Abstract
Several algorithms have been proposed to analysis the structure of high-dimensional data based on the notion of manifold learning. They have been used to extract the intrinsic characteristic of different type of high-dimensional data by performing nonlinear dimensionality reduction. Most of them operate in a “batch” mode and cannot be efficiently applied when data are collected sequentially. In this paper, we proposed an incremental version (ILTSA) of LTSA (Local Tangent Space Alignment), which is one of the key manifold learning algorithms. Besides, a landmark version of LTSA (LLTSA) is proposed, where landmarks are selected based on LASSO regression, which is well known to favor sparse approximations because it uses regularization with l1 norm. Furthermore, an incremental version (ILLTSA) of LLTSA is also proposed. Experimental results on synthetic data and real word data sets demonstrate the effectivity of our algorithms.
Chapter PDF
Similar content being viewed by others
References
Seung, S., Daniel, D.L.: The manifold ways of perception. Science 290(5500), 2268–2269 (2000)
Tenenbaum, J.B., de Silva, V., Langford, J.C.: A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290(5500), 2319–2323 (2000)
Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)
David, L.D., Caroe, G.: 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), 5591–5596 (2003)
Zhang, Z.Y., Zha, H.Y.: Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM Journal of Scientific Computing 26(1), 313–338 (2004)
Martin, H.C., Law, A.K.J.: Incremental Nonlinear Dimensionality Reduction by Manifold Learning. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(3), 377–391 (2006)
Olga Kouropteva, O.O., Pietikainen, M.: Incremental locally linear embedding. Pattern Recognition 38, 1764–1767 (2005)
ZhenYue Zhang, H.Z.: A Domain Decomposition Method for Fast Manifold Learning. In: Advances in Neural Information Processing Systems, MIT Press, Cambridge (2006)
Hastie, T., Tibshirani, R., Friedman, J.H.: The Elements of Statistical Learning. Springer, Heidelberg (2001)
Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least angle regression. Annals of Statistics (2003)
de Silva, V.J.B.T.: Global versus Local Approaches to Nonlinear Dimensionality Reduction. In: Advances in Neural Information Processing Systems, vol. 15 (2003)
Jorge Gomes da Silva, J.S.M.: Jo?o Manuel Lage de Miranda Lemos. Selecting Landmark Points for Sparse Manifold Learning. In: Advances in Neural Information Processing Systems, MIT Press, Vancouver, Canada (2006)
Golub, G.H., V.L., C.F.: Matrix Computations. Johns Hopkins University Press (1996)
Bjorck, A., Golub, G.H.: Numerical methods for computing angles between linear subspaces. Mathematics of Computation 27(123), 579–594 (1973)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, X., Yin, J., Feng, Z., Dong, J. (2006). Incremental Manifold Learning Via Tangent Space Alignment. In: Schwenker, F., Marinai, S. (eds) Artificial Neural Networks in Pattern Recognition. ANNPR 2006. Lecture Notes in Computer Science(), vol 4087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11829898_10
Download citation
DOI: https://doi.org/10.1007/11829898_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37951-5
Online ISBN: 978-3-540-37952-2
eBook Packages: Computer ScienceComputer Science (R0)