the analysis of DNA microarray data. BMC Bioinform., 8.","DOI":"10.1186\/1471-2105-8-3"},{"key":"ref_27","unstructured":"Jain, A.K., and Law, M.H.C. (2005, January 20\u201322). Data clustering: A user\u2032s dilemma. Proceedings of the Pattern Recognition and Machine Intelligence, First International Conference, Kolkata, India."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.patcog.2007.04.010","article-title":"Robust path-based spectral clustering","volume":"41","author":"Chang","year":"2008","journal-title":"Pattern Recognit."},{"key":"ref_29","unstructured":"Ankerst, M., Breunig, M.M., Kriegel, H.-P., and Sander, J. (June, January 31). OPTICS: Ordering points to identify the clustering structure. Proceedings of the ACM-SIGMOD International Conference on Management of Data, Philadelphia, PA, USA."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1080\/01621459.1971.10482356","article-title":"Objective criteria for the evaluation of clustering methods","volume":"66","author":"Rand","year":"1971","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_31","first-page":"2837","article-title":"Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance","volume":"11","author":"Vinh","year":"2010","journal-title":"J. Mach. Learn. Res."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/6\/7\/217\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:42:31Z","timestamp":1760208151000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/6\/7\/217"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,13]]},"references-count":31,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2017,7]]}},"alternative-id":["ijgi6070217"],"URL":"https:\/\/doi.org\/10.3390\/ijgi6070217","relation":{},"ISSN":["2220-9964"],"issn-type":[{"type":"electronic","value":"2220-9964"}],"subject":[],"published":{"date-parts":[[2017,7,13]]}}}