Editing Nonlinear dimensionality reduction (section)

=== Topologically constrained isometric embedding ===

[[Topologically constrained isometric embedding]] (TCIE)<ref>{{cite journal |last1=Rosman |first1=G. |last2=Bronstein |first2=M.M. |last3=Bronstein |first3=A.M. |last4=Kimmel |first4=R.  |url=https://www.cs.technion.ac.il/users/wwwb/cgi-bin/tr-get.cgi/2009/CIS/CIS-2009-05.pdf |title=Nonlinear Dimensionality Reduction by Topologically Constrained Isometric Embedding |journal=International Journal of Computer Vision |volume=89 |issue=1 |pages=56–68 |date=2010 |doi=10.1007/s11263-010-0322-1 |s2cid=1365750 }}</ref> is an algorithm based on approximating geodesic distances after filtering geodesics inconsistent with the Euclidean metric. Aimed at correcting the distortions caused when Isomap is used to map intrinsically non-convex data, TCIE uses weight least-squares MDS in order to obtain a more accurate mapping. The TCIE algorithm first detects possible boundary points in the data, and during computation of the geodesic length marks inconsistent geodesics, to be given a small weight in the weighted [[stress majorization]] that follows.