Editing Nonlinear dimensionality reduction (section)

=== Relational perspective map ===
Relational perspective map is a [[multidimensional scaling]] algorithm. The algorithm finds a configuration of data points on a manifold by simulating a multi-particle dynamic system on a closed manifold, where data points are mapped to particles and distances (or dissimilarity) between data points represent a repulsive force. As the manifold gradually grows in size the multi-particle system cools down gradually and converges to a configuration that reflects the distance information of the data points.

Relational perspective map was inspired by a physical model in which positively charged particles move freely on the surface of a ball.  Guided by the [[Charles-Augustin de Coulomb|Coulomb]] [[Coulomb's law|force]] between particles, the minimal energy configuration of the particles will reflect the strength of repulsive forces between the particles.

The Relational perspective map was introduced in.<ref>{{cite journal |first=James X. |last=Li |url=http://www.palgrave-journals.com/ivs/journal/v3/n1/pdf/9500051a.pdf |title=Visualizing high-dimensional data with relational perspective map |journal=Information Visualization |date=2004 |volume=3 |pages=49–59|doi=10.1057/palgrave.ivs.9500051 |s2cid=7566939 }}</ref>
The algorithm firstly used the flat [[torus]] as the image manifold, then it has been extended (in the software [http://www.VisuMap.com VisuMap] to use other types of closed manifolds, like the [[sphere]], [[projective space]], and [[Klein bottle]], as image manifolds.