Combiner mappings

(This topic is mainly important for PRTools programmers designing mappings)

Mappings of the combiner type operate on other mappings and not directly on data. They are used to modify the properties of a given mapping. An example is classc which converts a classifier that outputs class densities to one that results in posterior probabilities. In addition there are the fixed combiners designed of combining set of classifiers that are grouped in a stacked (i.e. in the same vector space) or parallel (in different vector spaces) way.

There are not many checks programmed for combiners. It is easy to apply a wrong mapping to a combiner. Usually only after applying data to mappings errors will be generated. This may confuse users as these errors are not always directly meaningful.

The main rules for combining  a combiner mapping V with arbitrary fixed and trained mappings W, untrained mappings U and trained mappings T are

W2 = W1*V
The mapping W1 is modified by V. Also if V is not a combiner then this holds. In that case, however, the two mappings W1 and V are just stored as a sequential combiner in W2 and executed in the given order without modifications.
A2 = A1*(W*V) Mappings should first by applied to combiners before data is processed.
T2 = A*(U*V) = A*U*V = T1*V
Untrained mappings are usually insensitive for combiners. Usually, order of processing makes in this case  no difference.

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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