A fixed mapping transforms one vector space into another in a data independent way. Its operation just depends on some user defined parameter settings. An example is the sigmoid scaling: F = sigm(,s) in which s defines the smoothness of the function. It is called by B = A*F in which A is an input dataset and B is the transformed result.
The following rules apply if a dataset A is processed by a sequential combination of a fixed mapping F with another fixed mapping,an untrained mapping U or a trained mapping T. W is an arbitrary mapping.
A2 = A*(F1*F2) = A*F1*F2
This is the same as F1*F2 is not combined
F2 = G*F
Fixed mapping, it generates as well
G2 = F*G
Generator, the data is transformed by a fixed mapping.
T = A*(F*U) = F*(A*F*U)
The untrained mapping U is trained by A*F. The resulting trained mapping is preceded by F to transform new data to the space in which U has been trained.
An example is:
U = pcam(,10)*ldc; T = A*(im_resize(,32,32)*U)
The untrained mapping defines a mapping on the first 10 principal components and performs in this space a linear classifier assuming normal class densities. Training preceded by resizing all images to 32*32 pixels in order to make the images comparable is . A can be a dataset as well as a datafile.