A method for choosing the number of hidden layers in the artificial neural network

An artiﬁcial neural network (ANN) is an information processing paradigm that is inspired by the way biological nervous systems, such as the brain, process information. It is composed of several processing elements (neurons) that are able of adapting their parameters to learn from a speciﬁc training set (inductive learning), in a systematic fashion (training mode). If the examples in the training set are accompanied by labels, we talk about supervised learning, otherwise, the learning is unsupervised.
For example, a three-layer supervised neural network chosen, with a 7-neuron input layer, a x-neuron hidden layer, and a 1-neuron output layer. The number x of the hidden layer neurons varied from 2 to 30.
In order to achieve an adequate classiﬁcation performance for each subject, we proceeded in the following way: for each test subject, the neural networks were trained using the remaining seven subjects’ data, and partitioning them using the leave one out technique: the data of one of the seven subjects at the time were used as the testing set, while the remaining six subjects’ data were equally divided into training set and validation set. With these data, and for each value of x,2<x<30, the neural networks were trained and restarted 10 times, and the one with the best performance was chosen, in order to avoid local minima problems. The network with the best performance, i.e., the one with the lowest testing error, was then chosen among those obtained with different values of x.
This modus operandi led to 7 ‘‘best’’ neural networks for each of the 8 subjects, for a total of 56 networks.
The seven networks were then simulated on the corresponding subject’s data, in order to obtain seven classiﬁcation vectors. The seven vectors were rounded to 0 or 1 by setting a threshold at 0.5 and the ﬁnal classiﬁcation vector was computed second by second thanks to a majority voting system. For each second, a voting system among the seven classiﬁers provides the ﬁnal classiﬁcation.