{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:34:50Z","timestamp":1772120090086,"version":"3.50.1"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2024,1,9]],"date-time":"2024-01-09T00:00:00Z","timestamp":1704758400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,9]],"date-time":"2024-01-09T00:00:00Z","timestamp":1704758400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"the Key Program of the National Natural Science Foundation of China","award":["62136005"],"award-info":[{"award-number":["62136005"]}]},{"name":"the Key Program of the National Natural Science Foundation of China","award":["62136005"],"award-info":[{"award-number":["62136005"]}]},{"name":"the Key Program of the National Natural Science Foundation of China","award":["62136005"],"award-info":[{"award-number":["62136005"]}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62276162"],"award-info":[{"award-number":["62276162"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. & Cyber."],"published-print":{"date-parts":[[2024,7]]},"DOI":"10.1007\/s13042-023-02061-8","type":"journal-article","created":{"date-parts":[[2024,1,9]],"date-time":"2024-01-09T01:02:33Z","timestamp":1704762153000},"page":"2749-2760","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Centrosymmetric constrained Convolutional Neural Networks"],"prefix":"10.1007","volume":"15","author":[{"given":"Keyin","family":"Zheng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuhua","family":"Qian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhian","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Furong","family":"Peng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,1,9]]},"reference":[{"key":"2061_CR1","doi-asserted-by":"crossref","unstructured":"(1980) Theory of edge detection. Proceedings of the Royal Society of London Series B Biological Sciences 207(1167):187\u2013217","DOI":"10.1098\/rspb.1980.0020"},{"issue":"12","key":"2061_CR2","doi-asserted-by":"publisher","first-page":"772","DOI":"10.1038\/s42256-020-00265-z","volume":"2","author":"Z Chen","year":"2020","unstructured":"Chen Z, Bei Y, Rudin C (2020) Concept whitening for interpretable image recognition. Nat Mach Intell 2(12):772\u2013782","journal-title":"Nat Mach Intell"},{"issue":"6","key":"2061_CR3","doi-asserted-by":"publisher","first-page":"824","DOI":"10.1360\/SSI-2020-0009","volume":"50","author":"H Cheng","year":"2020","unstructured":"Cheng H, Qian Y, Hu Z, Liang J (2020) Association mining method based on neighborhood perspective. Scientia Sinica Informationis 50(6):824\u2013844","journal-title":"Scientia Sinica Informationis"},{"key":"2061_CR4","doi-asserted-by":"crossref","unstructured":"Cheng H, Qian Y, Guo Y, Zheng K, Zhang Q (2022) Neighborhood information-based method for multivariate association mining. IEEE Trans Knowl Data Eng","DOI":"10.1109\/TKDE.2022.3178090"},{"key":"2061_CR5","doi-asserted-by":"crossref","unstructured":"Chen C, Li O, Tao D, Barnett A, Rudin C, Su JK (2019) This looks like that: deep learning for interpretable image recognition. Adv Neural Inf Process Syst 32","DOI":"10.1609\/hcomp.v7i1.5265"},{"key":"2061_CR6","unstructured":"Cohen T, Welling M (2016) Group equivariant convolutional networks. In: International conference on machine learning, PMLR, pp 2990\u20132999"},{"key":"2061_CR7","unstructured":"Dou H, Zhang L, Han F, Shen F, Zhao J (2023) Survey on convolutional neural network interpretability. J Software 1\u201327"},{"key":"2061_CR8","unstructured":"Gens R, Domingos PM (2014) Deep symmetry networks. Adv Neural Inf Process Syst 27"},{"key":"2061_CR9","doi-asserted-by":"crossref","unstructured":"Gulati A, Qin J, Chiu CC, Parmar N, Zhang Y, Yu J, Han W, Wang S, Zhang Z, Wu Y, et\u00a0al (2020) Conformer: convolution-augmented transformer for speech recognition. arXiv preprint arXiv:2005.08100","DOI":"10.21437\/Interspeech.2020-3015"},{"key":"2061_CR10","doi-asserted-by":"crossref","unstructured":"He K, Zhang X, Ren S, Sun J (2016) Deep residual learning for image recognition. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 770\u2013778","DOI":"10.1109\/CVPR.2016.90"},{"key":"2061_CR11","doi-asserted-by":"publisher","DOI":"10.3389\/fncom.2022.836498","volume":"16","author":"I Higgins","year":"2022","unstructured":"Higgins I, Racani\u00e8re S, Rezende D (2022) Symmetry-based representations for artificial and biological general intelligence. Front Comput Neurosci 16:836498","journal-title":"Front Comput Neurosci"},{"issue":"1","key":"2061_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0734-189X(83)90093-2","volume":"22","author":"EC Hildreth","year":"1983","unstructured":"Hildreth EC (1983) The detection of intensity changes by computer and biological vision systems. Comput Vis Graph Image Process 22(1):1\u201327","journal-title":"Comput Vis Graph Image Process"},{"issue":"1","key":"2061_CR13","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1113\/jphysiol.1962.sp006837","volume":"160","author":"DH Hubel","year":"1962","unstructured":"Hubel DH, Wiesel TN (1962) Receptive fields, binocular interaction and functional architecture in the cat\u2019s visual cortex. J Physiol 160(1):106","journal-title":"J Physiol"},{"key":"2061_CR14","unstructured":"Jeyakumar JV, Dickens L, Garcia L, Cheng YH, Echavarria DR, Noor J, Russo A, Kaplan L, Blasch E, Srivastava M (2022) Automatic concept extraction for concept bottleneck-based video classification. arXiv preprint arXiv:2206.10129"},{"key":"2061_CR15","doi-asserted-by":"crossref","unstructured":"Karpathy A, Toderici G, Shetty S, Leung T, Sukthankar R, Fei-Fei L (2014) Large-scale video classification with convolutional neural networks. In: Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, pp 1725\u20131732","DOI":"10.1109\/CVPR.2014.223"},{"key":"2061_CR16","doi-asserted-by":"crossref","unstructured":"Kim Y (2014) Convolutional neural networks for sentence classification. arXiv preprint arXiv:1408.5882","DOI":"10.3115\/v1\/D14-1181"},{"key":"2061_CR17","doi-asserted-by":"crossref","unstructured":"Kim E, Kim S, Seo M, Yoon S (2021) Xprotonet: diagnosis in chest radiography with global and local explanations. In: Proceedings of the IEEE\/CVF conference on computer vision and pattern recognition, pp 15719\u201315728","DOI":"10.1109\/CVPR46437.2021.01546"},{"key":"2061_CR18","unstructured":"Koh PW, Nguyen T, Tang YS, Mussmann S, Pierson E, Kim B, Liang P (2020) Concept bottleneck models. In: International conference on machine learning, PMLR, pp 5338\u20135348"},{"issue":"6","key":"2061_CR19","doi-asserted-by":"publisher","first-page":"1719","DOI":"10.1109\/TSMCB.2012.2228639","volume":"43","author":"H Kong","year":"2013","unstructured":"Kong H, Akakin HC, Sarma SE (2013) A generalized Laplacian of gaussian filter for blob detection and its applications. IEEE Trans Cybern 43(6):1719\u20131733","journal-title":"IEEE Trans Cybern"},{"key":"2061_CR20","unstructured":"Krizhevsky A, Sutskever I, Hinton GE (2012) Imagenet classification with deep convolutional neural networks. Adv Neural Inf Process Syst 25"},{"issue":"4","key":"2061_CR21","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1162\/neco.1989.1.4.541","volume":"1","author":"Y LeCun","year":"1989","unstructured":"LeCun Y, Boser B, Denker JS, Henderson D, Howard RE, Hubbard W, Jackel LD (1989) Backpropagation applied to handwritten zip code recognition. Neural Comput 1(4):541\u2013551","journal-title":"Neural Comput"},{"issue":"11","key":"2061_CR22","doi-asserted-by":"publisher","first-page":"2278","DOI":"10.1109\/5.726791","volume":"86","author":"Y LeCun","year":"1998","unstructured":"LeCun Y, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278\u20132324","journal-title":"Proc IEEE"},{"key":"2061_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2020.107495","volume":"171","author":"O Li","year":"2020","unstructured":"Li O, Pl S (2020) Subpixel blob localization and shape estimation by gradient search in parameter space of anisotropic gaussian kernels. Signal Process 171:107495","journal-title":"Signal Process"},{"issue":"12","key":"2061_CR24","doi-asserted-by":"publisher","first-page":"9236","DOI":"10.1109\/TPAMI.2021.3125995","volume":"44","author":"X Liang","year":"2021","unstructured":"Liang X, Qian Y, Guo Q, Cheng H, Liang J (2021) Af: an association-based fusion method for multi-modal classification. IEEE Trans Pattern Anal Mach Intell 44(12):9236\u20139254","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"2061_CR25","unstructured":"Losch M, Fritz M, Schiele B (2019) Interpretability beyond classification output: semantic bottleneck networks. arXiv preprint arXiv:1907.10882"},{"issue":"6","key":"2061_CR26","doi-asserted-by":"publisher","first-page":"4421","DOI":"10.1007\/s00521-022-08168-3","volume":"35","author":"KDG Maduranga","year":"2023","unstructured":"Maduranga KDG, Zadorozhnyy V, Ye Q (2023) Symmetry-structured convolutional neural networks. Neural Comput Appl 35(6):4421\u20134434","journal-title":"Neural Comput Appl"},{"key":"2061_CR27","doi-asserted-by":"crossref","unstructured":"Sainath TN, Vinyals O, Senior A, Sak H (2015) Convolutional, long short-term memory, fully connected deep neural networks. In: 2015 IEEE international conference on acoustics, speech and signal processing (ICASSP), IEEE, pp 4580\u20134584","DOI":"10.1109\/ICASSP.2015.7178838"},{"key":"2061_CR28","doi-asserted-by":"publisher","first-page":"41758","DOI":"10.1109\/ACCESS.2022.3167702","volume":"10","author":"Y Sawada","year":"2022","unstructured":"Sawada Y, Nakamura K (2022) Concept bottleneck model with additional unsupervised concepts. IEEE Access 10:41758\u201341765","journal-title":"IEEE Access"},{"key":"2061_CR29","unstructured":"Simonyan K, Zisserman A (2015) Very deep convolutional networks for large-scale image recognition. In: 3rd International Conference on Learning Representations (ICLR 2015), Computational and Biological Learning Society"},{"key":"2061_CR30","first-page":"4","volume-title":"Image local invariant features and descriptors","author":"Y Wang","year":"2010","unstructured":"Wang Y, Wang G (2010) Image local invariant features and descriptors. National Defense Industry Press, Beijing, p 4"},{"key":"2061_CR31","unstructured":"Yuksekgonul M, Wang M, Zou J (2022) Post-hoc concept bottleneck models. arXiv preprint arXiv:2205.15480"},{"key":"2061_CR32","doi-asserted-by":"crossref","unstructured":"Zhang Q, Wu YN, Zhu SC (2018) Interpretable convolutional neural networks. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 8827\u20138836","DOI":"10.1109\/CVPR.2018.00920"},{"key":"2061_CR33","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.ijar.2023.02.005","volume":"156","author":"K Zheng","year":"2023","unstructured":"Zheng K, Qian Y, Cheng H (2023) How to describe the spatial near-far relations among concepts? Int J Approx Reason 156:97\u2013113","journal-title":"Int J Approx Reason"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-023-02061-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13042-023-02061-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-023-02061-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,19]],"date-time":"2024-07-19T10:48:47Z","timestamp":1721386127000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13042-023-02061-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,9]]},"references-count":33,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2024,7]]}},"alternative-id":["2061"],"URL":"https:\/\/doi.org\/10.1007\/s13042-023-02061-8","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-3371556\/v1","asserted-by":"object"}]},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"value":"1868-8071","type":"print"},{"value":"1868-808X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,9]]},"assertion":[{"value":"20 September 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 December 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 January 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}