{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:16:32Z","timestamp":1760145392804,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T00:00:00Z","timestamp":1721865600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62373301","62173277","2023-JC-YB-526","20220058053002","20220058053002"],"award-info":[{"award-number":["62373301","62173277","2023-JC-YB-526","20220058053002","20220058053002"]}]},{"DOI":"10.13039\/501100007128","name":"Natural Science Foundation of Shaanxi Province","doi-asserted-by":"publisher","award":["62373301","62173277","2023-JC-YB-526","20220058053002","20220058053002"],"award-info":[{"award-number":["62373301","62173277","2023-JC-YB-526","20220058053002","20220058053002"]}],"id":[{"id":"10.13039\/501100007128","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012130","name":"Aeronautical Science Foundation of China","doi-asserted-by":"publisher","award":["62373301","62173277","2023-JC-YB-526","20220058053002","20220058053002"],"award-info":[{"award-number":["62373301","62173277","2023-JC-YB-526","20220058053002","20220058053002"]}],"id":[{"id":"10.13039\/501100012130","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012130","name":"Shaanxi Province Key Laboratory of Flight Control and Simulation Technology","doi-asserted-by":"publisher","award":["62373301","62173277","2023-JC-YB-526","20220058053002","20220058053002"],"award-info":[{"award-number":["62373301","62173277","2023-JC-YB-526","20220058053002","20220058053002"]}],"id":[{"id":"10.13039\/501100012130","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Support vector data description (SVDD) is widely regarded as an effective technique for addressing anomaly detection problems. However, its performance can significantly deteriorate when the training data are affected by outliers or mislabeled observations. This study introduces a universal truncated loss function framework into the SVDD model to enhance its robustness and employs the fast alternating direction method of multipliers (ADMM) algorithm to solve various truncated loss functions. Moreover, the convergence of the fast ADMM algorithm is analyzed theoretically. Within this framework, we developed the truncated generalized ramp, truncated binary cross entropy, and truncated linear exponential loss functions for SVDD. We conducted extensive experiments on synthetic and real-world datasets to validate the effectiveness of these three SVDD models in handling data with different noise levels, demonstrating their superior robustness and generalization capabilities compared to other SVDD models.<\/jats:p>","DOI":"10.3390\/e26080628","type":"journal-article","created":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T14:31:07Z","timestamp":1721917867000},"page":"628","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Robust Support Vector Data Description with Truncated Loss Function for Outliers Depression"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9184-9493","authenticated-orcid":false,"given":"Huakun","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Automatic Control, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8912-3418","authenticated-orcid":false,"given":"Yongxi","family":"Lyu","sequence":"additional","affiliation":[{"name":"Department of Automatic Control, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5700-2638","authenticated-orcid":false,"given":"Jingping","family":"Shi","sequence":"additional","affiliation":[{"name":"Department of Automatic Control, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8393-3185","authenticated-orcid":false,"given":"Weiguo","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Automatic Control, Northwestern Polytechnical University, Xi\u2019an 710072, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1145\/1541880.1541882","article-title":"Anomaly detection: A survey","volume":"41","author":"Chandola","year":"2009","journal-title":"ACM Comput. 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