Trained mappings

Trained mappings are very similar to fixed mappings. The difference how they are created, but once constituted they behave the same. Like fixed mappings, trained mappings transform one vector space into another one. During training parameters are optimized on the basis of the training set. All PRTools classifiers are trainable mappings. After training the outputs have a clear meaning: class confidences. Here is an important difference with the fixed mapping: it is expected that the outputs have a specific behavior.  This can be verified by an evaluation. So in relation with trained mapping are evaluation routines like testc, prcrossval, labeld and confmat.

In combining mappings, the following rules apply if a dataset A is processed by a sequential combination of a trained mapping T with another  trained mapping,an untrained mapping U, a fixed mapping F or a generator G. In addition there are some specific combiners mainly of importance to classifiers..

A2 = A*(T1*T2) = A*T1*T2 This is the same as T1*T2 is not combined, T1 or T2 may also be fixed mappings.
T2 = G*T Trained mapping, it generates as well
G2 = T*G Generator, the data is transformed by a fixed mapping.
T2 = A*(T*U) = T*(A*T*U)
The untrained mapping U is trained by A*T. The resulting trained mapping is preceded by T to transform new data to the space in which U has been trained.
Tn = [T1 T2 T3 ... Tk]*V Stacked combiner, combined by the fixed combiner V
Tn = [T1 T2 T3 ... Tk]*T Stacked combiner, combined by the trained combiner T
Tn = [T1;T2;T3;...;Tk]*V Parallel combiner, combined by the fixed combiner V
Tn = [T1;T2;T3;...;Tk]*T Parallel combiner, combined by the fixed combiner T

An example is:

T1 = A1*pcam([],10);
A2 = A1*T1;
T2 = A2*(T1*fisherc);
T3 = T1*T2

Note that in this example T2 is a classifier in the PC space computed by pcam. It can thereby only be applied to datasets that are projected in this space. The last line is needed to make it applicable to datasets in the original space. The above series of operations can also be performed implicitly by PRTools in a one-liner:

T3 = A1*(pcam([],10)*fisherc);

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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