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The problem of multiclass classification is often modeled by breaking it down into a collection of binary classifiers, as
opposed to jointly modeling all classes with a single primary classifier. Various methods can be found in the literature
for decomposing the multiclass problem into a collection of binary classifiers. Typical algorithms that are studied here
include each versus all remaining (EVAR), each versus all individually (EVAI), and output correction coding (OCC).
With each of these methods a classifier fusion based decision rule is formulated utilizing the various binary classifiers to
determine the correct classification of an unknown data point. For example, with EVAR the binary classifier with
maximum output is chosen. For EVAI, the correct class is chosen using a majority voting rule, and with OCC a
comparison algorithm based minimum Hamming distance metric is used. In this paper, it is demonstrated how these
various methods perform utilizing the Bayesian Reduction Algorithm (BDRA) as the primary classifier. BDRA is a
discrete data classification method that quantizes and reduces the dimensionality of feature data for best classification
performance. In this case, BDRA is used to not only train the appropriate binary classifier pairs, but it is also used to
train on the discrete classifier outputs to formulate the correct classification decision of unknown data points. In this
way, it is demonstrated how to predict which binary classification based algorithm method (i.e., EVAR, EVAI, or OCC)
performs best with BDRA. Experimental results are shown with real data sets taken from the Knowledge Extraction
based on Evolutionary Learning (KEEL) and University of California at Irvine (UCI) Repositories of classifier
Databases. In general, and for the data sets considered, it is shown that the best classification method, based on
performance with unlabeled test observations, can be predicted form performance on labeled training data. Specifically,
the best method is shown to have the least overall probability of error, and the binary classifiers have the least overall
average quantization complexity.
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