  In ensemble methods, the outputs of a collection of diverse classifiers are
combined in the expectation that the global prediction be more accurate than
the individual ones. Heterogeneous ensembles consist of predictors of different
types, which are likely to have different biases. If these biases are
complementary, the combination of their decisions is beneficial. In this work,
a family of heterogeneous ensembles is built by pooling classifiers from M
homogeneous ensembles of different types of size T. Depending on the fraction
of base classifiers of each type, a particular heterogeneous combination in
this family is represented by a point in a regular simplex in M dimensions. The
M vertices of this simplex represent the different homogeneous ensembles. A
displacement away from one of these vertices effects a smooth transformation of
the corresponding homogeneous ensemble into a heterogeneous one. The optimal
composition of such heterogeneous ensemble can be determined using
cross-validation or, if bootstrap samples are used to build the individual
classifiers, out-of-bag data. An empirical analysis of such combinations of
bootstraped ensembles composed of neural networks, SVMs, and random trees (i.e.
from a standard random forest) illustrates the gains that can be achieved by
this heterogeneous ensemble creation method.
