Universal Approximation Using Radial-Basis-Function Networks

1991 ◽  
Vol 3 (2) ◽  
pp. 246-257 ◽  
Author(s):  
J. Park ◽  
I. W. Sandberg
Keyword(s):  
Finite Number ◽  
Radial Basis Function ◽  
Basis Function ◽  
Universal Approximation ◽  
Radial Basis Function Networks ◽  
Feedforward Networks ◽  
Rbf Networks ◽  
Smoothing Factor ◽  
Radial Basis ◽  
Hidden Layer

There have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables. Some of these studies deal with cases in which the hidden-layer nonlinearity is not a sigmoid. This was motivated by successful applications of feedforward networks with nonsigmoidal hidden-layer units. This paper reports on a related study of radial-basis-function (RBF) networks, and it is proved that RBF networks having one hidden layer are capable of universal approximation. Here the emphasis is on the case of typical RBF networks, and the results show that a certain class of RBF networks with the same smoothing factor in each kernel node is broad enough for universal approximation.

Approximation and Radial-Basis-Function Networks

1993 ◽  
Vol 5 (2) ◽  
pp. 305-316 ◽  
Author(s):  
Jooyoung Park ◽  
Irwin W. Sandberg
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Universal Approximation ◽  
Radial Basis Function Networks ◽  
Approximation Of Functions ◽  
Radial Basis

This paper concerns conditions for the approximation of functions in certain general spaces using radial-basis-function networks. It has been shown in recent papers that certain classes of radial-basis-function networks are broad enough for universal approximation. In this paper these results are considerably extended and sharpened.

RADIAL BASIS FUNCTION NETWORKS AS CHAOTIC GENERATORS FOR SECURE COMMUNICATION SYSTEMS

1999 ◽  
Vol 09 (01) ◽  
pp. 221-232 ◽  
Author(s):  
S. PAPADIMITRIOU ◽  
A. BEZERIANOS ◽  
T. BOUNTIS
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Chaotic Maps ◽  
Training Data ◽  
Radial Basis Function Networks ◽  
Rbf Networks ◽  
Radial Basis

This paper improves upon a new class of discrete chaotic systems (i.e. chaotic maps) recently introduced for effective information encryption. The nonlinearity and adaptability of these systems are achieved by designing proper radial basis function networks. The potential for automatic synchronization, the lack of periodicity and the extremely large parameter spaces of these chaotic maps offer robust transmission security. The Radial Basis Function (RBF) networks offer a large number of parameters (i.e. the centers and spreads of the RBF kernels and the weights of the linear layer) while at the same time as universal approximators they have the flexibility to implement any function. The RBF networks can learn the dynamics of chaotic systems (maps or flows) and mimic them accurately by using many more parameters than the original dynamical recurrence. Since the parameter space size increases exponentially with respect to the number of parameters, the RBF based systems greatly outperform previous designs in terms of encryption security. Moreover, the learning of the dynamics from data generated by chaotic systems guarantees the chaoticity of the dynamics of the RBF networks and offers a convenient method of implementing any desirable chaotic dynamics. Since each sequence of training data gives rise to a distinct RBF configuration, theoretically there exists an infinity of possible configurations.

scholarly journals Modelling Temperature Variation of Mushroom Growing Hall Using Artificial Neural Networks

2019 ◽  
Author(s):  
Sina Ardabili ◽  
Amir Mosavi ◽  
Asghar Mahmoudi ◽  
Tarahom Mesri Gundoshmian ◽  
Saeed Nosratabadi ◽  
...  
Keyword(s):  
Neural Networks ◽  
Radial Basis Function ◽  
Temperature Variation ◽  
Basis Function ◽  
Intelligent Systems ◽  
Absolute Error ◽  
Radial Basis Function Networks ◽  
Radial Basis ◽  
Agricultural Industries ◽  
Hidden Layer

Recent advancements of computer and electronic systems have motivated the extensive use of intelligent systems for automation of agricultural industries. In this study, the temperature variation of the mushroom growing room is modeled through using a multi-layered perceptron (MLP) and radial basis function networks. Modeling has been done based on the independent parameters including ambient temperature, water temperature, fresh air and circulation air dampers, and water tap. According to the obtained results from the networks, the best network for MLP is found to be the second repetition with 12 neurons in the hidden layer and 20 neurons in the hidden layer for radial basis function networks. The obtained results from comparative parameters for two networks showed the highest correlation coefficient (0.966), the lowest root mean square error (RMSE) (0.787) and the lowest mean absolute error (MAE) (0.02746) for radial basis function. Therefore, the neural networks with radial basis function was selected as the optimal predictor for the behavior of the system.

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