{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T01:52:28Z","timestamp":1762998748742,"version":"3.37.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2009,4,7]],"date-time":"2009-04-07T00:00:00Z","timestamp":1239062400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mach Learn"],"published-print":{"date-parts":[[2009,10]]},"DOI":"10.1007\/s10994-009-5107-9","type":"journal-article","created":{"date-parts":[[2009,4,6]],"date-time":"2009-04-06T17:34:36Z","timestamp":1239039276000},"page":"1-25","source":"Crossref","is-referenced-by-count":36,"title":["Local procrustes for manifold embedding: a measure of\u00a0embedding quality and embedding algorithms"],"prefix":"10.1007","volume":"77","author":[{"given":"Yair","family":"Goldberg","sequence":"first","affiliation":[]},{"given":"Ya\u2019acov","family":"Ritov","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,4,7]]},"reference":[{"issue":"6","key":"5107_CR1","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1162\/089976603321780317","volume":"15","author":"M. Belkin","year":"2003","unstructured":"Belkin, M., & Niyogi, P. (2003). Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation, 15(6), 1373\u20131396.","journal-title":"Neural Computation"},{"key":"5107_CR2","unstructured":"Bernstein, M., de Silva, V., Langford, J. C., & Tenenbaum, J. B. (2000). Graph approximations to geodesics on embedded manifolds (Technical Report). Stanford University, Stanford. Available at http:\/\/isomap.stanford.edu ."},{"key":"5107_CR3","unstructured":"Chen, L. (2006) Local multidimensional scaling for nonlinear dimension reduction, graph layout and proximity analysis. PhD thesis, University of Pennsylvania."},{"issue":"10","key":"5107_CR4","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1080\/00029890.1987.12000742","volume":"94","author":"B. Cipra","year":"1987","unstructured":"Cipra, B. (1987). An introduction to the Ising model. American Mathematical Monthly, 94(10), 937\u2013959.","journal-title":"American Mathematical Monthly"},{"key":"5107_CR5","volume-title":"Introduction to algorithms","author":"T. Corman","year":"1990","unstructured":"Corman, T., Leiserson, C., & Rivest, R. (1990). Introduction to algorithms. Cambridge: MIT Press."},{"key":"5107_CR6","doi-asserted-by":"crossref","unstructured":"Dollar, P., Rabaud, V., & Belongie, S. J. (2007). Non-isometric manifold learning: analysis and an algorithm. In Z.\u00a0Ghahramani (Ed.), Proceedings of the 24th annual international conference on machine learning (ICML) (pp.\u00a0241\u2013248). Omnipress.","DOI":"10.1145\/1273496.1273527"},{"issue":"10","key":"5107_CR7","doi-asserted-by":"crossref","first-page":"5591","DOI":"10.1073\/pnas.1031596100","volume":"100","author":"D. Donoho","year":"2004","unstructured":"Donoho, D., & Grimes, C. (2004). Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. Proceedings of the National Academy of Sciences of the United States of America, 100(10), 5591\u20135596.","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"key":"5107_CR8","first-page":"1909","volume":"9","author":"Y. Goldberg","year":"2008","unstructured":"Goldberg, Y., Zakai, A., Kushnir, D., & Ritov, Y. (2008). Manifold learning: The price of normalization. The Journal of Machine Learning Research, 9, 1909\u20131939.","journal-title":"The Journal of Machine Learning Research"},{"key":"5107_CR9","volume-title":"Matrix computations","author":"G. H. Golub","year":"1983","unstructured":"Golub, G. H., & Loan, C. F. V. (1983). Matrix computations. Baltimore: Johns Hopkins University Press."},{"key":"5107_CR10","unstructured":"Hamm, J., Lee, D., & Saul, L. K. (2005). Semisupervised alignment of manifolds. In: R.\u00a0G.\u00a0Cowell & Z.\u00a0Ghahramani (Eds.), Proceedings of the tenth international workshop on artificial intelligence and statistics (pp.\u00a0120\u2013127)."},{"issue":"5","key":"5107_CR11","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1109\/34.291440","volume":"16","author":"J. J. Hull","year":"1994","unstructured":"Hull, J. J. (1994). A database for handwritten text recognition research. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(5), 550\u2013554.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"issue":"4598","key":"5107_CR12","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1126\/science.220.4598.671","volume":"220","author":"S. Kirkpatrick","year":"1983","unstructured":"Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598), 671\u2013680.","journal-title":"Science"},{"key":"5107_CR13","volume-title":"Multivariate analysis","author":"K. Mardia","year":"1979","unstructured":"Mardia, K., Kent, J., & Bibby, J. (1979). Multivariate analysis. New York: Academic."},{"issue":"2","key":"5107_CR14","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1145\/355887.355893","volume":"6","author":"N. Munksgaard","year":"1980","unstructured":"Munksgaard, N. (1980). Solving sparse symmetric sets of linear equations by preconditioned conjugate gradients. ACM Transactions on Mathematical Software, 6(2), 206\u2013219.","journal-title":"ACM Transactions on Mathematical Software"},{"key":"5107_CR15","unstructured":"Roweis, S. (retrieved Nov. 2006). Frey face on Sam Roweis\u2019 page. http:\/\/www.cs.toronto.edu\/~roweis\/data.html ."},{"issue":"5500","key":"5107_CR16","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","volume":"290","author":"S. T. Roweis","year":"2000","unstructured":"Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323\u20132326.","journal-title":"Science"},{"key":"5107_CR17","first-page":"889","volume-title":"Advances in neural information processing systems","author":"S. T. Roweis","year":"2001","unstructured":"Roweis, S. T., Saul, L. K., & Hinton, G. E. (2001). Global coordination of local linear models. In Advances in neural information processing systems, 14 (pp.\u00a0889\u2013896). Cambridge: MIT Press."},{"key":"5107_CR18","doi-asserted-by":"crossref","unstructured":"Sha, F., & Saul, L. K. (2005). Analysis and extension of spectral methods for nonlinear dimensionality reduction. In Machine learning, proceedings of the twenty-second international conference (ICML) (pp.\u00a0784\u2013791).","DOI":"10.1145\/1102351.1102450"},{"key":"5107_CR19","unstructured":"Shaw, B., & Jebara, T. (2007). Minimum volume embedding. In Proceedings of the international conference on artificial intelligence and statistics (Vol.\u00a011)."},{"issue":"2","key":"5107_CR20","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1145\/264029.264043","volume":"23","author":"P. Siarry","year":"1997","unstructured":"Siarry, P., Berthiau, G., Durdin, F., & Haussy, J. (1997). Enhanced simulated annealing for globally minimizing functions of many-continuous variables. ACM Transactions on Mathematical Software, 23(2), 209\u2013228.","journal-title":"ACM Transactions on Mathematical Software"},{"issue":"2","key":"5107_CR21","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1111\/j.2517-6161.1978.tb01669.x","volume":"40","author":"R. Sibson","year":"1978","unstructured":"Sibson, R. (1978). Studies in robustness of multidimensional-scaling: Procrustes statistics. Journal of the Royal Statistical Society, 40(2), 234\u2013238.","journal-title":"Journal of the Royal Statistical Society"},{"issue":"2","key":"5107_CR22","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1111\/j.2517-6161.1979.tb01076.x","volume":"41","author":"R. Sibson","year":"1979","unstructured":"Sibson, R. (1979). Studies in the robustness of multidimensional-scaling: Perturbational analysis of classical scaling. Journal of the Royal Statistical Society, 41(2), 217\u2013229.","journal-title":"Journal of the Royal Statistical Society"},{"key":"5107_CR23","first-page":"15","volume-title":"Advances in neural information processing systems","author":"V. Silva de","year":"2003","unstructured":"de Silva, V., & Tenenbaum, J. B. (2003). Global versus local methods in nonlinear dimensionality reduction. In Advances in neural information processing systems (p.\u00a015). Cambridge: MIT Press."},{"issue":"3","key":"5107_CR24","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1137\/0717034","volume":"17","author":"G. W. Stewart","year":"1980","unstructured":"Stewart, G. W. (1980). The efficient generation of random orthogonal matrices with an application to condition estimators. SIAM Journal on Numerical Analysis, 17(3), 403\u2013409.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"5107_CR25","first-page":"15","volume-title":"Advances in neural information processing systems","author":"Y. W. Teh","year":"2003","unstructured":"Teh, Y. W., & Roweis, S. (2003). Automatic alignment of local representations. In S. Becker, S. Thrun, & K. Obermayer (Eds.), Advances in neural information processing systems (p.\u00a015). Cambridge: MIT Press."},{"issue":"5500","key":"5107_CR26","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","volume":"290","author":"J. B. Tenenbaum","year":"2000","unstructured":"Tenenbaum, J. B., de Silva, V., & Langford, J. C. (2000). A global geometric framework for nonlinear dimensionality reduction. Science, 290(5500), 2319\u20132323.","journal-title":"Science"},{"issue":"6","key":"5107_CR27","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1016\/j.neunet.2006.05.014","volume":"19","author":"J. Venna","year":"2006","unstructured":"Venna, J., & Kaski, S. (2006). Local multidimensional scaling. Neural Networks, 19(6), 889\u2013899.","journal-title":"Neural Networks"},{"key":"5107_CR28","doi-asserted-by":"crossref","unstructured":"Verbeek, J., Vlassis, N., & Kr\u00f6se, B. (2002) Coordinating principal component analyzers. In Proceedings of international conference on artificial neural networks.","DOI":"10.1007\/3-540-46084-5_148"},{"issue":"1","key":"5107_CR29","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/s11263-005-4939-z","volume":"70","author":"K. Weinberger","year":"2006","unstructured":"Weinberger, K., & Saul, L. (2006). Unsupervised learning of image manifolds by semidefinite programming. International Journal of Computer Vision, 70(1), 77\u201390.","journal-title":"International Journal of Computer Vision"},{"issue":"1","key":"5107_CR30","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1137\/S1064827502419154","volume":"26","author":"Z. Zhang","year":"2004","unstructured":"Zhang, Z., & Zha, H. (2004). Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM Journal of Scientific Computing, 26(1), 313\u2013338.","journal-title":"SIAM Journal of Scientific Computing"}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-009-5107-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10994-009-5107-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-009-5107-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T21:34:47Z","timestamp":1739050487000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10994-009-5107-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4,7]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,10]]}},"alternative-id":["5107"],"URL":"https:\/\/doi.org\/10.1007\/s10994-009-5107-9","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"type":"print","value":"0885-6125"},{"type":"electronic","value":"1573-0565"}],"subject":[],"published":{"date-parts":[[2009,4,7]]}}}