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'''Local tangent space alignment''' ('''LTSA''')<ref>{{Cite journal |last=Zhang |first=Zhenyue |author2=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 |doi=10.1137/s1064827502419154|citeseerx=10.1.1.211.9957 }}</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 algorithm|''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.
== See also ==
* [[Isomap]]
==References==
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==Further reading==
*{{Cite journal | last1 = Ma | first1 = L. | last2 = Crawford | first2 = M. M. | last3 = Tian | first3 = J. W. | doi = 10.1049/el.2010.2613 | title = Generalised supervised local tangent space alignment for hyperspectral image classification | journal = Electronics Letters | volume = 46 | issue = 7 | pages = 497 | year = 2010 | bibcode = 2010ElL....46..497M }}
[[Category:Dimension reduction]]
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