Decision Forests - Data Mining with Decision Trees: Theory and Applications - page 114

at the meta-level and empirically showed that it performs better than
existing stacking approaches and better than selecting the best classifier
by cross-validation.
The SCANN (for Stacking, Correspondence Analysis and Nearest
Neighbor) combining method [ Merz (1999) ] uses the strategies of stacking
and correspondence analysis. Correspondence analysis is a method for
geometrically modeling the relationship between the rows and columns
of a matrix whose entries are categorical. In this context Correspondence
Analysis is used to explore the relationship between the training examples
and their classification by a collection of classifiers.
A nearest neighbor method is then applied to classify unseen examples.
Here, each possible class is assigned coordinates in the space derived by
correspondence analysis. Unclassified examples are mapped into the new
space, and the class label corresponding to the closest class point is assigned
to the example.

9.3.2.2 Arbiter Trees
According to Chan and Stolfo's approach [ Chan and Stolfo (1993) ] ,an
arbiter tree is built in a bottom-up fashion. Initially, the training set is
randomly partitioned into k disjoint subsets. The arbiter is induced from a
pair of classifiers and recursively a new arbiter is induced from the output
of two arbiters. Consequently for k classifiers, there are log 2 ( k ) levels in the
generated arbiter tree.
The creation of the arbiter is performed as follows. For each pair
of classifiers, the union of their training dataset is classified by the
two classifiers. A selection rule compares the classifications of the two
classifiers and selects instances from the union set to form the training
set for the arbiter. The arbiter is induced from this set with the same
learning algorithm used in the base level. The purpose of the arbiter is to
provide an alternate classification when the base classifiers present diverse
classifications. This arbiter, together with an arbitration rule, decides on
a final classification outcome, based upon the base predictions. Figure 9.4
shows how the final classification is selected based on the classification of
two base classifiers and a single arbiter.
The process of forming the union of data subsets; classifying it using
a pair of arbiter trees; comparing the classifications; forming a training
set; training the arbiter; and picking one of the predictions, is recursively
performed until the root arbiter is formed. Figure 9.5 illustrates an arbiter
tree created for k =4. T 1 − T 4 are the initial four training datasets from