I am reading the book "Advances in Intelligent Systems and Computing" and I cannot understand a paragraph.
Parametric approaches include the classical SOM and its probabilistic counterpart generative topographic mapping (GTM) [3]. Both approaches are based on a low dimensional latent space, the regular SOM grid or the real plane with a probability distribution peaked at regular grid positions for GTM. These points are associated to high dimensional coordinates in the data space, the parameters of the mapping, called prototypes wj, which are directly assigned to grid positions by means of the index in case of SOM, or which are images of a parameterized generalized linear function Φ : Y → X in case of GTM.
What is the meaning of Φ : Y → X in this context? In addition, what is "high dimensional coordinates in the data space"? Thanks in advance.
As rural reader pointed out in a comment, that ‘High dimensional coordinates’ here refers to measurements with a lot of entries, for example image color per pixel. Φ provides a dimensional reduction. As J.W.Tanner pointed out in a comment, Φ is a function that maps from set Y to set X.