Fixed mappings

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.

elements: datasets datafiles cells and doubles mappings classifiers mapping types.
operations: datasets datafiles cells and doubles mappings classifiers stacked parallel sequential dyadic.
user commands: datasets representation classifiers evaluation clustering examples support routines.
introductory examples: Introduction Scatterplots Datasets Datafiles Mappings Classifiers Evaluation Learning curves Feature curves Dimension reduction Combining classifiers Dissimilarities.
advanced examples.

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