RUS  ENG
Полная версия
ЖУРНАЛЫ // Ученые записки Казанского университета. Серия Физико-математические науки

Учен. зап. Казан. ун-та. Сер. Физ.-матем. науки, 2018, том 160, книга 2, страницы 220–228 (Mi uzku1446)

Estimation of smooth vector fields on manifolds by optimization on Stiefel group
E. N. Abramov, Yu. A. Yanovich

Литература

1. Bellman R. E., Dynamic Programming, Princeton Univ. Press, Princeton, 1957, 339 pp.  mathscinet  zmath
2. Donoho D. L., “High-dimensional data analysis: The curses and blessings of dimensionality”, Proc. AMS Conf. on Math Challenges of 21st Century, 2000, 1–33
3. Seung H. S., Lee D. D., “Cognition. The manifold ways of perception”, Science, 290:5500 (2000), 2268–2269  crossref
4. Huo X., Ni X. S., Smith A. K., “A survey of manifold-based learning methods”, Recent Advances in Data Mining of Enterprise Data, eds. Liao T. W., Triantaphyllou E., World Sci., Singapore, 2007, 691–745  crossref  mathscinet
5. Ma Y., Fu Y., Manifold Learning Theory and Applications, CRC Press, London, 2011, 314 pp.  mathscinet
6. Tenenbaum J. B., de Silva V., Langford J., “A global geometric framework for nonlinear dimensionality reduction”, Science, 290:5500 (2000), 2319–2323  crossref  adsnasa
7. Roweis S. T., Saul L. K., “Nonlinear dimensionality reduction by locally linear embedding”, Science, 290, no. 5500 (2000), 2323–2326  crossref  adsnasa
8. Zhang Z., Zha H., “Principal manifolds and nonlinear dimension reduction via local tangent space alignment”, SIAM J. Sci. Comput., 26:1 (2004), 313–338  crossref  mathscinet  zmath
9. Belkin M., Niyogi P., “Laplacian eigenmaps for dimensionality reduction and data representation”, J. Neural Comput., 15:6 (2003), 1373–1396  crossref  zmath
10. Belkin M., Niyogi P., “Convergence of Laplacian eigenmaps”, Adv. Neural Inf. Process. Syst., 19 (2007), 129–136
11. Donoho D. L., Grimes C., “Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data”, Proc. Natl. Acad. Sci. U. S. A., 100:10, 5591–5596  crossref  mathscinet  zmath
12. Bernstein A., Kuleshov A. P., “Manifold learning: Generalizing ability and tangent proximity”, Int. J. Software Inf., 7:3 (2013), 359–390
13. Bernstein A., Kuleshov A., Yanovich Y., “Manifold learning in regression tasks”, Statistical Learning and Data Sciences. SLDS 2015, Lecture Notes in Computer Science, 9047, eds. Gammerman A., Vovk V., Papadopoulos H., Springer, Cham, 2015, 414–423  crossref
14. Pelletier B., “Non-parametric regression estimation on closed Riemannian”, J. Nonparametric Stat., 18:1 (2006), 57–67  crossref  mathscinet  zmath
15. Niyogi P., Smale S., Weinberger S., “Finding the homology of submanifolds with high confidence from random samples”, Discrete Comput. Geom., 39:1 (2008), 419–441  crossref  mathscinet  zmath
16. Bernstein A. V., Kuleshov A. P., Yanovich Yu. A., “Locally isometric and conformal parameterization of image manifold”, Proc. 8th Int. Conf. on Machine Vision (ICMV 2015), Proc. SPIE, 9875, 2015, 987507, 7 pp.  crossref
17. Kachan O., Yanovich Y., Abramov E., “Vector fields alignment on manifolds via contraction mappings”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 160:2 (2018), 300–308
18. Yanovich Yu., “Asymptotic properties of local sampling on manifold”, J. Math. Stat., 12:3 (2016), 157–175  crossref
19. Absil P. A., Mahony R., Sepulchre R., Optimization Algorithms on Matrix Manifolds, Princeton Univ. Press, Princeton, 2007, 240 pp.  mathscinet
20. Boumal N., Mishra B., Absil P.-A., Sepulchre R., “Manopt, a Matlab toolbox for optimization on manifolds”, J. Mach. Learn. Res., 15:1 (2014), 1455–1459  mathscinet  zmath


© МИАН, 2025