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Components of Artificial Intelligence and Data Analytics 123

More recent networks commonly use a sigmoidal function to model the
transfer between input and output signals (Fig 4.7B):
1
P ¼ a (4.3)
1+ e t
where P is the probability of the node firing, t a constant that determines the
function steepness, and a is the activation node. The steepness of the acti-
vation function determines whether most of the input is transferred through
the nodes, or whether the output is only initiated by stronger inputs. This
feature attempts to imitate the behavior of real neurons, which often tend to
be either active or inactive.
A basic model often uses three layers of nodes (Fig 4.8A): the input layer
receives the data, the middle (hidden) layer draws stimulation from the input
layer, and transmits onward to the final output layer, which is the result of
the system. In “training” the network, a set of patterns is repeatedly pres-
ented and the weights of the arcs are modified such that the output makes
a better match with a desired result. The “training” is usually accomplished
by backward propagation of errors through the network that distributes the
difference between the desired result and the actual output as small incre-
mental adjustments in the interconnection weights. The process is gradual
and iterative, until the weights converge to an equilibrium setting and
the network is trained. The speed of the training is controlled by a learning
rate set by the user. If too high, the network learns quickly, but the weights
may oscillate with an unstable solution. Very slow learning rates ensure a
smoother passage to stability but may take excessive computing time.
At the end of the training, an unknown pattern can be entered for pur-
poses of classification or regression (prediction) as outlined in previous sections.
Fig 4.8B presents an example of an input-output model for application of
ANNs developed for the optimization of hydraulic fracturing in unconven-
tional gas reservoirs (Temizel et al., 2015).

4.2.2.2 Support Vector Machine
The SVM is widely perceived as one of the most powerful classification
“out-of-the-box” learning tools. It has been developed in the area of com-
puter science in the early 1990s and has recently been receiving more and
more attention in the widest range of engineering fields, mostly because
of the advent of Big Data applications. According to James et al. (2014),
the SVM is a generalization of a simple and intuitive classifier called a max-
imum margin classifier, which unfortunately cannot be applied to most data