{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T00:02:41Z","timestamp":1769558561053,"version":"3.49.0"},"reference-count":52,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2025,3,10]],"date-time":"2025-03-10T00:00:00Z","timestamp":1741564800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Knowl. Discov. Data"],"published-print":{"date-parts":[[2025,4,30]]},"abstract":"<jats:p>\n            Principal Component Analysis (PCA) is one of the most famous unsupervised dimensionality reduction algorithms and has been widely used in many fields. However, it is very sensitive to outliers, which reduces the robustness of the algorithm. In recent years, many studies have tried to employ\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\ell_{1}\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            -norm to improve the robustness of PCA, but they all lack rotation invariance or the solution is expensive. In this article, we propose a novel robust PCA, namely, Fuzzy Weighted Principal Component Analysis (FWPCA), which still uses squared\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\ell_{2}\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            -norm to minimize reconstruction error and maintains rotation invariance of PCA. The biggest bright spot is that the contribution of data is restricted by fuzzy weights, so that the contribution of normal samples is much greater than noise or abnormal data, and realizes anomaly detection. Besides, a more reasonable data center can be obtained by solving the optimal mean to make projection matrix more accurate. Subsequently, an effective iterative optimization algorithm is developed to solve this problem, and its convergence is strictly proved. Extensive experimental results on face datasets and RGB anomaly detection datasets show the superiority of our proposed method.\n          <\/jats:p>","DOI":"10.1145\/3715148","type":"journal-article","created":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T16:32:34Z","timestamp":1738168354000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Fuzzy Weighted Principal Component Analysis for Anomaly Detection"],"prefix":"10.1145","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9594-5370","authenticated-orcid":false,"given":"Sisi","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an, P. R., China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0871-6519","authenticated-orcid":false,"given":"Feiping","family":"Nie","sequence":"additional","affiliation":[{"name":"School of Computer Science, School of Artificial Intelligence, Optics and ElectroNics (iOPEN), and the Key Laboratory of Intelligent Interaction and Applications (Ministry of Industry and Information Technology), Northwestern Polytechnical University, Xi\u2019an, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4814-1115","authenticated-orcid":false,"given":"Zheng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science, School of Artificial Intelligence, Optics and ElectroNics (iOPEN), and the Key Laboratory of Intelligent Interaction and Applications (Ministry of Industry and Information Technology), Northwestern Polytechnical University, Xi\u2019an, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9240-6726","authenticated-orcid":false,"given":"Rong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science, School of Artificial Intelligence, Optics and ElectroNics (iOPEN), and the Key Laboratory of Intelligent Interaction and Applications (Ministry of Industry and Information Technology), Northwestern Polytechnical University, Xi\u2019an, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2924-946X","authenticated-orcid":false,"given":"Xuelong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Science, School of Artificial Intelligence, Optics and ElectroNics (iOPEN), and the Key Laboratory of Intelligent Interaction and Applications (Ministry of Industry and Information Technology), Northwestern Polytechnical University, Xi\u2019an, China"}]}],"member":"320","published-online":{"date-parts":[[2025,3,10]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-47578-3_1"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0098-3004(84)90020-7"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1145\/2910585"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/3332183"},{"key":"e_1_3_1_6_2","first-page":"281","volume-title":"23rd International Conference on Machine Learning","author":"Ding Chris","year":"2006","unstructured":"Chris Ding, Ding Zhou, Xiaofeng He, and Hongyuan Zha. 2006. 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