Mapping combining

Mapping combining

Various ways have been implemented to combine mappings. They are of significant importance for classifiers, but the implementation is general and combining other types of mappings can be useful as well. The combining options can be understood from the definition of a mapping W applied to a dataset A resulting in a dataset B, coded by B = A*W:

    input space (A) --> mapping (W) --> output space (B)

• Stacked combining combines sets of mappings from the same input space. This is done by a horizontal concatenation of mappings: W = [W1 W2 W3 ... Wn].
• Parallel combining combines sets of mappings from different input spaces. This is done by a vertical concatenation of mappings: W = [W1; W2; W3; ...; Wn].
• Sequential combining combines a first mapping with a second mapping into a new mapping using the output space of the first as input for the second mapping. The resulting mapping maps from the input space of the first into the output space of the next mapping. This is coded as W = W1*W2*W* ... *Wn
• Dyadic combining combines two mappings or mappings with doubles (scalars or matrices of the proper size), e.g. W = W1+W2, or W = s*W1 in which s is a scalar or W = W1>W2.

The mapping combining rules discussed in the separate sections are consistent with the combining rules for datasets and datafiles that follow from the operator overload. In general, a combined mapping applied to a dataset (datafile) is the combined set of the individual mappings applied to the same dataset (datafile). For this reason mappingss to be combined should be of the same type (untrained, fixed or trained) and have the same sizes. An exception is the sequential combining of mappings. They may combine mappings of all types. Therefor a set of special rules are related to that combining strategy.

• Stacked combining
• Parallel combining
• Sequential combining
• Dyadic combining

Mapping combining