Editing Nonlinear dimensionality reduction (section)

=== Curvilinear component analysis ===

[[Curvilinear component analysis]] (CCA) looks for the configuration of points in the output space that preserves original distances as much as possible while focusing on small distances in the output space (conversely to [[Sammon's mapping]] which focus on small distances in original space).<ref name="Demart">{{cite journal |first1=P. |last1=Demartines |first2=J. |last2=Hérault |url=http://chronos.isir.upmc.fr/~gas/pam/img_auth.php/2/23/Demartines1997.pdf |title=Curvilinear Component Analysis: A Self-Organizing Neural Network for Nonlinear Mapping of Data Sets |journal=IEEE Transactions on Neural Networks |volume=8 |issue=1 |year=1997 |pages=148–154 |doi=10.1109/72.554199 |pmid=18255618 }}</ref>

It should be noticed that CCA, as an iterative learning algorithm, actually starts with focus on large distances (like the Sammon algorithm), then gradually change focus to small distances. The small distance information will overwrite the large distance information, if compromises between the two have to be made.

The stress function of CCA is related to a sum of right Bregman divergences.<ref name="Jigang">{{cite book |first1=Jigang |last1=Sun |first2=Malcolm |last2=Crowe |first3=Colin |last3=Fyfe |chapter-url=http://www.dice.ucl.ac.be/Proceedings/esann/esannpdf/es2010-107.pdf |chapter=Curvilinear component analysis and Bregman divergences |title=European Symposium on Artificial Neural Networks (Esann) |pages=81–86 |publisher=d-side publications |year=2010 }}</ref>