{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T23:29:35Z","timestamp":1749511775469,"version":"3.37.3"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,4,17]],"date-time":"2021-04-17T00:00:00Z","timestamp":1618617600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,17]],"date-time":"2021-04-17T00:00:00Z","timestamp":1618617600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61976027, 61572082"],"award-info":[{"award-number":["61976027, 61572082"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s40314-021-01482-x","type":"journal-article","created":{"date-parts":[[2021,4,17]],"date-time":"2021-04-17T05:02:32Z","timestamp":1618635752000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Convex hull-based distance metric learning for image classification"],"prefix":"10.1007","volume":"40","author":[{"given":"Xue","family":"Zhang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4136-2433","authenticated-orcid":false,"given":"Changzhong","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Xiaodong","family":"Fan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,4,17]]},"reference":[{"key":"1482_CR1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2010.5539965","author":"H Cevikalp","year":"2010","unstructured":"Cevikalp H, Triggs B (2010) Face recognition based on image sets. IEEE Conf Comput Vis Pattern Recogn. https:\/\/doi.org\/10.1109\/CVPR.2010.5539965","journal-title":"IEEE Conf Comput Vis Pattern Recogn"},{"doi-asserted-by":"crossref","unstructured":"Chang CC, Lin CJ (2011) LIBSVM: a library for support vector machines. Software available at\u00a0http:\/\/www.csie.ntu.edu.tw\/~cjlin\/libsvm","key":"1482_CR2","DOI":"10.1145\/1961189.1961199"},{"issue":"12","key":"1482_CR3","doi-asserted-by":"publisher","first-page":"1644","DOI":"10.1109\/TPAMI.2002.1114855","volume":"24","author":"JT Chien","year":"2002","unstructured":"Chien JT, Wu CC (2002) Discriminant waveletfaces and nearest feature classifiers for face recognition. IEEE Trans Pattern Anal Mach Intell 24(12):1644\u20131649. https:\/\/doi.org\/10.1109\/TPAMI.2002.1114855","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"doi-asserted-by":"publisher","unstructured":"Davis JV, Kulis B, Jain P, Sra S, Dhillon IS (2007) Information-theoretic metric learning. In: Paper presented at the Proceedings of the 24th international conference on Machine learning 209\u2013216. https:\/\/doi.org\/10.1145\/1273496.1273523","key":"1482_CR4","DOI":"10.1145\/1273496.1273523"},{"key":"1482_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10846-005-9016-2","volume":"7","author":"J Demsar","year":"2006","unstructured":"Demsar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1\u201330. https:\/\/doi.org\/10.1007\/s10846-005-9016-2","journal-title":"J Mach Learn Res"},{"issue":"6","key":"1482_CR6","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1109\/34.927464","volume":"23","author":"AS Georghiades","year":"2001","unstructured":"Georghiades AS, Belhumeur PN, Kriegman DJ (2001) From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE Trans Pattern Anal Mach Intell 23(6):643\u2013660. https:\/\/doi.org\/10.1109\/34.927464","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"doi-asserted-by":"publisher","unstructured":"Globerson A, Roweis ST (2006) Metric learning by collapsing classes. Adv Neural Inform Process Syst. https:\/\/doi.org\/10.5555\/2976248.2976305","key":"1482_CR7","DOI":"10.5555\/2976248.2976305"},{"doi-asserted-by":"publisher","unstructured":"Goldberger J, Hinton GE, Roweis ST, Salakhutdinov R (2004) Neighbourhood components analysis. In: NIPS'04: Proceedings of the 17th International Conference on Neural Information Processing Systems 513\u2013520. https:\/\/doi.org\/10.5555\/2976040.2976105","key":"1482_CR8","DOI":"10.5555\/2976040.2976105"},{"doi-asserted-by":"publisher","unstructured":"Ham J, Lee D (2008) Grassmann discriminant analysis: a unifying view on subspace-based learning. In: ICML'08: Proceedings of the 25th international conference on Machine learning 376\u2013383. https:\/\/doi.org\/10.1145\/1390156.1390204","key":"1482_CR9","DOI":"10.1145\/1390156.1390204"},{"key":"1482_CR10","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2011.5995564","author":"M Harandi","year":"2011","unstructured":"Harandi M, Sanderson C, Shirazi S, Lovell B (2011) Graph embedding discriminant analysis on Grassmannian manifolds for improved image set matching. IEEE Conf Comput Vis Pattern Recogn. https:\/\/doi.org\/10.1109\/CVPR.2011.5995564","journal-title":"IEEE Conf Comput Vis Pattern Recogn"},{"issue":"4","key":"1482_CR11","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1109\/TPAMI.2014.2353635","volume":"37","author":"M Hayat","year":"2015","unstructured":"Hayat M, Bennamoun M, An S (2015) Deep Reconstruction models for image set classification. IEEE Trans Pattern Anal Mach Intell 37(4):713\u2013727. https:\/\/doi.org\/10.1109\/TPAMI.2014.2353635","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"1482_CR12","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2011.5995500","author":"Y Hu","year":"2011","unstructured":"Hu Y, Mian AS, Owens R (2011a) Sparse approximated nearest points for image set classification. IEEE Comput Soc Conf Comput Vis Pattern Recogn. https:\/\/doi.org\/10.1109\/CVPR.2011.5995500","journal-title":"IEEE Comput Soc Conf Comput Vis Pattern Recogn"},{"key":"1482_CR13","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2011.283","author":"Y Hu","year":"2011","unstructured":"Hu Y, Mian A, Owens R (2011b) Face recognition using sparse approximated nearest points between image sets. IEEE Trans Pattern Anal Mach Intell. https:\/\/doi.org\/10.1109\/TPAMI.2011.283","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"doi-asserted-by":"publisher","unstructured":"Hu J, Lu J, Tan Y-P (2014) Discriminative deep metric learning for face verification in the wild. In: CVPR'14: Proceedings of the 2014 IEEE Conference on Computer Vision and Pattern Recognition 1875\u20131882. https:\/\/doi.org\/10.1109\/CVPR.2014.242","key":"1482_CR14","DOI":"10.1109\/CVPR.2014.242"},{"key":"1482_CR15","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1109\/CVPR.2015.7298609","volume":"2015","author":"Z Huang","year":"2015","unstructured":"Huang Z, Wang R, Shan S, Chen X (2015) Projection metric learning on grassmann manifold with application to video based face recognition. IEEE Conf Comput Vis Pattern Recogn 2015:140\u2013149. https:\/\/doi.org\/10.1109\/CVPR.2015.7298609","journal-title":"IEEE Conf Comput Vis Pattern Recogn"},{"key":"1482_CR16","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2015.2507130","author":"D Johnson","year":"2014","unstructured":"Johnson D, Xiong C, Corso J (2014) Semi-supervised nonlinear distance metric learning via forests of max-margin cluster hierarchies. IEEE Trans Knowl Data Eng. https:\/\/doi.org\/10.1109\/TKDE.2015.2507130","journal-title":"IEEE Trans Knowl Data Eng"},{"key":"1482_CR17","doi-asserted-by":"publisher","first-page":"1005","DOI":"10.1109\/TPAMI.2007.1037","volume":"29","author":"TK Kim","year":"2007","unstructured":"Kim TK, Kittler J, Cipolla R (2007) Discriminative learning and recognition of image set classes using canonical correlations. IEEE Trans Pattern Anal Mach Intell 29:1005. https:\/\/doi.org\/10.1109\/TPAMI.2007.1037","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"1482_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/CVPR.2008.4587572","volume":"2008","author":"M Kim","year":"2008","unstructured":"Kim M, Kumar S, Pavlovic V, Rowley H (2008) Face tracking and recognition with visual constraints in real-world videos. IEEE Conf Comput Vis Pattern Recogn 2008:1\u20138. https:\/\/doi.org\/10.1109\/CVPR.2008.4587572","journal-title":"IEEE Conf Comput Vis Pattern Recogn"},{"doi-asserted-by":"publisher","unstructured":"K\u00f6stinger M, Hirzer M, Wohlhart P, Roth PM, Bischof H (2012) Large scale metric learning from equivalence constraints. In: 2012 IEEE Conference on Computer Vision and Pattern Recognition, Providence 2288\u20132295. https:\/\/doi.org\/10.1109\/CVPR.2012.6247939.","key":"1482_CR19","DOI":"10.1109\/CVPR.2012.6247939"},{"key":"1482_CR20","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1016\/j.patcog.2017.02.032","volume":"75","author":"J Liang","year":"2018","unstructured":"Liang J, Hu Q, Zhu P, Wang W (2018) Efficient multi-modal geometric mean metric learning. Pattern Recogn 75:188\u2013198. https:\/\/doi.org\/10.1016\/j.patcog.2017.02.032","journal-title":"Pattern Recogn"},{"issue":"6","key":"1482_CR21","doi-asserted-by":"publisher","first-page":"1234","DOI":"10.1109\/tmm.2016.2646180","volume":"19","author":"VE Liong","year":"2017","unstructured":"Liong VE, Lu J, Tan Y-P, Zhou J (2017) Deep coupled metric learning for cross-modal matching. Trans Multi 19(6):1234\u20131244. https:\/\/doi.org\/10.1109\/tmm.2016.2646180","journal-title":"Trans Multi"},{"key":"1482_CR22","doi-asserted-by":"publisher","first-page":"1137","DOI":"10.1109\/CVPR.2015.7298717","volume":"2015","author":"J Lu","year":"2015","unstructured":"Lu J, Wang G, Deng W, Moulin P, Zhou J (2015) Multi-manifold deep metric learning for image set classification. IEEE Conf Comput Vis Pattern Recogn 2015:1137\u20131145. https:\/\/doi.org\/10.1109\/CVPR.2015.7298717","journal-title":"IEEE Conf Comput Vis Pattern Recogn"},{"key":"1482_CR23","doi-asserted-by":"publisher","first-page":"2666","DOI":"10.1109\/CVPR.2012.6247987","volume":"2012","author":"A Mignon","year":"2012","unstructured":"Mignon A, Jurie F (2012) PCCA: a new approach for distance learning from sparse pairwise constraints. IEEE Conf Comput Vis Pattern Recogn 2012:2666\u20132672. https:\/\/doi.org\/10.1109\/CVPR.2012.6247987","journal-title":"IEEE Conf Comput Vis Pattern Recogn"},{"key":"1482_CR24","doi-asserted-by":"publisher","first-page":"1447","DOI":"10.1109\/CVPR.2006.42","volume":"2006","author":"ME Nilsback","year":"2006","unstructured":"Nilsback ME, Zisserman A (2006) A visual vocabulary for flower classification a visual vocabulary for flower classification. IEEE Comput Soc Conf Comput Vis Pattern Recogn 2006:1447\u20131454. https:\/\/doi.org\/10.1109\/CVPR.2006.42","journal-title":"IEEE Comput Soc Conf Comput Vis Pattern Recogn"},{"issue":"1","key":"1482_CR25","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1109\/TPAMI.2017.2666151","volume":"40","author":"Y Noh","year":"2018","unstructured":"Noh Y, Zhang B, Lee DD (2018) Generative local metric learning for nearest neighbor classification. IEEE Trans Pattern Anal Mach Intell 40(1):106\u2013118. https:\/\/doi.org\/10.1109\/TPAMI.2017.2666151","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"1","key":"1482_CR26","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1134\/S1054661806010068","volume":"16","author":"OG Okun","year":"2006","unstructured":"Okun OG (2006) K-local hyperplane distance nearest-neighbor algorithm and protein fold recognition. Pattern Recogn Image Anal 16(1):19\u201322. https:\/\/doi.org\/10.1134\/S1054661806010068","journal-title":"Pattern Recogn Image Anal"},{"key":"1482_CR27","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.patrec.2016.03.018","volume":"83","author":"J Peng","year":"2016","unstructured":"Peng J, Zhang L, Li L (2016) Regularized set-to-set distance metric learning for hyperspectral image classification. Pattern Recogn Lett 83:143\u2013151. https:\/\/doi.org\/10.1016\/j.patrec.2016.03.018","journal-title":"Pattern Recogn Lett"},{"key":"1482_CR28","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1109\/CVPR.2015.7298682","volume":"2015","author":"F Schroff","year":"2015","unstructured":"Schroff F, Kalenichenko D, Philbin J (2015) FaceNet: a unified embedding for face recognition and clustering. IEEE Conf Comput Vis Pattern Recogn 2015:815\u2013823. https:\/\/doi.org\/10.1109\/CVPR.2015.7298682","journal-title":"IEEE Conf Comput Vis Pattern Recogn"},{"key":"1482_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TITS.2015.2506182","volume":"17","author":"M Tan","year":"2016","unstructured":"Tan M, Wang B, Wu Z, Wang J, Pan G (2016) Weakly supervised metric learning for traffic sign recognition in a LIDAR-equipped vehicle. IEEE Trans Intell Transp Syst 17:1\u201313. https:\/\/doi.org\/10.1109\/TITS.2015.2506182","journal-title":"IEEE Trans Intell Transp Syst"},{"key":"1482_CR30","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1109\/CVPR.2009.5206850","volume":"2009","author":"R Wang","year":"2009","unstructured":"Wang R, Chen X (2009) Manifold discriminant analysis. IEEE Conf Comput Vis Pattern Recogn 2009:429\u2013436. https:\/\/doi.org\/10.1109\/CVPR.2009.5206850","journal-title":"IEEE Conf Comput Vis Pattern Recogn"},{"issue":"10","key":"1482_CR31","doi-asserted-by":"publisher","first-page":"4466","DOI":"10.1109\/TIP.2012.2206039","volume":"21","author":"R Wang","year":"2012","unstructured":"Wang R, Shan S, Chen X, Dai Q, Gao W (2012) Manifold-manifold distance and its application to face recognition with image sets. IEEE Trans Image Process 21(10):4466\u20134479. https:\/\/doi.org\/10.1109\/TIP.2012.2206039","journal-title":"IEEE Trans Image Process"},{"issue":"1","key":"1482_CR32","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1109\/TIP.2017.2746993","volume":"27","author":"W Wang","year":"2017","unstructured":"Wang W, Wang R, Huang Z, Shan S, Chen X (2017) Discriminant analysis on riemannian manifold of gaussian distributions for face recognition with image sets. IEEE Trans Image Process 27(1):151\u2013163. https:\/\/doi.org\/10.1109\/TIP.2017.2746993","journal-title":"IEEE Trans Image Process"},{"key":"1482_CR33","doi-asserted-by":"publisher","DOI":"10.1007\/s10845-008-0108-2","author":"K Weinberger","year":"2006","unstructured":"Weinberger K, Blitzer J, Saul L (2006) Distance metric learning for large margin nearest neighbor classification. J Mach Learn Res. https:\/\/doi.org\/10.1007\/s10845-008-0108-2","journal-title":"J Mach Learn Res"},{"doi-asserted-by":"publisher","unstructured":"Xing EP, Ng AY, Jordan MI, Russell SJ (2002) Distance metric learning with application to clustering with side-information. InL NIPS'02: Proceedings of the 15th International Conference on Neural Information Processing Systems 521\u2013528. https:\/\/doi.org\/10.5555\/2968618.2968683","key":"1482_CR34","DOI":"10.5555\/2968618.2968683"},{"key":"1482_CR35","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1016\/j.knosys.2016.01.032","volume":"98","author":"J Xu","year":"2016","unstructured":"Xu J, Liu J, Yin J, Sun C (2016) A multi-label feature extraction algorithm via maximizing feature variance and feature-label dependence simultaneously. Knowl Based Syst 98:172\u2013184. https:\/\/doi.org\/10.1016\/j.knosys.2016.01.032","journal-title":"Knowl Based Syst"},{"doi-asserted-by":"publisher","unstructured":"Yamaguchi O, Fukui K, Maeda K-I (1998) Face recognition using temporal image sequence. In: Proceedings Third IEEE International Conference on Automatic Face and Gesture Recognition 318\u2013323. https:\/\/doi.org\/10.1109\/AFGR.1998.670968","key":"1482_CR36","DOI":"10.1109\/AFGR.1998.670968"},{"doi-asserted-by":"publisher","unstructured":"Yang M, Zhu P, Van Gool L, Zhang L (2013) Face recognition based on regularized nearest points between image sets. In: 2013 10th IEEE International Conference and Workshops on Automatic Face and Gesture Recognition 1\u20137. https:\/\/doi.org\/10.1109\/FG.2013.6553727","key":"1482_CR37","DOI":"10.1109\/FG.2013.6553727"},{"key":"1482_CR38","doi-asserted-by":"publisher","first-page":"2664","DOI":"10.1109\/ICCV.2013.331","volume":"2013","author":"P Zhu","year":"2013","unstructured":"Zhu P, Zhang L, Zuo W, Zhang D (2013) From point to set: extend the learning of distance metrics. IEEE Int Conf Comput Vis 2013:2664\u20132671. https:\/\/doi.org\/10.1109\/ICCV.2013.331","journal-title":"IEEE Int Conf Comput Vis"},{"key":"1482_CR39","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/j.ins.2014.06.017","volume":"282","author":"P Zhu","year":"2014","unstructured":"Zhu P, Hu Q, Zuo W, Yang M (2014) Multi-granularity distance metric learning via neighborhood granule margin maximization. Inf Sci 282:321\u2013331. https:\/\/doi.org\/10.1016\/j.ins.2014.06.017","journal-title":"Inf Sci"},{"doi-asserted-by":"publisher","unstructured":"Zhu P, Qi R, Hu Q, Wang Q, Zhang C, Yang L (2018) Beyond similar and dissimilar relations: a kernel regression formulation for metric learning. In: IJCAI'18: Proceedings of the 27th International Joint Conference on Artificial Intelligence 3242\u20133248. https:\/\/doi.org\/10.5555\/3304889.3305111","key":"1482_CR40","DOI":"10.5555\/3304889.3305111"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01482-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-021-01482-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01482-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,7]],"date-time":"2021-06-07T11:46:11Z","timestamp":1623066371000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-021-01482-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,17]]},"references-count":40,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["1482"],"URL":"https:\/\/doi.org\/10.1007\/s40314-021-01482-x","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2021,4,17]]},"assertion":[{"value":"6 July 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 March 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 March 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"113"}}