{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T15:29:51Z","timestamp":1761060591359,"version":"3.41.0"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2018,6,5]],"date-time":"2018-06-05T00:00:00Z","timestamp":1528156800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U1636205"],"award-info":[{"award-number":["U1636205"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. & Cyber."],"published-print":{"date-parts":[[2019,6]]},"DOI":"10.1007\/s13042-018-0829-2","type":"journal-article","created":{"date-parts":[[2018,6,5]],"date-time":"2018-06-05T04:24:25Z","timestamp":1528172665000},"page":"1503-1511","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Statistical learning with group invariance: problem, method and consistency"],"prefix":"10.1007","volume":"10","author":[{"given":"Weixia","family":"Xu","sequence":"first","affiliation":[]},{"given":"Dingjiang","family":"Huang","sequence":"additional","affiliation":[]},{"given":"Shuigeng","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,6,5]]},"reference":[{"key":"829_CR1","volume-title":"Statistical learning theory","author":"VN Vapnik","year":"1998","unstructured":"Vapnik VN (1998) Statistical learning theory. Wiley, New York"},{"doi-asserted-by":"crossref","unstructured":"von Luxburg, U, Sch\u00f6lkopf B (2011) Statistical learning theory: models, concepts, and results. In: Handbook of the history of logic, vol\u00a010, pp 651\u2013706. Elsevier","key":"829_CR2","DOI":"10.1016\/B978-0-444-52936-7.50016-1"},{"key":"829_CR3","volume-title":"Learning with kernels: support vector machines, regularization, optimization and beyond","author":"B Sch\u00f6lkopf","year":"2002","unstructured":"Sch\u00f6lkopf B, Smola AJ (2002) Learning with kernels: support vector machines, regularization, optimization and beyond. MIT Press, Cambridge, MA"},{"issue":"7","key":"829_CR4","doi-asserted-by":"publisher","first-page":"1578","DOI":"10.1016\/j.neucom.2007.04.010","volume":"71","author":"F Lauer","year":"2008","unstructured":"Lauer F, Bloch G (2008) Incorporating prior knowledge in support vector machines for classification: a review. Neurocomputing 71(7):1578\u20131594","journal-title":"Neurocomputing"},{"issue":"1","key":"829_CR5","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1109\/4235.585893","volume":"1","author":"DH Wolpert","year":"1997","unstructured":"Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67\u201382","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"829_CR6","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/s10994-007-5009-7","volume":"68","author":"B Haasdonk","year":"2007","unstructured":"Haasdonk B, Burkhardt H (2007) Invariant kernel functions for pattern analysis and machine learning. Mach Learn 68(1):35\u201361","journal-title":"Mach Learn"},{"issue":"1","key":"829_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0031-3203(95)00069-0","volume":"29","author":"J Wood","year":"1996","unstructured":"Wood J (1996) Invariant pattern recognition: a review. Pattern Recogn 29(1):1\u201317","journal-title":"Pattern Recogn"},{"unstructured":"Kondor R (2008) Group theoretical methods in machine learning. Ph.D. thesis, Columbia University","key":"829_CR8"},{"key":"829_CR9","first-page":"50","volume-title":"Advances in neural information processing systems 5","author":"PY Simard","year":"1993","unstructured":"Simard PY, Cun YL, Denker JS (1993) Efficient pattern recognition using a new transformation distance. In: Hanson S, Cowan J, Giles C (eds) Advances in neural information processing systems 5. Morgan Kaufmann Publishers Inc, San Francisco, CA, pp 50\u201358"},{"doi-asserted-by":"crossref","unstructured":"Simard PY, Cun YL, Denker JS, Victorri B (1998) Transformation invariance in pattern recognition - tangent distance and tangent propagation. In: Orr GB, M\u00fcller KR (eds) Neural networks: tricks of the trade, Lecture Notes in Computer Science, vol 1524, pp 239\u2013274. Springer","key":"829_CR10","DOI":"10.1007\/3-540-49430-8_13"},{"doi-asserted-by":"crossref","unstructured":"Sch\u00f6lkopf B, Burges C, Vapnik VN (1996) Incorporating invariances in support vector learning machines. In: von\u00a0der Malsburg C, von Seelen W, Vorbr\u00fcggen JC, Sendhoff B (eds) Proceedings of ICANN 96: Artificial Neural Networks, pp 47\u201352. Springer(1996)","key":"829_CR11","DOI":"10.1007\/3-540-61510-5_12"},{"issue":"11","key":"829_CR12","doi-asserted-by":"publisher","first-page":"2196","DOI":"10.1109\/5.726787","volume":"86","author":"P Niyogi","year":"1998","unstructured":"Niyogi P, Girosi F, Poggio T (1998) Incorporating prior information in machine learning by creating virtual examples. Proc IEEE 86(11):2196\u20132209","journal-title":"Proc IEEE"},{"issue":"1\u20133","key":"829_CR13","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1023\/A:1012454411458","volume":"46","author":"D DeCoste","year":"2002","unstructured":"DeCoste D, Sch\u00f6lkopf B (2002) Training invariant support vector machines. Mach Learn 46(1\u20133):161\u2013190","journal-title":"Mach Learn"},{"doi-asserted-by":"crossref","unstructured":"Schulz-Mirbach H, Sch\u00f6lkopf B (1994) Constructing invariant features by averaging techniques. In: Proceedings of the 12th International Conference on Pattern Recognition (ICPR\u201994), pp 387\u2013390. IEEE, Jerusalem, Israel","key":"829_CR14","DOI":"10.1109\/ICPR.1994.576950"},{"unstructured":"Kondor R, Jebara T (2003) A kernel between sets of vectors. In: Fawcett T, Mishra N (eds) Proceedings of the 20th International Conference on Machine Learning (ICML\u201903), pp 361\u2013368. AAAI Press, Washington, DC (2003)","key":"829_CR15"},{"doi-asserted-by":"crossref","unstructured":"Wang L, Gao Y, Chan KL, Xue P, Yau WY (2005) Retrieval with knowledge-driven kernel design: an approach to improving svm based cbir with relevance feedback. In: Proceedings of the 10th International Conference on Computer Vision (ICCV\u201905), vol\u00a02, pp 1355\u20131362. IEEE, Beijing, China","key":"829_CR16","DOI":"10.1109\/ICCV.2005.208"},{"issue":"3","key":"829_CR17","first-page":"385","volume":"8","author":"M Reisert","year":"2007","unstructured":"Reisert M, Burkhardt H (2007) Learning equivariant functions with matrix valued kernels. J Mach Learn Res 8(3):385\u2013408","journal-title":"J Mach Learn Res"},{"unstructured":"Graepel T, Herbrich R (2004) Invariant pattern recognition by semidefinite programming machines. In: Thrun S, Saul LK, Sch\u00f6lkopf B (eds) Advances in Neural Information Processing Systems 16 (NIPS 2003), pp 33\u201340. MIT Press","key":"829_CR18"},{"unstructured":"Bhattacharyya C, Shivaswamy PK, Smola AJ (2005) A second order cone programming formulation for classifying missing data. In: Saul L, Weiss Y, Bottou L (eds) Advances in Neural Information Processing Systems 17 (NIPS 2004), pp 153\u2013160. MIT Press","key":"829_CR19"},{"doi-asserted-by":"crossref","unstructured":"Shivaswamy PK, Jebara T (2006) Permutation invariant svms. In: Cohen WW, Moore A (eds) Proceedings of the 23rd International Conference on Machine Learning (ICML\u201906), pp 817\u2013824. ACM, Pittsburgh, USA","key":"829_CR20","DOI":"10.1145\/1143844.1143947"},{"unstructured":"Jebara T (2003) Convex invariance learning. In: Bishop CM, Frey BJ (eds) Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics (AI & Statistics\u201903). Key West, Florida","key":"829_CR21"},{"unstructured":"Teo CH, Globerson A, Roweis ST, Smola AJ (2008) Convex learning with invariances. In: Advances in Neural Information Processing Systems 20 (NIPS 2007), pp 1489\u20131496. Curran Associates, Inc.","key":"829_CR22"},{"doi-asserted-by":"crossref","unstructured":"Kumar MP, Torr PHS, Zisserman A (2007) An invariant large margin nearest neighbour classifier. In: Proceedings of the 11th International Conference on Computer Vision (ICCV 2007), pp 1\u20138. IEEE, Rio de Janeiro","key":"829_CR23","DOI":"10.1109\/ICCV.2007.4409041"},{"issue":"1","key":"829_CR24","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s10994-007-5035-5","volume":"70","author":"F Lauer","year":"2008","unstructured":"Lauer F, Bloch G (2008) Incorporating prior knowledge in support vector regression. Mach Learn 70(1):89\u2013118","journal-title":"Mach Learn"},{"doi-asserted-by":"crossref","unstructured":"Vedaldi A, Blaschko M, Zisserman A (2011) Learning equivariant structured output svm regressors. In: Proceedings of the 13th International Conference on Computer Vision (ICCV\u201911). pp 959\u2013966. IEEE, Barcelona","key":"829_CR25","DOI":"10.1109\/ICCV.2011.6126339"},{"doi-asserted-by":"crossref","unstructured":"Eaton ML (1989) Group invariance applications in statistics. In: Regional conference series in Probability and Statistics, vol\u00a01, pp i\u2013v+1\u2013133. Institute of Mathematical Statistics","key":"829_CR26","DOI":"10.1214\/cbms\/1462061029"},{"key":"829_CR27","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3264-1","volume-title":"The nature of statistical learning theory","author":"VN Vapnik","year":"2000","unstructured":"Vapnik VN (2000) The nature of statistical learning theory, 2nd edn. Springer, Berlin","edition":"2"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-018-0829-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13042-018-0829-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-018-0829-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T23:49:21Z","timestamp":1751672961000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13042-018-0829-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,5]]},"references-count":27,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["829"],"URL":"https:\/\/doi.org\/10.1007\/s13042-018-0829-2","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"type":"print","value":"1868-8071"},{"type":"electronic","value":"1868-808X"}],"subject":[],"published":{"date-parts":[[2018,6,5]]},"assertion":[{"value":"4 February 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 May 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 June 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}