ANALYSIS OF DECISION BOUNDARIES IN LINEARLY COMBINED NEURAL
CLASSIFIERS
Kagan Tumer and Joydeep Ghosh
Combining or integrating the outputs of several pattern
classifiers has led
to improved performance in a multitude of applications.
This paper provides an analytical framework to quantify the
improvements in classification results due to combining.
We show that combining networks linearly in output space
reduces the variance of the actual decision region boundaries
around the optimum boundary. This result is valid
under the assumption that the a posteriori probability distributions
for each class are locally monotonic around the Bayes optimum boundary.
In the absence of classifier bias, the error is shown to be
proportional to the boundary variance, resulting in a simple
expression for error rate improvements.
In the presence of bias, the error reduction, expressed in terms of
a bias reduction factor, is shown to be less than or equal to the
reduction obtained in the absence of bias.
The analysis presented here facilitates the
understanding of the relationships among error rates,
classifier boundary distributions, and combining in output space.
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