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NEURAL NETWORKS SATISFYING STONEWEIESTRASS THEOREM AND APPROXIMATING SCATTERED DATABYKOHONEN NEURAL NETWORKS
 Date Issued:
 2004
 Abstract/Description:
 Neural networks are an attempt to build computer networks called artificial neurons, which imitate the activities of the human brain. Its origin dates back to 1943 when neurophysiologist Warren Me Cello and logician Walter Pits produced the first artificial neuron. Since then there has been tremendous development of neural networks and their applications to pattern and optical character recognition, speech processing, time series prediction, image processing and scattered data approximation. Since it has been shown that neural nets can approximate all but pathological functions, Neil Cotter considered neural network architecture based on StoneWeierstrass Theorem. Using exponential functions, polynomials, rational functions and Boolean functions one can follow the method given by Cotter to obtain neural networks, which can approximate bounded measurable functions. Another problem of current research in computer graphics is to construct curves and surfaces from scattered spatial points by using BSplines and NURBS or Bezier surfaces. Hoffman and Varady used Kohonen neural networks to construct appropriate grids. This thesis is concerned with two types of neural networks viz. those which satisfy the conditions of the StoneWeierstrass theorem and Kohonen neural networks. We have used selforganizing maps for scattered data approximation. Neural network Tool Box from MATLAB is used to develop the required grids for approximating scattered data in one and two dimensions.
Title:  NEURAL NETWORKS SATISFYING STONEWEIESTRASS THEOREM AND APPROXIMATING SCATTERED DATABYKOHONEN NEURAL NETWORKS. 
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Name(s): 
Thakkar, Pinal, Author Mohapatra, Ram , Committee Chair University of Central Florida, Degree Grantor 

Type of Resource:  text  
Date Issued:  2004  
Publisher:  University of Central Florida  
Language(s):  English  
Abstract/Description:  Neural networks are an attempt to build computer networks called artificial neurons, which imitate the activities of the human brain. Its origin dates back to 1943 when neurophysiologist Warren Me Cello and logician Walter Pits produced the first artificial neuron. Since then there has been tremendous development of neural networks and their applications to pattern and optical character recognition, speech processing, time series prediction, image processing and scattered data approximation. Since it has been shown that neural nets can approximate all but pathological functions, Neil Cotter considered neural network architecture based on StoneWeierstrass Theorem. Using exponential functions, polynomials, rational functions and Boolean functions one can follow the method given by Cotter to obtain neural networks, which can approximate bounded measurable functions. Another problem of current research in computer graphics is to construct curves and surfaces from scattered spatial points by using BSplines and NURBS or Bezier surfaces. Hoffman and Varady used Kohonen neural networks to construct appropriate grids. This thesis is concerned with two types of neural networks viz. those which satisfy the conditions of the StoneWeierstrass theorem and Kohonen neural networks. We have used selforganizing maps for scattered data approximation. Neural network Tool Box from MATLAB is used to develop the required grids for approximating scattered data in one and two dimensions.  
Identifier:  CFE0000226 (IID), ucf:46262 (fedora)  
Note(s): 
20041201 M.S. Arts and Sciences, Department of Mathematics Masters This record was generated from author submitted information. 

Subject(s): 
NEURAL NETWORKS STONEWEIESTRASS THEOREM KOHONEN NEURAL NETWORKS APPROXIMATION OF SCATTERED DATA 

Persistent Link to This Record:  http://purl.flvc.org/ucf/fd/CFE0000226  
Restrictions on Access:  public  
Host Institution:  UCF 