Evaluation of molecular integral of Cartesian Gaussian type basis function with complex-valued center coordinates and exponent via the McMurchie-Davidson recursion formula, and its application to electron dynamics

2009 ◽  
Vol 109 (3) ◽  
pp. 540-548 ◽  
Author(s):  
T. Kuchitsu ◽  
J. Okuda ◽  
M. Tachikawa
Keyword(s):  
Basis Function ◽  
Recursion Formula ◽  
Electron Dynamics ◽  
Molecular Integral ◽  
Gaussian Type ◽  
Complex Valued

scholarly journals Using Radial Basis Function Networks for Function Approximation and Classification

2012 ◽  
Vol 2012 ◽  
pp. 1-34 ◽  
Author(s):  
Yue Wu ◽  
Hui Wang ◽  
Biaobiao Zhang ◽  
K.-L. Du
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Function Approximation ◽  
System Modeling ◽  
Rbf Network ◽  
Network Learning ◽  
Radial Basis ◽  
Comprehensive Survey ◽  
Dynamic System Modeling ◽  
Complex Valued

The radial basis function (RBF) network has its foundation in the conventional approximation theory. It has the capability of universal approximation. The RBF network is a popular alternative to the well-known multilayer perceptron (MLP), since it has a simpler structure and a much faster training process. In this paper, we give a comprehensive survey on the RBF network and its learning. Many aspects associated with the RBF network, such as network structure, universal approimation capability, radial basis functions, RBF network learning, structure optimization, normalized RBF networks, application to dynamic system modeling, and nonlinear complex-valued signal processing, are described. We also compare the features and capability of the two models.

A FULLY COMPLEX-VALUED RADIAL BASIS FUNCTION NETWORK AND ITS LEARNING ALGORITHM

2009 ◽  
Vol 19 (04) ◽  
pp. 253-267 ◽  
Author(s):  
R. SAVITHA ◽  
S. SURESH ◽  
N. SUNDARARAJAN
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Learning Algorithm ◽  
Radial Basis Function Network ◽  
Activation Function ◽  
Rbf Network ◽  
Practical Applications ◽  
Xor Problem ◽  
Radial Basis ◽  
Complex Valued

In this paper, a fully complex-valued radial basis function (FC-RBF) network with a fully complex-valued activation function has been proposed, and its complex-valued gradient descent learning algorithm has been developed. The fully complex activation function, sech(.) of the proposed network, satisfies all the properties needed for a complex-valued activation function and has Gaussian-like characteristics. It maps Cn → C, unlike the existing activation functions of complex-valued RBF network that maps Cn → R. Since the performance of the complex-RBF network depends on the number of neurons and initialization of network parameters, we propose a K-means clustering based neuron selection and center initialization scheme. First, we present a study on convergence using complex XOR problem. Next, we present a synthetic function approximation problem and the two-spiral classification problem. Finally, we present the results for two practical applications, viz., a non-minimum phase equalization and an adaptive beam-forming problem. The performance of the network was compared with other well-known complex-valued RBF networks available in literature, viz., split-complex CRBF, CMRAN and the CELM. The results indicate that the proposed fully complex-valued network has better convergence, approximation and classification ability.

A Medical Decision Support System Based on Ensemble of Complex-Valued Radial Basis Function Networks

2018 ◽  
pp. 22-45
Author(s):  
Musa Peker ◽  
Hüseyin Gürüler ◽  
Ayhan İstanbullu
Keyword(s):  
Decision Support ◽  
Decision Support System ◽  
Radial Basis Function ◽  
Support System ◽  
Basis Function ◽  
Medical Diagnosis ◽  
Computer Aided ◽  
Radial Basis ◽  
Encoding Method ◽  
Complex Valued

The use of machine learning techniques for medical diagnosis has become increasingly common in recent years because, most importantly, the computer-aided diagnostic systems developed for supporting the experts have provided effective results. The authors aim in this chapter to improve the performance of classification in computer-aided medical diagnosis. Within the scope of the study, experiments have been performed on three different datasets, which include heart disease, hepatitis, and BUPA liver disorders datasets. First, all features obtained from these datasets were converted into complex-valued number format using phase encoding method. After complex-valued feature set was obtained, these features were then classified by an ensemble of complex-valued radial basis function (ECVRBF) method. In order to test the performance and the effectiveness of the medical diagnostic system, ROC analysis, classification accuracy, specificity, sensitivity, kappa statistic value, and f-measure were used. Experimental results show that the developed system gives better results compared to other methods described in the literature. The proposed method can then serve as a useful decision support system for medical diagnosis.

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