{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T17:06:52Z","timestamp":1778605612343,"version":"3.51.4"},"reference-count":19,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,18]],"date-time":"2018-01-18T00:00:00Z","timestamp":1516233600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The Internet of Things (IoT) generates lots of high-dimensional sensor intelligent data. The processing of high-dimensional data (e.g., data visualization and data classification) is very difficult, so it requires excellent subspace learning algorithms to learn a latent subspace to preserve the intrinsic structure of the high-dimensional data, and abandon the least useful information in the subsequent processing. In this context, many subspace learning algorithms have been presented. However, in the process of transforming the high-dimensional data into the low-dimensional space, the huge difference between the sum of inter-class distance and the sum of intra-class distance for distinct data may cause a bias problem. That means that the impact of intra-class distance is overwhelmed. To address this problem, we propose a novel algorithm called Hierarchical Discriminant Analysis (HDA). It minimizes the sum of intra-class distance first, and then maximizes the sum of inter-class distance. This proposed method balances the bias from the inter-class and that from the intra-class to achieve better performance. Extensive experiments are conducted on several benchmark face datasets. The results reveal that HDA obtains better performance than other dimensionality reduction algorithms.<\/jats:p>","DOI":"10.3390\/s18010279","type":"journal-article","created":{"date-parts":[[2018,1,18]],"date-time":"2018-01-18T12:19:48Z","timestamp":1516277988000},"page":"279","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Hierarchical Discriminant Analysis"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5540-1632","authenticated-orcid":false,"given":"Di","family":"Lu","sequence":"first","affiliation":[{"name":"State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chuntao","family":"Ding","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinliang","family":"Xu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shangguang","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,18]]},"reference":[{"key":"ref_1","unstructured":"Turk, M.A., and Pentland, A.P. 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