{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T19:53:48Z","timestamp":1760385228684,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2012,4,30]],"date-time":"2012-04-30T00:00:00Z","timestamp":1335744000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>When extracting discriminative features from multimodal data, current methods rarely concern themselves with the data distribution. In this paper, we present an assumption that is consistent with the viewpoint of discrimination, that is, a person\u2019s overall biometric data should be regarded as one class in the input space, and his different biometric data can form different Gaussians distributions, i.e., different subclasses. Hence, we propose a novel multimodal feature extraction and recognition approach based on subclass discriminant analysis (SDA). Specifically, one person\u2019s different bio-data are treated as different subclasses of one class, and a transformed space is calculated, where the difference among subclasses belonging to different persons is maximized, and the difference within each subclass is minimized. Then, the obtained multimodal features are used for classification. Two solutions are presented to overcome the singularity problem encountered in calculation, which are using PCA preprocessing, and employing the generalized singular value decomposition (GSVD) technique, respectively. Further, we provide nonlinear extensions of SDA based multimodal feature extraction, that is, the feature fusion based on KPCA-SDA and KSDA-GSVD. In KPCA-SDA, we first apply Kernel PCA on each single modal before performing SDA. While in KSDA-GSVD, we directly perform Kernel SDA to fuse multimodal data by applying GSVD to avoid the singular problem. For simplicity two typical types of biometric data are considered in this paper, i.e., palmprint data and face data. Compared with several representative multimodal biometrics recognition methods, experimental results show that our approaches outperform related multimodal recognition methods and KSDA-GSVD achieves the best recognition performance.<\/jats:p>","DOI":"10.3390\/s120505551","type":"journal-article","created":{"date-parts":[[2012,4,30]],"date-time":"2012-04-30T11:06:04Z","timestamp":1335783964000},"page":"5551-5571","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Palmprint and Face Multi-Modal Biometric Recognition Based on SDA-GSVD and Its Kernelization"],"prefix":"10.3390","volume":"12","author":[{"given":"Xiao-Yuan","family":"Jing","sequence":"first","affiliation":[{"name":"State Key Laboratory of Software Engineering, Wuhan University, Wuhan 430072, China"},{"name":"College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210046, China"},{"name":"State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210046, China"}]},{"given":"Sheng","family":"Li","sequence":"additional","affiliation":[{"name":"College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210046, China"}]},{"given":"Wen-Qian","family":"Li","sequence":"additional","affiliation":[{"name":"College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210046, China"}]},{"given":"Yong-Fang","family":"Yao","sequence":"additional","affiliation":[{"name":"College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210046, China"}]},{"given":"Chao","family":"Lan","sequence":"additional","affiliation":[{"name":"College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210046, China"}]},{"given":"Jia-Sen","family":"Lu","sequence":"additional","affiliation":[{"name":"College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210046, China"}]},{"given":"Jing-Yu","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Computer Science, Nanjing University of Science and Technology, Nanjing 210094, China"}]}],"member":"1968","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3209","DOI":"10.1016\/j.patcog.2007.01.034","article-title":"Face and palmprint pixel level fusion and Kernel DCV-RBF classifier for small sample biometric recognition","volume":"40","author":"Jing","year":"2007","journal-title":"Pattern Recognit."},{"unstructured":"Petrovi, V., and Xydeas, C. 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