Abstract
Compared with the linear projection assumption used previously, a polynomial mapping provides high-order approximation to the unknown nonlinear mapping and therefore is more accurate for data samples lying on nonlinear manifolds.
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References
S. Yan, D. Xu, B. Zhang, H.J. Zhang, Q. Yang, S. Lin, IEEE Trans. Pattern Anal. Mach. Intell. 29(1), 40 (2007)
J.R. Magnus, H. Neudecker, Wiley Series in Probability and Mathematical Statistics (1988)
S.T. Roweis, L.K. Saul, Science 290(5500), 2323 (2000)
S. Vishwanathan, K.M. Borgwardt, O. Guttman, A. Smola, Neurocomputing 69(7–9), 721 (2006)
L.K. Saul, S.T. Roweis, J. Mach. Learn. Res. 4, 119 (2003)
E. Kokiopoulou, Y. Saad, IEEE Trans. Pattern Anal. Mach. Intell. 29(12), 2143 (2007)
Y. Pang, L. Zhang, Z. Liu, N. Yu, H. Li, in International Conference on Intelligent Computing (Springer, 2005), pp. 117–125
G.A. Seber, Multivariate Observations, vol. 252 (Wiley, Hoboken, 2009)
S. Xiang, F. Nie, C. Zhang, C. Zhang, IEEE Trans. Knowl. Data Eng. 21(9), 1285 (2009)
Y. Goldberg, Y. Ritov, Mach. Learn. 77(1), 1 (2009)
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Qiao, H., Ma, C., Li, R. (2022). Explicit Nonlinear Mapping for Manifold Learning with Neighborhood Preserving Polynomial Embedding. In: The “Hand-eye-brain” System of Intelligent Robot. Research on Intelligent Manufacturing. Springer, Singapore. https://doi.org/10.1007/978-981-16-3575-5_9
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DOI: https://doi.org/10.1007/978-981-16-3575-5_9
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