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. © Springer-Verlag 2003.
CITATION STYLE
Zhang, Z., & Zha, H. (2004). Nonlinear dimension reduction via local tangent space alignment. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2690, 477–481. https://doi.org/10.1007/978-3-540-45080-1_66
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