Binary Output Layer of Feedforward Neural Networks for Solving Multi-Class Classification Problems

Considered in this short note is the design of output layer nodes of feedforward neural networks for solving multiple-class classification problems with
$r$
(
$r\geq 3$
) classes of samples. The common and conventional setting of the output layer called “
$one - to - one~approach$
” in this paper, is as follows: The output layer contains
$r$
output nodes corresponding to the
$r$
classes. And for an input sample of the
$i$
-th class (
$1\leq i\leq r$
), the ideal output is 1 for the
$i$
-th output node, and 0 for all the other output nodes. We propose in this paper a new “
$binary~approach$
”: Suppose
$2^{q-1}< r\leq 2^{q}$
with
$q\geq 2$
, then we let the output layer contain
$q$
output nodes, and let the ideal outputs for the
$r$
classes be designed in a binary manner. This idea of binary output is also applied for other classifiers, such as support vector machines and associative pulsing neural networks. Numerical simulations are carried out on eight real-world data sets, showing that our binary approach performs as well as, but uses less output nodes and hidden-output weights than, the traditional one-to-one approach.