# Functional Networks with Applications: A Neural-Based by Enrique Castillo, Angel Cobo, Jose Antonio Gutierrez, Rosa

By Enrique Castillo, Angel Cobo, Jose Antonio Gutierrez, Rosa Eva Pruneda

Artificial neural networks were well-known as a robust software to profit and reproduce platforms in a variety of fields of purposes. Neural web works are encouraged via the mind habit and encompass one or a number of layers of neurons, or computing devices, hooked up through hyperlinks. every one man made neuron gets an enter price from the enter layer or the neurons within the previ ous layer. Then it computes a scalar output from a linear blend of the got inputs utilizing a given scalar functionality (the activation function), that's assumed a similar for all neurons. one of many major homes of neural networks is their skill to benefit from information. There are varieties of studying: structural and parametric. Structural studying involves studying the topology of the community, that's, the variety of layers, the variety of neurons in each one layer, and what neurons are hooked up. This procedure is finished through trial and blunder till an excellent healthy to the knowledge is acquired. Parametric studying involves studying the burden values for a given topology of the community. because the neural services are given, this studying strategy is completed through estimating the relationship weights in keeping with the given info. To this objective, an mistakes functionality is minimized utilizing a number of popular studying tools, akin to the backpropagation set of rules. regrettably, for those tools: (a) The functionality as a result of the educational strategy has no actual or engineering interpretation. hence, neural networks are noticeable as black boxes.

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Two competitive neural network with (a) two and (b) three output units. 1 Determine the number of parameters of a multi-layer perceptron with k hidden units, j input units and i output units. 2 Show that for networks with tanh or logistic sigmoidal hidden unit activation function, the network mapping is invariant if all of the weights and the bias feeding into and out of a unit have their signs changed. 44 1. Introduction to Neural Networks lr---~----------~----' e'. • ... t:. 1IiC!.... , I i ; •• I --:~,- ....

2 Improvements and Modifications With the aim of improving the efficiency of the above learning methods, several modifications have been proposed in the literature. One of them 24 1. 1. Data points (x, y) classified in two categories represented by c = 0 and c = 1, respectively. Wij to accelerate the convergence to the minimum. Wij (in the previous iteration step) and a is the momentum parameter. 18) i,j where'\ is a regularization parameter, which controls the balance between fitting the model and avoiding the penalty.

If the variables measure symptoms which are directly related to the disease, it is reasonable to assume that the functions F, K, L, G, Nand Mare invertible (strictly monotonic) with respect to both variables. This means that the higher (lower) level of one symptom the higher (lower) probability of the disease. , the values coming from each of the links must be the same. However, this network is not a neural network because: 1. The neuron functions are arbitrary. 2. , F, G, K, L, M and N). 3. , leading to the same output u.