Three-layer network

Fortunately, ANNs can overcome these limitations and be used to develop models for these types of data. Some of the earliest work with neural networks was done by McCulloch and Pitts in 1943. ANNs can be used for the evaluation of nonlinear data for the development of a predictive model. Thus, a nonlinear data set, such as the class system of CPT data in the USDA archive, can be used to develop a model and predict compound activities based on the compound structures and associated repellent activities that were incorporated into the neural network. Three-layer neural networks with different architectures were applied to the data sets of acylpiperidines in this chapter. 

An ANN is a network of single neurons jointed together by synaptie eonneetions. Figure 10.22 shows a three-layer feedforward neural network. 

Consider a three layer network. Let the input layer be layer one ( = 1), the hidden layer be layer two ( = 2) and the output layer be layer three ( = 3). The baek-propagation eommenees with layer three where dj is known and henee 8j ean be ealeulated using equation (10.69), and the weights adjusted using equation (10.71). To adjust the weights on the hidden layer = 2) equation (10.69) is replaeed by... 

Kolmogorov s Theorem (Reformulated by Hecht-Nielson) Any real-valued continuous function f defined on an N-dimensional cube can be implemented by a three layered neural network consisting of 2N -)-1 neurons in the hidden layer with transfer functions from the input to the hidden layer and (f> from all of... 

Radial basis function networks (RBF) are a variant of three-layer feed forward networks (see Fig 44.18). They contain a pass-through input layer, a hidden layer and an output layer. A different approach for modelling the data is used. The transfer function in the hidden layer of RBF networks is called the kernel or basis function. For a detailed description the reader is referred to references [62,63]. Each node in the hidden unit contains thus such a kernel function. The main difference between the transfer function in MLF and the kernel function in RBF is that the latter (usually a Gaussian function) defines an ellipsoid in the input space. Whereas basically the MLF network divides the input space into regions via hyperplanes (see e.g. Figs. 44.12c and d), RBF networks divide the input space into hyperspheres by means of the kernel function with specified widths and centres. This can be compared with the density or potential methods in pattern recognition (see Section 33.2.5). 

Independent studies (Cybenko, 1988 Homik et al., 1989) have proven that a three-layered back propagation network will exist that can implement any arbitrarily complex real-valued mapping. The issue is determining the number of nodes in the three-layer network to produce a mapping with a specified accuracy. In practice, the number of nodes in the hidden layer are determined empirically by cross-validation with testing data. 

PPR is a linear projection-based method with nonlinear basis functions and can be described with the same three-layer network representation as a BPN (see Fig. 16). Originally proposed by Friedman and Stuetzle (1981), it is a nonlinear multivariate statistical technique suitable for analyzing high-dimensional data, Again, the general input-output relationship is again given by Eq. (22). In PPR, the basis functions 9m can adapt their shape to provide the best fit to the available data. 

Figure 20.3 Schematic representation of a three-layered artificial neural network.

The entire system is based on a tiered approach where three layers of technology are integrated into the overall treatment system, as illustrated in Chart 2. First, a distributed process control system is network linked to the various component subunits of the waste management system such as pH control, ion-exchange control, tank level control, etc. Next, are the recovery/treatment processes themselves. The final tier is a monitoring system which controls both the performance of the treatment systems and the discharge assurance of the plant effluent... 

An artificial neural network (ANN) model was developed to predict the structure of the mesoporous materials based on the composition of their synthesis mixtures. The predictive ability of the networks was tested through comparison of the mesophase structures predicted by the model and those actually determined by XRD. Among the various ANN models available, three-layer feed-forward neural networks with one hidden layer are known to be universal approximators [11, 12]. The neural network retained in this work is described by the following set of equations that correlate the network output S (currently, the structure of the material) to the input variables U, which represent here the normalized composition of the synthesis mixture ... 

Typically, a neural network consists of three layers of neurons, input, hidden and output layers, and of information flow channels between the neurons called interconnects (Figure 33). 

The next three layers reside on an application middleware server, although in some systems, there is a further physical separation between the presentation layer, which runs on a different hardware from the domain and data access layers. If EJB is used in a J2EE application, the presentation layer runs on a Web container and the domain layer runs on an EJB container. With the EJB local interface in J2EE 1.3, the separation becomes unnecessary, which eliminates the network overhead between the two. 

As a chemometric quantitative modeling technique, ANN stands far apart from all of the regression methods mentioned previously, for several reasons. First of all, the model structure cannot be easily shown using a simple mathematical expression, but rather requires a map of the network architecture. A simplified example of a feed-forward neural network architecture is shown in Figure 8.17. Such a network structure basically consists of three layers, each of which represent a set of data values and possibly data processing instructions. The input layer contains the inputs to the model (11-14). 

Wong, G. C. L., Tang, J. X., Lin, A., Li, Y., Janmey, P. A. Safinya, C. R. Hierarchical self-assembly of F-actin and cationic lipid complexes Stacked three-layer tubule networks. Science (Washington, D. C.) 288, 2035-2039 (2000). 

The glomerular basement membrane (GBM) forms the backbone of the glomerular tuft. It is composed of three layers lamina rara interna, lamina densa, and lamina rara externa. The glomerular basement membrane is composed of a network of collagen type IV molecules (H5) intertwined with nidogen to another network composed of molecules of laminin. Type IV collagen and laminin are responsible for the firmness of the glomerular basement membrane and enable adhesion of endothelial cells and podocytes as well. 

Fig. 2. Structure of an artificial neural network. The network consists of three layers the input layer, the hidden layer, and the output layer. The input nodes take the values of the normalized QSAR descriptors. Each node in the hidden layer takes the weighted sum of the input nodes (represented as lines) and transforms the sum into an output value. The output node takes the weighted sum of these hidden node values and transforms the sum into an output value between 0 and 1.

Figure 1.16. Schematic architecture of a three layer feed-forward network...

Example of a three-layer back-propagation network describing the application of physical property prediction. 

Fig. 4. Simple three-layer artificial neural network (ANN).

Based on this in-house dataset, an in-silico prediction model [27] (three-layered neural network, Ghose and Crippen [28,29] descriptors) was constructed to evaluate the frequent hitter potential before compound libraries are purchased or synthesized. This model was validated with a dataset of the above-mentioned promiscuous ligands published by McGovern et al. [26], in which 25 out of 31 compounds were correctly recognized. 

Granjeon and Tarroux (1995) studied the compositional constraints in introns and exons by using a three-layer network, a binary sequence representation, and three output units to train for intron, exon, and counter-example separately. They found that an efficient learning required a hidden layer, and demonstrated that neural network can detect introns if the counter-examples are preferentially random sequences, and can detect exons if the counter-examples are defined using the probabilities of the second-order Markov chains computed in junk DNA sequences. 

---