Radial basis function , artificial

Seven parameters of physicochemical properties, such as acid number, color, density, refractive index, moisture and volatility, saponification value and PV, were measured for quality and adnlter-ated soybean, as well as quality and rancid rapeseed oils. The chemometric methods were then applied for qualitative and quantitative discrimination and prediction of the oils by methods snch as exploratory principal component analysis (PCA), partial least squares (PLS), radial basis function-artificial neural networks (RBF-ANN), and multi-criteria decision making methods (MCDM), PROMETHEE and GAIA.260... 

Girosi, F., and Anzellotti, G., Rales of convergence for radial basis functions and neural networks. Artificial Neural Networks with Applications in Speech and Vision, (R. J. Matttmone, ed.), p. 97. Chapman Hall, London, 1993. 

Models of the form y =f(x) or v =/(x1, x2,..., xm) can be linear or nonlinear they can be formulated as a relatively simple equation or can be implemented as a less evident algorithmic structure, for instance in artificial neural networks (ANN), tree-based methods (CART), local estimations of y by radial basis functions (RBF), k-NN like methods, or splines. This book focuses on linear models of the form... 

Not all neural networks are the same their connections, elemental functions, training methods and applications may differ in significant ways. The types of elements in a network and the connections between them are referred to as the network architecture. Commonly used elements in artificial neural networks will be presented in Chapter 2. The multilayer perception, one of the most commonly used architectures, is described in Chapter 3. Other architectures, such as radial basis function networks and self organizing maps (SOM) or Kohonen architectures, will be described in Chapter 4. 

Some historically important artificial neural networks are Hopfield Networks, Per-ceptron Networks and Adaline Networks, while the most well-known are Backpropa-gation Artificial Neural Networks (BP-ANN), Kohonen Networks (K-ANN, or Self-Organizing Maps, SOM), Radial Basis Function Networks (RBFN), Probabilistic Neural Networks (PNN), Generalized Regression Neural Networks (GRNN), Learning Vector Quantization Networks (LVQ), and Adaptive Bidirectional Associative Memory (ABAM). 

Radial Basis functions (RBF) belong to the class of Artificial Neural Networks (ANNs) and are a popular choice for approximating nonlinear functions. RBF (f> has its output symmetric around an associated centre p. 

Network analysis Artificial neural network (ANN) and Radial basis function (RBF). 

The ANNs were developed in an attempt to imitate, mathematically, the characteristics of the biological neurons. They are composed by intercoimected artificial neurons responsible for the processing of input-output relationships, these relationships are learned by training the ANN with a set of irqmt-output patterns. The ANNs can be used for different proposes approximation of functions and classification are examples of such applications. The most common types of ANNs used for classification are the feedforward neural networks (FNNs) and the radial basis function (RBF) networks. Probabilistic neural networks (PNNs) are a kind of RBFs that uses a Bayesian decision strategy (Dehghani et al., 2006). 

Selection of the supervised classification technique or the combination of techniques suitable for accomplishing the classification task. Popular supervised classifiers are Multi-Layer Perceptron Artificial Neural Networks (MLP-ANN), Support Vector Machines (SVM), k-Nearest Neighbours (k-NN), combinations of genetic algorithms (GA) for feature selection with Linear Discriminant Analysis (LDA), Decision Trees and Radial Basis Function (RBF) classifiers. 

Artificial neural networks (ANNs) are good at classifying non-linearly separable data. There are at least 30 different types of ANNs, including multilayer perceptron, radial basis functions, self-organizing maps, adaptive resonance theory networks and time-delay neural netwoiks. Indeed, the majority of ATI applications discussed later employ ANNs - most commonly, MLP (multilayer perceptron), RBF (radial basis function) or SOM (self-organizing map). A detailed treatise of neural networks for ATI is beyond the scope of this chapter and the reader is referred to the excellent introduction to ANNs in Haykin (1994) and neural networks applied to pattern recognition in Looney (1997) and Bishop (2(X)0). Classifiers for practical ATI systems are also described in other chapters of this volume. 

Using the SVM-BFS method, we select the features for the three artificial problems. The selected subset and its corresponding errors of each step are listed in Table 4.5. The SVM used in the feature selection of these three data sets are linear SVM, nonlinear SVM with radial basis function (RBF) kernel (cr = 1.54) and SVM with RBF kernel ([Pg.69]

A basic information about Artificial Neural Networks (ANNs) and their applications was introduced. A special attention was given to description of dynamic processes by mean of ANN. The drying kinetics of agricultural products are presented in the paper. Multilayer Perceptron (MLP) and Radial Basis Function (RBF) network types are proposed for predicting changes of moisture content and temperature of material in during drying in the vibrofluidized bed. Capability of prediction of Artificial Neural Networks is evaluated in feed forward and recurrent structures. 

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