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m year of citation 1 was wrong, check out:http://epubs.siam.org/action/doSearch?searchText=Principal+Manifolds+and+Nonlinear+Dimension+Reduction+via+Local+Tangent+Space+Alignment+&publication=all& for verification. |
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'''Local tangent space alignment''' ('''LTSA''')<ref>{{Cite journal |last=Zhang |first=Zhenyue |coauthors=Hongyuan Zha |title=Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment |journal=SIAM Journal on Scientific Computing |volume=26 |issue=1 |year=2004 |pages=313–338 }}</ref> is a method for [[manifold learning]], which can efficiently learn a [[Nonlinear system|nonlinear]] embedding into [[Dimension|low-dimensional]] coordinates from [[high-dimensional]] data, and can also reconstruct high-dimensional coordinates from embedding coordinates. It is based on the intuition that when a [[manifold]] is correctly unfolded, all of the [[tangent]] [[hyperplane]]s to the manifold will become aligned. It begins by computing the ''k''-nearest neighbors of every point. It computes the [[tangent space]] at every point by computing the ''d''-first principal components in each local neighborhood. It then optimizes to find an embedding that aligns the tangent spaces, but it ignores the label information conveyed by [[Sample (statistics)|data samples]], and thus can not be used for classification directly.
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