{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:02:15Z","timestamp":1760144535740,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,4,28]],"date-time":"2024-04-28T00:00:00Z","timestamp":1714262400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"],"award-info":[{"award-number":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"]}]},{"name":"the National Natural Science Foundation of China","award":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"],"award-info":[{"award-number":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"]}]},{"name":"the National Statistical Science Research Project","award":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"],"award-info":[{"award-number":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"]}]},{"name":"Jinan Science and Technology Bureau","award":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"],"award-info":[{"award-number":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"]}]},{"name":"the China Academy of Engineering Science and Technology Development Strategy Shandong Research Institute Consulting Research Project","award":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"],"award-info":[{"award-number":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"]}]},{"name":"the State Scholarship Fund from China Scholarship Council","award":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"],"award-info":[{"award-number":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"]}]},{"name":"the Alberta Machine Intelligence Institute (AMII)","award":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"],"award-info":[{"award-number":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"]}]},{"name":"Natural Sciences and Engineering Council of Canada (NSERC)","award":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"],"award-info":[{"award-number":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"]}]},{"name":"Canada Research Chair program from NSERC","award":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"],"award-info":[{"award-number":["2023YFA1008701","12371292","12171279","2022LY080","2021GXRC056","202302SDZD04","202208370132"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In unsupervised learning, clustering is a common starting point for data processing. The convex or concave fusion clustering method is a novel approach that is more stable and accurate than traditional methods such as k-means and hierarchical clustering. However, the optimization algorithm used with this method can be slowed down significantly by the complexity of the fusion penalty, which increases the computational burden. This paper introduces a random projection ADMM algorithm based on the Bernoulli distribution and develops a double random projection ADMM method for high-dimensional fusion clustering. These new approaches significantly outperform the classical ADMM algorithm due to their ability to significantly increase computational speed by reducing complexity and improving clustering accuracy by using multiple random projections under a new evaluation criterion. We also demonstrate the convergence of our new algorithm and test its performance on both simulated and real data examples.<\/jats:p>","DOI":"10.3390\/e26050376","type":"journal-article","created":{"date-parts":[[2024,4,30]],"date-time":"2024-04-30T08:14:31Z","timestamp":1714464871000},"page":"376","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fast Fusion Clustering via Double Random Projection"],"prefix":"10.3390","volume":"26","author":[{"given":"Hongni","family":"Wang","sequence":"first","affiliation":[{"name":"School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Na","family":"Li","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanqiu","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Science, Guangxi University of Science and Technology, Liuzhou 545006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingxin","family":"Yan","sequence":"additional","affiliation":[{"name":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bei","family":"Jiang","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3011-9216","authenticated-orcid":false,"given":"Linglong","family":"Kong","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9972-6888","authenticated-orcid":false,"given":"Xiaodong","family":"Yan","sequence":"additional","affiliation":[{"name":"Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,28]]},"reference":[{"key":"ref_1","first-page":"2","article-title":"CDLSTM: A novel model for climate change forecasting","volume":"71","author":"Haq","year":"2022","journal-title":"Comput. 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