{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:53:40Z","timestamp":1753887220543,"version":"3.41.2"},"reference-count":47,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T00:00:00Z","timestamp":1576108800000},"content-version":"vor","delay-in-days":345,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61972278","61602340","61572348"],"award-info":[{"award-number":["61972278","61602340","61572348"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004735","name":"Natural Science Foundation of Hunan Province","doi-asserted-by":"publisher","award":["2016JJ1024"],"award-info":[{"award-number":["2016JJ1024"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>We present a novel loss function, namely, GO loss, for classification. Most of the existing methods, such as center loss and contrastive loss, dynamically determine the convergence direction of the sample features during the training process. By contrast, GO loss decomposes the convergence direction into two mutually orthogonal components, namely, tangential and radial directions, and conducts optimization on them separately. The two components theoretically affect the interclass separation and the intraclass compactness of the distribution of the sample features, respectively. Thus, separately minimizing losses on them can avoid the effects of their optimization. Accordingly, a stable convergence center can be obtained for each of them. Moreover, we assume that the two components follow Gaussian distribution, which is proved as an effective way to accurately model training features for improving the classification effects. Experiments on multiple classification benchmarks, such as MNIST, CIFAR, and ImageNet, demonstrate the effectiveness of GO loss.<\/jats:p>","DOI":"10.1155\/2019\/9206053","type":"journal-article","created":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T23:32:04Z","timestamp":1576193524000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["GO Loss: A Gaussian Distribution\u2010Based Orthogonal Decomposition Loss for Classification"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5262-2563","authenticated-orcid":false,"given":"Mengxin","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9047-4231","authenticated-orcid":false,"given":"Wenyuan","family":"Tao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2854-3344","authenticated-orcid":false,"given":"Xiao","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4141-0554","authenticated-orcid":false,"given":"Yi","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6511-4090","authenticated-orcid":false,"given":"Jie","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2106-7226","authenticated-orcid":false,"given":"Chung-Ming","family":"Own","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2019,12,12]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"crossref","unstructured":"HuangG. LiuZ. van der MaatenL. andWeinbergerK. Q. Densely connected convolutional networks Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition July 2017 Honolulu HI USA 4700\u20134708 https:\/\/doi.org\/10.1109\/cvpr.2017.243 2-s2.0-85035343801.","DOI":"10.1109\/CVPR.2017.243"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.26599\/tst.2019.9010005"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/9385947"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/9248410"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/7130146"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2018.2882449"},{"key":"e_1_2_10_7_2","first-page":"1097","volume-title":"Advances in Neural Information Processing Systems","author":"Krizhevsky A.","year":"2012"},{"key":"e_1_2_10_8_2","unstructured":"IoffeS.andSzegedyC. Batch normalization: accelerating deep network training by reducing internal covariate shift 2015 http:\/\/arxiv.org\/abs\/1502.03167."},{"key":"e_1_2_10_9_2","doi-asserted-by":"crossref","unstructured":"HeK. ZhangX. RenS. andSunJ. Deep residual learning for image recognition Proceedings of the The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) June 2016 Las Vegas NV USA https:\/\/doi.org\/10.1109\/cvpr.2016.90 2-s2.0-84986274465.","DOI":"10.1109\/CVPR.2016.90"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/8524825"},{"key":"e_1_2_10_11_2","unstructured":"ZhangC. BengioS. HardtM. RechtB. andVinyalsO. Understanding deep learning requires rethinking generalization 2016 http:\/\/arxiv.org\/abs\/1611.03530."},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/2861695"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1109\/tasl.2011.2134090"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/msp.2012.2205597"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/7143586"},{"key":"e_1_2_10_16_2","doi-asserted-by":"crossref","unstructured":"WenY. LiZ. andQiaoY. Latent factor guided convolutional neural networks for age-invariant face recognition In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) June 2016 Las Vegas NV USA https:\/\/doi.org\/10.1109\/cvpr.2016.529 2-s2.0-84986330157.","DOI":"10.1109\/CVPR.2016.529"},{"key":"e_1_2_10_17_2","doi-asserted-by":"crossref","unstructured":"SzegedyC. VincentV. IoffeS. ShlensJ. andWojnaZ. Rethinking the inception architecture for computer vision Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) June 2016 Las Vegas NV USA https:\/\/doi.org\/10.1109\/cvpr.2016.308 2-s2.0-84986296808.","DOI":"10.1109\/CVPR.2016.308"},{"key":"e_1_2_10_18_2","doi-asserted-by":"crossref","unstructured":"ZagoruykoS.andKomodakisN. Wide residual networks 2016 http:\/\/arxiv.org\/abs\/1605.07146.","DOI":"10.5244\/C.30.87"},{"key":"e_1_2_10_19_2","unstructured":"LarssonG. MaireM. andShakhnarovichG. Fractalnet: ultra-deep neural networks without residuals 2016 http:\/\/arxiv.org\/abs\/1605.07648."},{"volume-title":"Computer Vision\u2013ACCV 2010","year":"2010","author":"Nguyen H. V.","key":"e_1_2_10_20_2"},{"key":"e_1_2_10_21_2","doi-asserted-by":"publisher","DOI":"10.1109\/tnnls.2017.2691005"},{"key":"e_1_2_10_22_2","first-page":"207","article-title":"Distance metric learning for large margin nearest neighbor classification","volume":"10","author":"Weinberger K. Q.","year":"2009","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_10_23_2","doi-asserted-by":"crossref","unstructured":"ZhengY. PalD. K. andSavvidesM. Ring loss: convex feature normalization for face recognition 2018 http:\/\/arxiv.org\/abs\/1803.00130.","DOI":"10.1109\/CVPR.2018.00534"},{"key":"e_1_2_10_24_2","unstructured":"LiuW. WenY. YuZ. andYangM. Large-margin softmax loss for convolutional neural networks Proceedings of the International Conference on Machine Learning 2016 Newyork NY USA 507\u2013516."},{"key":"e_1_2_10_25_2","first-page":"1988","volume-title":"Advances in Neural Information Processing Systems","author":"Sun Y.","year":"2014"},{"key":"e_1_2_10_26_2","doi-asserted-by":"crossref","unstructured":"SchroffF. KalenichenkoD. andPhilbinJ. Facenet: a unified embedding for face recognition and clustering Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) June 2015 Boston MA USA https:\/\/doi.org\/10.1109\/cvpr.2015.7298682 2-s2.0-84946751287.","DOI":"10.1109\/CVPR.2015.7298682"},{"key":"e_1_2_10_27_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-46478-7_31"},{"key":"e_1_2_10_28_2","doi-asserted-by":"crossref","unstructured":"WanW. ZhongY. LiT. andChenJ. Rethinking feature distribution for loss functions in image classification Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) June 2018 Salt Lake City UT USA https:\/\/doi.org\/10.1109\/cvpr.2018.00950 2-s2.0-85060872316.","DOI":"10.1109\/CVPR.2018.00950"},{"key":"e_1_2_10_29_2","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/6516253"},{"key":"e_1_2_10_30_2","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/3581419"},{"key":"e_1_2_10_31_2","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/5238028"},{"key":"e_1_2_10_32_2","doi-asserted-by":"crossref","unstructured":"GuillauminM. VerbeekJ. andSchmidC. Is that you? metric learning approaches for face identification Proceedings of the 2009 IEEE 12th International Conference on Computer Vision September 2009 Kyoto Japan IEEE 498\u2013505 https:\/\/doi.org\/10.1109\/iccv.2009.5459197 2-s2.0-77953178820.","DOI":"10.1109\/ICCV.2009.5459197"},{"key":"e_1_2_10_33_2","first-page":"31","volume-title":"Computer Vision\u2013ACCV 2012","author":"Li W.","year":"2012"},{"key":"e_1_2_10_34_2","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/8917393"},{"key":"e_1_2_10_35_2","doi-asserted-by":"publisher","DOI":"10.1109\/tvcg.2018.2851227"},{"key":"e_1_2_10_36_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2018.2889054"},{"key":"e_1_2_10_37_2","doi-asserted-by":"crossref","unstructured":"YangH.-M. ZhangX.-Y. YinF. andLiuC.-L. Robust classification with convolutional prototype learning Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition June 2018 Salt Lake City UT USA 3474\u20133482 https:\/\/doi.org\/10.1109\/cvpr.2018.00366 2-s2.0-85060879158.","DOI":"10.1109\/CVPR.2018.00366"},{"key":"e_1_2_10_38_2","unstructured":"LiangZ. YangM. andWangC. 3D graph embedding learning with a structure-aware loss function for point cloud semantic instance segmentation 2019 http:\/\/arxiv.org\/abs\/1902.05247."},{"key":"e_1_2_10_39_2","first-page":"6466","volume-title":"Advances in Neural Information Processing Systems","author":"Wu L.","year":"2018"},{"key":"e_1_2_10_40_2","first-page":"8778","volume-title":"Advances in Neural Information Processing Systems","author":"Zhang Z.","year":"2018"},{"key":"e_1_2_10_41_2","doi-asserted-by":"crossref","unstructured":"WangY. MaX. ChenZ. LuoY. YiJ. andBaileyJ. Symmetric cross entropy for robust learning with noisy labels 2019 http:\/\/arxiv.org\/abs\/1908.06112.","DOI":"10.1109\/ICCV.2019.00041"},{"key":"e_1_2_10_42_2","doi-asserted-by":"publisher","DOI":"10.1109\/5.726791"},{"key":"e_1_2_10_43_2","unstructured":"HanX. RasulK. andRolandV. Fashion-MNIST: a novel image dataset for benchmarking machine learning algorithms 2017 http:\/\/arxiv.org\/abs\/1708.07747."},{"key":"e_1_2_10_44_2","unstructured":"KrizhevskyA. Learning multiple layers of features from tiny images 2009 University of Toronto Toronto Canada Technical Report TR-2009."},{"key":"e_1_2_10_45_2","doi-asserted-by":"crossref","unstructured":"HeK. ZhangX. RenS. andSunJ. Delving deep into rectifiers: surpassing human-level performance on imagenet classification Proceedings of the IEEE International Conference on Computer Vision December 2015 Santiago Chile 1026\u20131034 https:\/\/doi.org\/10.1109\/iccv.2015.123 2-s2.0-84973911419.","DOI":"10.1109\/ICCV.2015.123"},{"key":"e_1_2_10_46_2","doi-asserted-by":"crossref","unstructured":"JiaD. SocherR. Fei-FeiL. DongW. LiK. andLiLi-J. Imagenet: a large-scale hierarchical image database Proceedings of the 2009 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) June 2009 Miami FL USA 248\u2013255 https:\/\/doi.org\/10.1109\/cvprw.2009.5206848.","DOI":"10.1109\/CVPRW.2009.5206848"},{"key":"e_1_2_10_47_2","doi-asserted-by":"crossref","unstructured":"ZhangX. ZhaoR. QiaoY. WangX. andLiH. Adacos: adaptively scaling cosine logits for effectively learning deep face representations Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition 2019 Salt Lake City UT USA 10823\u201310832.","DOI":"10.1109\/CVPR.2019.01108"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2019\/9206053.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2019\/9206053.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2019\/9206053","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T12:06:01Z","timestamp":1723032361000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2019\/9206053"}},"subtitle":[],"editor":[{"given":"Mahardhika","family":"Pratama","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":47,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1155\/2019\/9206053"],"URL":"https:\/\/doi.org\/10.1155\/2019\/9206053","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2019,1]]},"assertion":[{"value":"2019-06-17","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-11-20","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-12-12","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"9206053"}}