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Operations on Mappings

Mappings can be combined in many ways, with each other and with scalars and with matrices of doubles. Here it will be discussed what the standard Matlab operators do with mappings. As classifiers are a special type of mapping these operations are of significant importance for combining classifiers, but the implementation is general and combining other types of mappings can be useful as well.

Combining of mappings can be understood from the definition of a mapping: it maps one space into another:

 input space --> mapping --> output space

Applied to a collection of objects represented in these spaces by datasets A and B, coded by B = A*W:

 input dataset A --> mapping W --> output dataset B

The PRTools rules for operations on mapping and the various ways to combine them are such that an a dataset A mapped by a combination of (operation on) mappings is the same as the combination (operation) applied to the resulting individual dataset.:

 input dataset A --> C(W1,W2, ... ,Wn) --> C(B1,B2, ... ,Bn)
    input dataset A --> C(W1,W2, ... ,Wn) --> C(A*W1,A*W2, ... , A*Wn)

There are some special cases and consequences, in particular in relation with the training of mappings. They are discussed separately.


operations: basic, datasets, datafiles, mappings, classifiers, stacked, parallel, sequential, dyadic
commands: datasets, representation , classifiers, evaluation, clustering and regression, examples, support