{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:44:01Z","timestamp":1760035441712,"version":"build-2065373602"},"reference-count":58,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T00:00:00Z","timestamp":1751414400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Jinan University, the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62272198","2023B1212060036","2023B1212120007","2024A1515010121","pdjh2025ak028"],"award-info":[{"award-number":["62272198","2023B1212060036","2023B1212120007","2024A1515010121","pdjh2025ak028"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Guangdong Key Laboratory of Data Security and Privacy Preserving","award":["62272198","2023B1212060036","2023B1212120007","2024A1515010121","pdjh2025ak028"],"award-info":[{"award-number":["62272198","2023B1212060036","2023B1212120007","2024A1515010121","pdjh2025ak028"]}]},{"name":"Guangdong\u2013Hong Kong Joint Laboratory for Data Security and Privacy Preserving","award":["62272198","2023B1212060036","2023B1212120007","2024A1515010121","pdjh2025ak028"],"award-info":[{"award-number":["62272198","2023B1212060036","2023B1212120007","2024A1515010121","pdjh2025ak028"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["62272198","2023B1212060036","2023B1212120007","2024A1515010121","pdjh2025ak028"],"award-info":[{"award-number":["62272198","2023B1212060036","2023B1212120007","2024A1515010121","pdjh2025ak028"]}]},{"name":"Special Funds for the Cultivation of Guangdong College Students\u2019 Scientific and Technological Innovation","award":["62272198","2023B1212060036","2023B1212120007","2024A1515010121","pdjh2025ak028"],"award-info":[{"award-number":["62272198","2023B1212060036","2023B1212120007","2024A1515010121","pdjh2025ak028"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["BDCC"],"abstract":"<jats:p>Online learning has become increasingly prevalent in real-world applications, where data streams often comprise heterogeneous feature types\u2014both nominal and numerical\u2014and labels may not arrive synchronously with features. However, most existing online learning methods assume homogeneous data types and synchronous arrival of features and labels. In practice, data streams are typically heterogeneous and exhibit asynchronous label feedback, making these methods insufficient. To address these challenges, we propose a novel algorithm, termed Online Asynchronous Learning over Streaming Nominal Data (OALN), which maps heterogeneous data into a continuous latent space and leverages a model pool alongside a hint mechanism to effectively manage asynchronous labels. Specifically, OALN is grounded in three core principles: (1) It utilizes a Gaussian mixture copula in the latent space to preserve class structure and numerical relationships, thereby addressing the encoding and relational learning challenges posed by mixed feature types. (2) It performs adaptive imputation through conditional covariance matrices to seamlessly handle random missing values and feature drift, while incrementally updating copula parameters to accommodate dynamic changes in the feature space. (3) It incorporates a model pool and hint mechanism to efficiently process asynchronous label feedback. We evaluate OALN on twelve real-world datasets; the average cumulative error rates are 23.31% and 28.28% under the missing rates of 10% and 50%, respectively, and the average AUC scores are 0.7895 and 0.7433, which are the best results among the compared algorithms. And both theoretical analyses and extensive empirical studies confirm the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/bdcc9070177","type":"journal-article","created":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T09:08:44Z","timestamp":1751447324000},"page":"177","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Online Asynchronous Learning over Streaming Nominal Data"],"prefix":"10.3390","volume":"9","author":[{"given":"Hongrui","family":"Li","sequence":"first","affiliation":[{"name":"Jinan University & University of Birmingham Joint Institution, Jinan University, Guangzhou 510632, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5610-005X","authenticated-orcid":false,"given":"Shengda","family":"Zhuo","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Jinan University, Guangzhou 510632, China"}]},{"given":"Lin","family":"Li","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Jinan University, Guangzhou 510632, China"}]},{"given":"Jiale","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Jinan University, Guangzhou 510632, China"}]},{"given":"Tianbo","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Intelligent Science and Technology, Beijing University of Civil Engineering and Architecture, Beijing 100044, China"}]},{"given":"Jun","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Jinan University, Guangzhou 510632, China"}]},{"given":"Shaorui","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Jinan University, Guangzhou 510632, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9551-022X","authenticated-orcid":false,"given":"Shuqiang","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Cyber Security, Jinan University, Guangzhou 510632, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,2]]},"reference":[{"key":"ref_1","unstructured":"Bhatia, K., and Sridharan, K. 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