PARALLEL

Combining classifiers in different feature spaces

     WC = PARALLEL(W1,W2,W3, ....) or WC = [W1;W2;W3; ...]
     WC = PARALLEL({W1;W2;W3; ...}) or WC = [{W1;W2;W3; ...}]
     WC = PARALLEL(WC,W1,W2, ....) or WC = [WC;W2;W3; ...]
     WC = PARALELL(C);
     WC = PARALLEL(WC,N);

Input
W1,W2,...	Base classifiers to be combined.
WC	Parallel combined classifier
C	Cell array of classifiers
N	Integer array

Output
WC	Combined classifier.

Description

The base classifiers (or mappings) W1, W2, W3, ... defined in different  feature spaces are combined in WC. This is a classifier defined for the  total number of features and with the combined set of outputs. So, for three  two-class classifiers defined for the classes 'c1' and 'c2', a dataset A is  mapped by D = A*WC on the outputs 'c1','c2','c1','c2','c1','c2' which are  the feature labels of D. Note that classification by LABELD(D) finds for  each vector in D the feature label of the column with the maximum value.  This is equivalent to using the maximum combiner MAXC.

Other fixed combining rules like PRODC, MEANC, and VOTEC can be applied  by D = A*WC*PRODC etc. A trained combiner like FISHERC has to be supplied  with the appropriate training set by AC = A*WC; VC = AC*FISHERC. So the  expression VC = A*WC*FISHERC yields a classifier and not a dataset as with  fixed combining rules. This classifier operates in the intermediate feature  space, the output space of the set of base classifiers. A new dataset B has  to be mapped to this intermediate space first by BC = B*WC before it can be  classified by D = BC*VC. As this is equivalent to D = B*WC*VC, the total  trained combiner is WTC = WC*VC = WC*A*WC*FISHERC. To simplify this procedure  PRTools executes the training of a combined classifier by  WTC = A*(WC*FISHERC) as WTC = WC*A*WC*FISHERC.

In order to allow for training an untrained parallel combined classifier by  A*WC the subsets of the features of A that apply for the individual base  classifiers of WC should be known to WC. Subset sizes are stored in the  dataset description if constructed by horizontal concatenation
A = [A1 A2 A3}; This can be overruled by storing them in the classifier  by the call WC = PARALLEL(WC,N), in which N is an array of integers, such  that sum(N) equals the feature size of A.

See also

mappings, datasets, maxc, minc, meanc, medianc, prodc, fisherc, stacked,

Example(s)