{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T11:02:30Z","timestamp":1778324550423,"version":"3.51.4"},"reference-count":52,"publisher":"Copernicus GmbH","issue":"8","license":[{"start":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T00:00:00Z","timestamp":1682294400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006559","name":"University of Tsukuba","doi-asserted-by":"publisher","award":["n\/a"],"award-info":[{"award-number":["n\/a"]}],"id":[{"id":"10.13039\/501100006559","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Geosci. Model Dev."],"abstract":"<jats:p>Abstract. Dramatic increases in climate data underlie a gradual\nparadigm shift in knowledge acquisition methods from physically based models\nto data-based mining approaches. One of the most popular data clustering\/mining techniques is k-means, and it has been used to\ndetect hidden patterns in climate systems; k-means is established based on distance metrics for\npattern recognition, which is relatively ineffective when dealing with \u201cstructured\u201d data, that is,\ndata in time and space domains, which are dominant in climate science. Here, we propose (i)\u00a0a novel structural-similarity-recognition-based k-means algorithm called structural k-means or S k-means for\nclimate data mining and (ii)\u00a0a new clustering uncertainty representation\/evaluation framework based on the information entropy concept. We\ndemonstrate that the novel S k-means could provide higher-quality clustering\noutcomes in terms of general silhouette analysis, although it requires\nhigher computational resources compared with conventional algorithms. The\nresults are consistent with different demonstration problem settings using\ndifferent types of input data, including two-dimensional weather patterns,\nhistorical climate change in terms of time series, and tropical cyclone\npaths. Additionally, by quantifying the uncertainty underlying the\nclustering outcomes we, for the first time, evaluated the \u201cmeaningfulness\u201d\nof applying a given clustering algorithm for a given dataset. We expect that\nthis study will constitute a new standard of k-means clustering with\n\u201cstructural\u201d input data, as well as a new framework for uncertainty\nrepresentation\/evaluation of clustering algorithms for (but not limited to)\nclimate science.<\/jats:p>","DOI":"10.5194\/gmd-16-2215-2023","type":"journal-article","created":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T06:22:55Z","timestamp":1682317375000},"page":"2215-2233","source":"Crossref","is-referenced-by-count":14,"title":["Structural\n                    <i>k<\/i>\n                    -means (S\n                    <i>k<\/i>\n                    -means) and clustering uncertainty evaluation framework (CUEF) for mining climate data"],"prefix":"10.5194","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2794-5309","authenticated-orcid":false,"given":"Quang-Van","family":"Doan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toshiyuki","family":"Amagasa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thanh-Ha","family":"Pham","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takuto","family":"Sato","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fei","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hiroyuki","family":"Kusaka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"3145","published-online":{"date-parts":[[2023,4,24]]},"reference":[{"key":"ref1","unstructured":"Arthur, D. and Vassilvitskii, S.: k-means++: the advantages of careful\nseeding, in: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on\nDiscrete Algorithms, SODA 2007, New Orleans, Louisiana, USA, 7\u20139\u00a0January 2007, 1027\u20131035, https:\/\/theory.stanford.edu\/~sergei\/papers\/kMeansPP-soda.pdf (last access: 23\u00a0January 2023), 2007."},{"key":"ref2","doi-asserted-by":"crossref","unstructured":"Barua, D. 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