{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T08:33:35Z","timestamp":1725698015020},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2017,4,9]],"date-time":"2017-04-09T00:00:00Z","timestamp":1491696000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2017,4,9]],"date-time":"2017-04-09T00:00:00Z","timestamp":1491696000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1118971"],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["SC0013838"],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11371220","11671005"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2017,12]]},"DOI":"10.1007\/s10915-017-0421-z","type":"journal-article","created":{"date-parts":[[2017,4,9]],"date-time":"2017-04-09T02:23:37Z","timestamp":1491704617000},"page":"1164-1177","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["Weighted Nonlocal Laplacian on Interpolation from Sparse Data"],"prefix":"10.1007","volume":"73","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-9122-0302","authenticated-orcid":false,"given":"Zuoqiang","family":"Shi","sequence":"first","affiliation":[]},{"given":"Stanley","family":"Osher","sequence":"additional","affiliation":[]},{"given":"Wei","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,4,9]]},"reference":[{"key":"421_CR1","doi-asserted-by":"publisher","first-page":"490","DOI":"10.1137\/040616024","volume":"4","author":"A Buades","year":"2005","unstructured":"Buades, A., Coll, B., Morel, J.-M.: A review of image denoising algorithms, with a new one. Multiscale Model. Simul. 4, 490\u2013530 (2005)","journal-title":"Multiscale Model. Simul."},{"key":"421_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00211-006-0029-y","volume":"105","author":"A Buades","year":"2006","unstructured":"Buades, A., Coll, B., Morel, J.-M.: Neighborhood filters and PDE\u2019s. Numer. Math. 105, 1\u201334 (2006)","journal-title":"Numer. Math."},{"key":"421_CR3","unstructured":"Burges, C.J., LeCun, Y., Cortes, C.: MNIST database"},{"key":"421_CR4","volume-title":"Spectral Graph Theory","author":"FRK Chung","year":"1997","unstructured":"Chung, F.R.K.: Spectral Graph Theory. American Mathematical Society, Providence (1997)"},{"key":"421_CR5","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/j.matcom.2014.01.007","volume":"102","author":"LZLO Elmoataz Abderrahim","year":"2014","unstructured":"Elmoataz Abderrahim, L.Z.L.O., Xavier, Desquesnes: Nonlocal infinity Laplacian equation on graphs with applications in image processing and machine learning. Math. Comput. Simul. 102, 153\u2013163 (2014)","journal-title":"Math. Comput. Simul."},{"key":"421_CR6","doi-asserted-by":"crossref","unstructured":"Ghoniem, M., Elmoataz, A., Lezoray, O.: Discrete infinity harmonic functions: towards a unified interpolation framework on graphs. In: IEEE International Conference on Image Processing (2011)","DOI":"10.1109\/ICIP.2011.6115690"},{"key":"421_CR7","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1137\/060669358","volume":"6","author":"G Gilboa","year":"2007","unstructured":"Gilboa, G., Osher, S.: Nonlocal linear image regularization and supervised segmentation. Multiscale Model. Simul. 6, 595\u2013630 (2007)","journal-title":"Multiscale Model. Simul."},{"key":"421_CR8","doi-asserted-by":"publisher","first-page":"1005","DOI":"10.1137\/070698592","volume":"7","author":"G Gilboa","year":"2008","unstructured":"Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. Multiscale Model. Simul. 7, 1005\u20131028 (2008)","journal-title":"Multiscale Model. Simul."},{"key":"421_CR9","doi-asserted-by":"publisher","first-page":"874","DOI":"10.1137\/15M102592X","volume":"14","author":"Z Li","year":"2016","unstructured":"Li, Z., Shi, Z.: A convergent point integral method for isotropic elliptic equations on point cloud. SIAM Multiscale Model. Simul. 14, 874\u2013905 (2016)","journal-title":"SIAM Multiscale Model. Simul."},{"key":"421_CR10","unstructured":"Li, Z., Shi, Z., Sun, J.: Point integral method for solving Poisson-type equations on manifolds from point clouds with convergence guarantees. \n arXiv:1409.2623"},{"key":"421_CR11","unstructured":"Nadler, B., Srebro, N., Zhou, X.: Semi-supervised learning with the graph Laplacian: the limit of infinite unlabelled data. In: NIPS (2009)"},{"key":"421_CR12","unstructured":"Osher, S., Shi, Z., Zhu, W.: Low dimensional manifold model for image processing. Technical report, CAM report 16-04, UCLA (2016)"},{"key":"421_CR13","unstructured":"Shi, Z., Sun, J.: Convergence of the point integral method for Poisson equation on point cloud. \n arXiv:1403.2141"},{"key":"421_CR14","unstructured":"Shi, Z., Sun, J.: Convergence of the point integral method for the Poisson equation with Dirichlet boundary on point cloud. \n arXiv:1312.4424"},{"key":"421_CR15","unstructured":"Shi, Z., Sun, J., Tian, M.: Harmonic extension on point cloud. \n arXiv:1509.06458"},{"key":"421_CR16","unstructured":"Yin, K., Tai, X.-C., Osher, S.: An effective region force for some variational models for learning and clustering. Technical report, CAM report 16-18, UCLA (2016)"},{"key":"421_CR17","unstructured":"Zhou, X., Belkin, M.: Semi-supervised learning by higher order regularization. In: NIPS (2011)"},{"key":"421_CR18","unstructured":"Zhu, W., Chayes, V., Tiard, A., Sanchez, S., Dahlberg, D., Kuang, D., Bertozzi, A., Osher, S., Zosso, D.: Nonlocal total variation with primal dual algorithm and stable simplex clustering in unspervised hyperspectral imagery analysis. Technical report, CAM report 15-44, UCLA (2015)"},{"key":"421_CR19","unstructured":"Zhu, X., Ghahramani, Z., Lafferty, J.D.: Semi-supervised learning using Gaussian fields and harmonic functions. In: Machine Learning, Proceedings of the Twentieth International Conference ICML 2003, 21\u201324 Aug 2003, Washington, DC, USA, pp. 912\u2013919 (2003)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0421-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0421-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0421-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T09:19:22Z","timestamp":1589707162000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0421-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,9]]},"references-count":19,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["421"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0421-z","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,4,9]]},"assertion":[{"value":"15 January 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 March 2017","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 March 2017","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 April 2017","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}