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The multilayer perceptron as an approximation to a Bayes optimal discriminant function
IEEE Transactions on Neural Networks · 1990 · Vol. 1(4) · pp. 296–298
D.W. Ruck✉(U.S. Air Force Institute of Technology)Steven K. Rogers(U.S. Air Force Institute of Technology)Matthew Kabrisky(U.S. Air Force Institute of Technology)Mark E. Oxley(U.S. Air Force Institute of Technology)Bruce W. Suter(U.S. Air Force Institute of Technology)
Abstract
The multilayer perceptron, when trained as a classifier using backpropagation, is shown to approximate the Bayes optimal discriminant function. The result is demonstrated for both the two-class problem and multiple classes. It is shown that the outputs of the multilayer perceptron approximate the a posteriori probability functions of the classes being trained. The proof applies to any number of layers and any type of unit activation function, linear or nonlinear.
Neural Networks and ApplicationsFace and Expression RecognitionBlind Source Separation TechniquesBayes error rateDiscriminantBayes' theoremMultilayer perceptronLinear discriminant analysisPerceptronArtificial intelligencePattern recognition (psychology)Optimal discriminant analysisBackpropagation
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References
Learning in Artificial Neural Networks: A Statistical Perspective
Neural Computation · 1989 · 920 citations
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