Manifold learning in regression tasks

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 9047, Issue , 2015, Pages 414-423

  Bernstein, Alexander ^a,b   Kuleshov, Alexander ^a,b   Yanovich, Yury ^a,b  

^a INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS   (Russian Federation)

^b NATIONAL RESEARCH UNIVERSITY HIGHER SCHOOL OF ECONOMICS   (Russian Federation)

Author keywords

Dimensionality reduction; Manifold learning; Manifold learning regression; Nonlinear regression; Tangent bundle manifold learning

Indexed keywords

JACOBIAN MATRICES; LEARNING SYSTEMS; MAPPING; VECTOR SPACES;

DIMENSIONAL SPACES; DIMENSIONALITY REDUCTION; INPUT-OUTPUT; MANIFOLD LEARNING; NON-LINEAR REGRESSION; PREDICTIVE FUNCTION; REGRESSION PROBLEM; TRAINING DATA SETS;

REGRESSION ANALYSIS;

EID: 84949752569     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-319-17091-6_36     Document Type: Conference Paper

References (34)

1. Vapnik, V.: Statistical Learning Theory. John Wiley, New-York (1998)
2. James, G., Witten, D., Hastie, T., Tibshirani, R.: An Introduction to Statistical Learning with Applications in R. Springer Texts in Statistics, New-York
3. Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edn. Springer (2009)
4. Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, Heidelberg (2007)
5. Deng, L., Yu, D.: Deep Learning: Methods and Applications. NOW Publishers, Boston (2014)
6. Breiman, L.: Random Forests. Machine Learning 45(1), 5-32 (2001)
7. Friedman, J.H.: Greedy Function Approximation: A Gradient Boosting Machine. Annals of Statistics 29(5), 1189-1232 (2001)
8. Rasmussen, C.E., Williams, C.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006)
9. Belyaev, M., Burnaev, E., Kapushev, Y.: Gaussian process regression for structured data sets. To appear in Proceedings of the SLDS 2015, London, England, UK (2015)
10. Burnaev E., Panov M.: Adaptive design of experiments based on gaussian processes. To appear in Proceedings of the SLDS 2015, London, England, UK (2015)
11. Loader, C.: Local Regression and Likelihood. Springer, New York (1999)
12. Vejdemo-Johansson, M.: Persistent homology and the structure of data. In: Topological Methods for Machine Learning, an ICML 2014 Workshop, Beijing, China, June 25 (2014). http://topology.cs.wisc.edu/MVJ1.pdf
13. Carlsson, G.: Topology and Data. Bull. Amer. Math. Soc. 46, 255-308 (2009)
14. Edelsbrunner, H., Harer, J.: Computational Topology: An Introduction. Amer. Mathematical Society (2010)
15. Cayton, L.: Algorithms for manifold learning. Univ of California at San Diego (UCSD), Technical Report CS2008-0923, pp. 541-555. Citeseer (2005)
16. Huo, X., Ni, X., Smith, A.K.: Survey of manifold-based learning methods. In: Liao, T.W., Triantaphyllou, E. (eds.) Recent Advances in Data Mining of Enterprise Data, pp. 691-745. World Scientific, Singapore (2007)
17. Ma, Y., Fu, Y. (eds.): Manifold Learning Theory and Applications. CRC Press, London (2011)
18. Bernstein, A.V., Kuleshov, A.P.: Tangent bundle manifold learning via grassmann&stiefel eigenmaps. In: arXiv:1212.6031v1 [cs.LG], pp. 1-25, December 2012
19. Bernstein, A.V., Kuleshov, A.P.: Manifold Learning: generalizing ability and tangent proximity. International Journal of Software and Informatics 7(3), 359-390 (2013)
20. Kuleshov, A., Bernstein, A.: Manifold learning in data mining tasks. In: Perner, P. (ed.) MLDM 2014. LNCS, vol. 8556, pp. 119-133. Springer, Heidelberg (2014)
21. Kuleshov, A., Bernstein, A., Yanovich, Yu.: Asymptotically optimal method in Manifold estimation. In: Markus, L., Prokaj, V. (eds.) Abstracts of the XXIX-th European Meeting of Statisticians, July 20-25, Budapest, p. 325 (2013)
22. Genovese, C.R., Perone-Pacifico, M., Verdinelli, I., Wasserman, L.: Minimax Manifold Estimation. Journal Machine Learning Research 13, 1263-1291 (2012)
23. Kuleshov, A.P., Bernstein, A.V.: Cognitive Technologies in Adaptive Models of Complex Plants. Information Control Problems in Manufacturing 13(1), 1441-1452 (2009)
24. Bunte, K., Biehl, M., Hammer B.: Dimensionality reduction mappings. In: Proceedings of the IEEE Symposium on Computational Intelligence and Data Mining (CIDM 2011), pp. 349-356. IEEE, Paris (2011)
25. Lee, J.A.: Verleysen, M.: Quality assessment of dimensionality reduction: Rank-based criteria. Neurocomputing 72(7-9), 1431-1443 (2009)
26. Saul, L.K., Roweis, S.T.: Think globally, fit locally: unsupervised learning of low dimensional manifolds. Journal of Machine Learning Research 4, 119-155 (2003)
27. Saul, L.K., Roweis, S.T.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323-2326 (2000)
28. Zhang, Z., Zha, H.: Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment. SIAM Journal on Scientific Computing 26(1), 313-338 (2005)
29. Hamm, J., Lee, D.D.: Grassmann discriminant analysis: A unifying view on subspace- based learning. In: Proceedings of the 25th International Conference on Machine Learning (ICML 2008), pp. 376-83 (2008)
30. Tyagi, H., Vural, E., Frossard, P.: Tangent space estimation for smooth embeddings of riemannian manifold. In: arXiv:1208.1065v2 [stat.CO], pp. 1-35, May 17 (2013)
31. Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation 15, 1373-1396 (2003)
32. Bengio, Y., Monperrus, M.: Non-local manifold tangent learning. In: Advances in Neural Information Processing Systems, vol. 17, pp. 129-136. MIT Press, Cambridge (2005)
33. Dollar, P., Rabaud, V., Belongie, S.: Learning to traverse image manifolds. In: Advances in Neural Information Processing Systems, vol. 19, pp. 361-368. MIT Press, Cambridge (2007)
34. Xiong, Y., Chen, W., Apley, D., Ding, X.: A Nonstationary Covariance-Based Kriging Method for Metamodeling in Engineering Design. International Journal for Numerical Methods in Engineering 71(6), 733-756 (2007)