Abstract
In this paper we present a new algorithm for manifold learning and nonlinear dimension reduction. Based on a set of unorganized data points sampled with noise from the manifold, we represent the local geometry of the manifold using tangent spaces learned by fitting an affine subspace in a neighborhood of each data point. Those tangent spaces are aligned to give the internal global coordinates of the data points with respect to the underlying manifold by way of a partial eigendecomposition of the neighborhood connection matrix. We present a careful error analysis of our algorithm and show that the reconstruction errors are of second-order accuracy. Numerical experiments including 64-by-64 pixel face images are given to illustrate our algorithm.
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Zhang, Z., Zha, H. (2003). Nonlinear Dimension Reduction via Local Tangent Space Alignment. In: Liu, J., Cheung, Ym., Yin, H. (eds) Intelligent Data Engineering and Automated Learning. IDEAL 2003. Lecture Notes in Computer Science, vol 2690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45080-1_66
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DOI: https://doi.org/10.1007/978-3-540-45080-1_66
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40550-4
Online ISBN: 978-3-540-45080-1
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