Multiclass Classification Through Multidimensional Clustering 227
Specialized class transformationsNew set of specialized class transformationsClass 1 Class 2 Class 3 Class nClass 1 Class 2 Class 3 Class nTrue Positive
False PositiveTrue Positive
False Positive4949203531 32231811 011 10 01441New evaluated Tree improvement inLooking for
new treesFig. 2 Identification of the best transformation for each class based on true and false positives
1.Specialized class transformations:First, we are interested in identifying the
best transformationk^0 i for each class!i, and building a set of specialized
class transformationsSD.k 10 ;:::;k^0 M/. At the beginning of the search, when
the first individual is evaluated,Mcopies are stored inS. For all subsequent
transformations evolved during the search, we compute the number of True
Positives (TP) and False Positives (FP) it produces for each class. If at least one
of these numbers improves (TP gets higher or FP gets lower) and neither value
deteriorates relative toki^0 , then the new tree replaceski^0 withinS. This is done for
every individual evaluated during the run—see Fig. 2 for an illustration of this
process.
2.Ensemble classifier:Our proposal builds an ensembleED.e 1 ;:::;eM/of trans-
formations for each new individualk, by combiningkwith the transformations
stored inS. Eacheirepresents ad-dimensional transformation, such that given a
data pointxtheeitransformation is used to compute the distance to thei-th class
cluster. After computing the distance to each class cluster, the minimum distance
determines the class label assigned.
3.Ensemble construction:One possible approach is to useSas an ensemble,
however preliminary tests using this approach have shown a substantial decrease
in test performance. Therefore, an ensembleEis constructed for each individual
treekand used to assign fitness. First, every elementeiin the ensemble is
set equal tok, i.e.,ei D kfor alli. Then, the accuracy ofEis computed.
Afterwards, in a random order we replace eacheiby its corresponding specialized