{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T18:34:03Z","timestamp":1776882843637,"version":"3.51.2"},"publisher-location":"Cham","reference-count":29,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030865221","type":"print"},{"value":"9783030865238","type":"electronic"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-86523-8_43","type":"book-chapter","created":{"date-parts":[[2021,9,10]],"date-time":"2021-09-10T06:05:16Z","timestamp":1631253916000},"page":"713-728","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Invertible Manifold Learning for Dimension Reduction"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6806-2468","authenticated-orcid":false,"given":"Siyuan","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haitao","family":"Lin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zelin","family":"Zang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lirong","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Xia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2961-8096","authenticated-orcid":false,"given":"Stan Z.","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,9,11]]},"reference":[{"key":"43_CR1","unstructured":"Behrmann, J., Grathwohl, W., Chen, R.T.Q., Duvenaud, D., Jacobsen, J.: Invertible residual networks. In: International Conference on Machine Learning (ICML) (2019)"},{"key":"43_CR2","unstructured":"Clanuwat, T., Bober-Irizar, M., Kitamoto, A., Lamb, A., Yamamoto, K., Ha, D.: Deep learning for classical japanese literature. arXiv preprint arXiv:1812.01718 (2018)"},{"key":"43_CR3","unstructured":"Dinh, L., Krueger, D., Bengio, Y.: NICE: non-linear independent components estimation. In: International Conference on Learning Representations (ICLR) (2015)"},{"key":"43_CR4","unstructured":"Dinh, L., Sohl-Dickstein, J., Bengio, S.: Density estimation using real NVP. In: International Conference on Learning Representations (ICLR) (2017)"},{"key":"43_CR5","doi-asserted-by":"publisher","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","volume":"52","author":"DL Donoho","year":"2006","unstructured":"Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52, 1289\u20131306 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"43_CR6","doi-asserted-by":"crossref","unstructured":"Duque, A.F., Morin, S., Wolf, G., Moon, K.R.: Extendable and invertible manifold learning with geometry regularized autoencoders. arXiv preprint arXiv:2007.07142 (2020)","DOI":"10.1109\/BigData50022.2020.9378049"},{"issue":"5786","key":"43_CR7","doi-asserted-by":"publisher","first-page":"504","DOI":"10.1126\/science.1127647","volume":"313","author":"GE Hinton","year":"2006","unstructured":"Hinton, G.E., Salakhutdinov, R.R.: Reducing the dimensionality of data with neural networks. Science 313(5786), 504\u2013507 (2006)","journal-title":"Science"},{"key":"43_CR8","doi-asserted-by":"publisher","first-page":"550","DOI":"10.1109\/34.291440","volume":"16","author":"J Hull","year":"1994","unstructured":"Hull, J.: Database for handwritten text recognition research. IEEE Trans. Pattern Anal. Mach. Intell. 16, 550\u2013554 (1994)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"43_CR9","unstructured":"Jacobsen, J., Smeulders, A.W.M., Oyallon, E.: i-revnet: deep invertible networks. In: International Conference on Learning Representations (ICLR) (2018)"},{"key":"43_CR10","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1090\/conm\/026\/737400","volume":"26","author":"WB Johnson","year":"1984","unstructured":"Johnson, W.B., Lindenstrauss, J.: Extensions of lipschitz maps into a hilbert space. Contemp. Math. 26, 189\u2013206 (1984)","journal-title":"Contemp. Math."},{"key":"43_CR11","unstructured":"Kaski, S., Venna, J.: Visualizing gene interaction graphs with local multidimensional scaling. In: European Symposium on Artificial Neural Networks, pp. 557\u2013562 (2006)"},{"key":"43_CR12","unstructured":"Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. In: International Conference on Learning Representations (ICLR) (2015)"},{"key":"43_CR13","unstructured":"Kingma, D.P., Welling, M.: Auto-encoding variational bayes. In: International Conference on Learning Representations (ICLR) (2014)"},{"issue":"11","key":"43_CR14","doi-asserted-by":"publisher","first-page":"2278","DOI":"10.1109\/5.726791","volume":"86","author":"Y LeCun","year":"1998","unstructured":"LeCun, Y., Bottou, L., Haffner, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86(11), 2278\u20132324 (1998)","journal-title":"Proc. IEEE"},{"key":"43_CR15","unstructured":"Li, S.Z., Zhang, Z., Wu, L.: Markov-lipschitz deep learning. arXiv preprint arXiv:2006.08256 (2020)"},{"key":"43_CR16","first-page":"2579","volume":"9","author":"LVD Maaten","year":"2008","unstructured":"Maaten, L.V.D., Hinton, G.: Visualizing data using t-sne. J. Mach. Learn. Res. 9, 2579\u20132605 (2008)","journal-title":"J. Mach. Learn. Res."},{"key":"43_CR17","unstructured":"McQueen, J., Meila, M., Joncas, D.: Nearly isometric embedding by relaxation. In: Proceedings of the 29th Neural Information Processing Systems (NIPS), pp. 2631\u20132639 (2016)"},{"key":"43_CR18","unstructured":"Mei, J.: Introduction to Manifold and Geometry. Beijing Science Press, Beijing (2013)"},{"key":"43_CR19","unstructured":"Moor, M., Horn, M., Rieck, B., Borgwardt, K.: Topological autoencoders. In: International Conference on Machine Learning (ICML) (2020)"},{"key":"43_CR20","doi-asserted-by":"publisher","first-page":"20","DOI":"10.2307\/1969989","volume":"63","author":"J Nash","year":"1956","unstructured":"Nash, J.: The imbedding problem for riemannian manifolds. Ann. Math. 63, 20\u201363 (1956)","journal-title":"Ann. Math."},{"key":"43_CR21","unstructured":"Nene, S.A., Nayar, S.K., Murase, H.: Columbia object image library (coil-20). Technical Report, Columbia University (1996). https:\/\/www.cs.columbia.edu\/CAVE\/software\/softlib\/coil-20.php"},{"key":"43_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"442","DOI":"10.1007\/978-3-030-33676-9_31","volume-title":"Pattern Recognition","author":"T-GL Nguyen","year":"2019","unstructured":"Nguyen, T.-G.L., Ardizzone, L., K\u00f6the, U.: Training Invertible Neural Networks as Autoencoders. In: Fink, G.A., Frintrop, S., Jiang, X. (eds.) DAGM GCPR 2019. LNCS, vol. 11824, pp. 442\u2013455. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-33676-9_31"},{"issue":"85","key":"43_CR23","first-page":"2825","volume":"12","author":"F Pedregosa","year":"2011","unstructured":"Pedregosa, F., et al.: \u00c9douard Duchesnay: Scikit-learn: machine learning in python. J. Mach. Learn. Res. 12(85), 2825\u20132830 (2011)","journal-title":"J. Mach. Learn. Res."},{"key":"43_CR24","doi-asserted-by":"crossref","unstructured":"Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323\u20132326 (2000)","DOI":"10.1126\/science.290.5500.2323"},{"issue":"9","key":"43_CR25","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1007\/s12045-016-0387-4","volume":"21","author":"H Seshadri","year":"2016","unstructured":"Seshadri, H., Verma, K.: The embedding theorems of Whitney and Nash. Resonance 21(9), 815\u2013826 (2016). https:\/\/doi.org\/10.1007\/s12045-016-0387-4","journal-title":"Resonance"},{"key":"43_CR26","doi-asserted-by":"crossref","unstructured":"Tenenbaum, J.B., De Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319\u20132323 (2000)","DOI":"10.1126\/science.290.5500.2319"},{"key":"43_CR27","unstructured":"Xiao, H., Rasul, K., Vollgraf, R.: Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms. arXiv preprint arXiv:1708.07747 (2017)"},{"key":"43_CR28","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Wang, J.: Mlle: modified locally linear embedding using multiple weights. In: Advances in Neural Information Processing systems, pp. 1593\u20131600 (2007)","DOI":"10.7551\/mitpress\/7503.003.0204"},{"issue":"1","key":"43_CR29","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1137\/S1064827502419154","volume":"26","author":"Z Zhang","year":"2004","unstructured":"Zhang, Z., Zha, H.: Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM J. Sci. Comput. 26(1), 313\u2013338 (2004)","journal-title":"SIAM J. Sci. Comput."}],"container-title":["Lecture Notes in Computer Science","Machine Learning and Knowledge Discovery in Databases. Research Track"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-86523-8_43","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T22:04:21Z","timestamp":1757455461000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-86523-8_43"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030865221","9783030865238"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-86523-8_43","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"11 September 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ECML PKDD","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Joint European Conference on Machine Learning and Knowledge Discovery in Databases","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Bilbao","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Spain","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13 September 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 September 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ecml2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/2021.ecmlpkdd.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"869","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"210","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"24% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3-4","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3-9","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"The conference was held online due to the COVID-19 pandemic.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}