Clasificación de los diferentes tipos de Dislexia

Artificial neural networks (ANN) are used to model complex & high dimensional real-world problems. The characteristics of this modelling principle are non-linearity, high parallelism in the training algorithms, robustness, fault and failure tolerance, learning ability, ability to handle imprecise and fuzzy information, and capability to generalize [3].

The underlying principle of artificial neural network is an abstraction of the biological neural networks. Figure 4.3 illustrates the structure of a feed-forward artificial neural network which is applied in this thesis. Such a neural network is composed of a different number of layers

.. . .. . ... . . . w(2)_1,1 w(2)_m,n w(2_1,k+h) w(2_1,1+h) b(1₁+h) b_k(1+h) b₁(2) b_m(2) b(2)₃ b₁(1+h) b(2₁+h)

Input Layer Hidden Layers 1 . . .h Output Layer

Layer 2 Layer 1+h Layer 1 Layer 2+h xn x2 x1 N(2)₁ N(2)₂ N(2)₃ N(2)_m N(1_k+h) N(1₃+h) N(1₂+h) N(1₁+h) b y

FIGURE4.3:A generalised representation of a multi-layer feed forward artificial neural network.

which are called the input layer, a variable number of hidden layers, and an output layer. Each layer consists of an arbitrary number of neurons. These neurons are represented by different

4.2. Method Overview

transfer functions (according to their biological counterparts often also called activation functions) which are multiplied with some weightsw_{i j}(l), whereldefines the corresponding layer, the indexirepresents the affiliation to theith neuron of the corresponding layer, and the indexjrepresents the affiliation to thejth neuron of the previous (l−1) layer. Additionally, to every neuron a biasb(_il)can be assigned which adds to the output value of the transfer function, see [21]. Furthermore, the number of connections, connection recycles, connection hierarchies, and neuron grouping may be applied to alternate the structure and results of a neural network by applying specialised algorithms.

Each neuron inherits a transfer function which transfers the weighted inputs of the neuron into the output value of the neuron. The simplest transfer function is a linear output transfer function which is the weighted sum of the neuron inputs. There are other transfer function definitions like the Sigmoid transfer function

S(t)= 1

1+e−t , (4.26)

wheretis the sum of the weighted inputsPNl−1

i=1 w (l) i jx

l−1

i . The linear output transfer function

and the Sigmoid transfer function are the most commonly used transfer functions [3, 50].

Artificial neural networks and the radial basis function approach have a common definition. Equation (4.3) in section 4.2.2.2 is actually identical to the expression of a single-layer neural network with radial coordinate neurons, with an input~x, hidden unitsψ~, weightsw~, linear output transfer functions, and output fb(~x) [29]. These models are then often called radial basis function neural networks [25, 26, 116, 118]. The two methods then only differ in the way how the model parameters are estimated (trained). Artificial neural networks are categorised into feed-forward networks (Perceptron network), competitive networks (Hamming network), and recurrent networks (Hopfield network) [118]. The radial basis function neural networks and the in this thesis applied feed-forward artificial neural network types the multi-layer perceptron neural network with back-propagation training are two of the most widely used artificial neural network [118]. The latter is realised in different software solutions (e.g. Matlab Neural Network Toolbox) and allows therefore an ease of access to neural network modelling for the engineering community.

The process of estimating the parameters of neural networks is called training or learning. The corresponding trained parameters are the weightsw(_{i j}l)and the biasesb(_jl), but could also include the number of neurons and layers. This process of training an artificial neural network is defined in a so called training or learning rule. There are different learning rules which are applied to artificial neural networks. A learning rule defines how the parameters or the structure of an artificial neural network are adapted between successive iteration cycles of the training. These cycles are commonly called epochs.

The most commonly used method is the back-propagation algorithm. Briefly, the algorithm of the back-propagation training measures the error between the output of the neural network calculation and the training data and uses this error measurement to change the parameter values (weights) according to their influence on the output, such that the next calculation converges to the training data. The name back-propagation is based on the fact that the error measured in the result is propagated back to the neurons to change the input / output relations. Dua [21] introduced a mixed-inter programming approach for optimising the configuration of the neural network. Each considered neuron has a binary variable controlling the existence of the respective node. Thus, not only the reduction of the prediction error but also the reduction in the number of neurons is achieved during the training procedure.

For a more detailed introduction into artificial neural network modelling the work by Basheer and Hajmeer [3] is recommended. Also the review on applications in energy systems given by Kalogirou [50].

Simpson et al. [94] recommend the use of artificial neural networks for highly non-linear very large problems with 10000 and more sample points. It is best suited for deterministic applications such as the design of computer experiments and it is recommended for appli- cations which require repeated use of the model since training of artificial neural networks goes along with high computational expense. Artificial neural networks are predestined for high-dimensional problems with a large number of input variables where other concepts hit their limits.