Multilayered neural network

Let us start with a classic example. We had a dataset of 31 steroids. The spatial autocorrelation vector (more about autocorrelation vectors can be found in Chapter 8) stood as the set of molecular descriptors. The task was to model the Corticosteroid Ringing Globulin (CBG) affinity of the steroids. A feed-forward multilayer neural network trained with the back-propagation learning rule was employed as the learning method. The dataset itself was available in electronic form. More details can be found in Ref. [2]. 

Wythoff BJ, Levine SP, Tomellini A (1990) Spectral peak verification and recognition using a multilayered neural network. Anal Chem 62 2702... 

M. Karpenko, N. Sepehri, and D. Scuse. Diagnosis of process valve actuator faults using a multilayer neural network. Control Engineering Practice, 11 1289-1299, 2003. 

The architecture of an ANFIS model is shown in Figure 14.4. As can be seen, the proposed neuro-fuzzy model in ANFIS is a multilayer neural network-based fuzzy system, which has a total of five layers. The input (layer 1) and output (layer 5) nodes represent the descriptors and the response, respectively. Layer 2 is the fuzzification layer in which each node represents a membership. In the hidden layers, there are nodes functioning as membership functions (MFs) and rules. This eliminates the disadvantage of a normal NN, which is difficult for an observer to understand or to modify. The detailed description of ANFIS architecture is given elsewhere (31). 

Chen, C.-T., Lin, W.-L., Kuo, T.-S., and Wang, C.-Y. 1997. Adaptive control of arterial blood pressure with a learning controller based on multilayer neural networks. IEEE Trans. BME, 44 601-609. 

This implementation is equivalent to Fig. 1 and is shown in Fig. 1, the only differences being that the threshold function is displaced by an amount and that the constant unit input is no longer present. We return to the equivalence of these two formulations later in this section when we discuss implementation of multilayer neural networks. 

T. Aoyama and H. Ichikawa, /. Chem. Inf Comput. Sci., 32,492 (1992). Neural Networks as Nonlinear Structure-Activity Relationship Analyzers. Useful Functions of the Partial Derivative Method in Multilayer Neural Networks. 

Multilayer neural networks usually use continuous activation functions, either unipolar... 

Backpropi ation Training technique for multilayer neural networks. 

Having successfully implemented conventional MRAC techniques, the next logical step was to try to incorporate the MRAC techniques into a neural network-based adaptive control system. The ability of multilayered neural networks to approximate linear as well as nonlinear functions is well documented and has foimd extensive application in the area of system identification and adaptive control. The noise-rejection properties of neural networks makes them particularly useful in smart structure applications. Adaptive control schemes require only limited a priori knowledge about the system to be controlled. The methodology also involves identification of the plant model, followed by adaptation of the controller parameters based on a continuously updated plant model. These properties of adaptive control methods makes neural networks ideally suited for both identification and control aspects [7-11]. 

Figure 3 Multilayer neural network with feedforward and error backpropagation.

Figure 2. Schematic of a multilayer neural network [own elaboration].

Hornik, K. (1991). Approximation capahihties of multilayer neural networks. Neural Netw., 4, 251-257. 

Rataj, T. and Schindler, J. (1991) Identification of bacteria by multilayer neural networks. Binary, 3 159-164. 

The multilayer neural network is made up of simple components. A singlelayer network of neurons having numbers of neutron S, with multiple inputs R, is shown in Figure 12.32. Each scalar input p (i = 1,... R) is multiplied by the scalar weight Wi to form Wf) which is sent to the summer. The other input, 1, is multiplied by a bias bj j = 1,... S) and is then passed to the summer. The summer output, often referred to as the net input, goes into a transfer function, which produces the scalar neuron output a j, or in matrix form ... 

Doan C D, liong S (2004) Generalization for Multilayer Neural Network Bayesian Regularization or Early Stopping... 

Figure 7.12 Multilayer neural network with three layers.

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