PRTools Contents

PRTools User Guide



Combining classifiers in the same feature space

WC = STACKED(W1,W2,W3, ....) or WC = [W1,W2,W3, ...] WC = STACKED({W1,W2,W3, ...}) or WC = [{W1,W2,W3, ...}] WC = STACKED(WC,W1,W2, ....) or WC = [WC,W2,W3, ...]

     W1,W2,W3 Set of classifiers

 WC Combined classifier


The base classifiers (or mappings) W1, W2, W3, ... defined in the same  feature space are combined in WC. This is a classifier defined for the  same number of features as each of the base classifiers 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. 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, 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.

It is also possible to combine a set of untrained classifiers, e.g. WC = [LDC NMC KNNC([],1)]*CLASSC, in which CLASSC takes care that all outputs  will be transformed to appropriate posterior probabilities. Training of  all base classifiers is done by WC = A*WC. Again, this may be combined  with training of a combiner by WTC = A*(WC*FISHERC).



PRTools Contents

PRTools User Guide

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