Local tangent space alignment: Difference between revisions

Revision as of 12:57, 8 September 2009

Latest revision as of 00:57, 17 April 2025

(25 intermediate revisions by 20 users not shown)

Line 1:

{{Multiple issues|

{{article issues|article=yes|confusing=September 2009|unreferenced=September 2009|wikify=September 2009}}

{{uncategorizedrefimprove|date=September 2009}}

Local Tangent Space Alignment (LTSA) is a method for manifold learning, which can efficiently learn nonlinear embedding low-dimensional coordinates of [[high-dimensional]] data, and can also reconstruct high dimensional coordinates from embedding coordinates. But it ignores the label information conveyed by data samples, and can not be used for classification directly.

{{confusing|date=September 2009}}

}}

'''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]]

{{uncategorized|date=September 2009}}

==References==

{{Reflist}}

==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]]

[[Category:Manifolds]]

{{Statistics-stub}}