{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:50:11Z","timestamp":1760057411089,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T00:00:00Z","timestamp":1738972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71272161"],"award-info":[{"award-number":["71272161"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>To efficiently reduce the dimensionality of time series and enhance the efficiency of subsequent data-mining tasks, this study introduces cloud model theory to propose a novel information granulation method and its corresponding similarity measurement. First, we present an information granulation validity index of time series (IGV) based on the entropy and expectation of the cloud model. Taking IGV as the granulation target for time series, an adaptive information granulation algorithm for time series (CMAIG) is proposed, which can transform a time series into a granular time series consisting of several normal clouds without pre-specifying the number of information granules, achieving efficient dimensionality reduction. Then, a new similarity measurement method (CMAIG_ECM) is designed to calculate the similarity between two granular time series. Finally, the hierarchical clustering algorithm based on the proposed time series information granulation method and granular time series similarity measurement method (CMAIG_ECM_HC) is carried out on some UCR datasets and a real stock dataset, and experimental studies demonstrate that CMAIG_ECM_HC has superior performance in clustering time series with different shapes and trends.<\/jats:p>","DOI":"10.3390\/e27020180","type":"journal-article","created":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T05:53:22Z","timestamp":1739166802000},"page":"180","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Cloud Model-Based Adaptive Time-Series Information Granulation Algorithm and Its Similarity Measurement"],"prefix":"10.3390","volume":"27","author":[{"given":"Hailan","family":"Chen","sequence":"first","affiliation":[{"name":"School of Business, Sichuan Normal University, Chengdu 610101, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuedong","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qi","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Finance, Hebei University of Economics and Business, Shijiazhuang 050061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruojin","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Business, Sichuan Normal University, Chengdu 610101, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,8]]},"reference":[{"key":"ref_1","unstructured":"Box, G.E.P., and Jenkins, G.M. 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