Wavelets Based Neural Network for Function Approximation

2006 ◽  
pp. 80-85 ◽  
Author(s):  
Yong Fang ◽  
Tommy W. S. Chow
Keyword(s):  
Neural Network ◽  
Function Approximation

Function approximation using a sinc neural network

1996 ◽  
Author(s):  
Wael R. Elwasif ◽  
Laurene V. Fausett
Keyword(s):  
Neural Network ◽  
Function Approximation

scholarly journals Kernel-blending connection approximated by a neural network for image classification

2020 ◽  
Vol 6 (4) ◽  
pp. 467-476
Author(s):  
Xinxin Liu ◽  
Yunfeng Zhang ◽  
Fangxun Bao ◽  
Kai Shao ◽  
Ziyi Sun ◽  
...  
Keyword(s):  
Neural Network ◽  
Image Classification ◽  
Function Approximation ◽  
Feature Space ◽  
Neural Network Learning ◽  
Network Learning ◽  
Hinge Loss ◽  
The Neural Network ◽  
Good Classification ◽  
Kernel Mapping

AbstractThis paper proposes a kernel-blending connection approximated by a neural network (KBNN) for image classification. A kernel mapping connection structure, guaranteed by the function approximation theorem, is devised to blend feature extraction and feature classification through neural network learning. First, a feature extractor learns features from the raw images. Next, an automatically constructed kernel mapping connection maps the feature vectors into a feature space. Finally, a linear classifier is used as an output layer of the neural network to provide classification results. Furthermore, a novel loss function involving a cross-entropy loss and a hinge loss is proposed to improve the generalizability of the neural network. Experimental results on three well-known image datasets illustrate that the proposed method has good classification accuracy and generalizability.

A CONSTRUCTIVE NEURAL NETWORK ALGORITHM FOR FUNCTION APPROXIMATION USING LOCALLY FIT SIGMOIDS

1998 ◽  
Vol 07 (03) ◽  
pp. 373-398
Author(s):  
TIM DRAELOS ◽  
DON HUSH
Keyword(s):  
Neural Network ◽  
Function Approximation ◽  
Piecewise Linear ◽  
Target Function ◽  
Approximation Problem ◽  
Sigmoidal Functions ◽  
Network Algorithm ◽  
Neural Network Algorithm ◽  
Training Error ◽  
Hidden Layer

A study of the function approximation capabilities of single hidden layer neural networks strongly motivates the investigation of constructive learning techniques as a means of realizing established error bounds. Learning characteristics employed by constructive algorithms provide ideas for development of new algorithms applicable to the function approximation problem. In addition, constructive techniques offer efficient methods for network construction and weight determination. The development of a novel neural network algorithm, the Constructive Locally Fit Sigmoids (CLFS) function approximation algorithm, is presented in detail. Basis functions of global extent (piecewise linear sigmoidal functions) are locally fit to the target function, resulting in a pool of candidate hidden layer nodes from which a function approximation is obtained. This algorithm provides a methodology of selecting nodes in a meaningful way from the infinite set of possibilities and synthesizes an n node single hidden layer network with empirical and analytical results that strongly indicate an O(1/n) mean squared training error bound under certain assumptions. The algorithm operates in polynomial time in the number of network nodes and the input dimension. Empirical results demonstrate its effectiveness on several multidimensional function approximate problems relative to contemporary constructive and nonconstructive algorithms.

Computer-Generated Hologram Compression Research Based on BP Neural Network in Wavelet Domain

2014 ◽  
Vol 971-973 ◽  
pp. 1884-1887 ◽  
Author(s):  
A Lin Hou ◽  
Liang Wu ◽  
Qing Liao ◽  
Chong Jin Wang ◽  
Jun Liang Guo ◽  
...  
Keyword(s):  
Neural Network ◽  
Feature Extraction ◽  
Bp Neural Network ◽  
Function Approximation ◽  
Simple Structure ◽  
Inner Product ◽  
Compression Rate ◽  
Wavelet Domain ◽  
Fast Calculation ◽  
Computer Generated Hologram

The algorithm of hologram compression using BP neural network in wavelet domain is proposed. Firstly, computer-generated hologram pretreatment is carried out by wavelet transform. And then the inner product of wavelet and holograms are weighted and used to implement the feature extraction of hologram. Finally, the extracted feature vectors are substituted into neural network so as to implement the function approximation, classification and hologram compression. The experimental results clearly show the feasibility and effectiveness of the method. The compression rate can reach 0.803%and still gets a clear reconstructed image. And the algorithm has the advantages of simple structure and fast calculation speed.

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