Fast and Efficient Second-Order Method for Training Radial Basis Function Networks

This paper proposes an improved second order (ISO) algorithm for training radial basis function (RBF) networks. Besides the traditional parameters, including centers, widths and output weights, the input weights on the connections between input layer and hidden layer are also adjusted during the tra...

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Veröffentlicht in:	IEEE transaction on neural networks and learning systems Jg. 23; H. 4; S. 609 - 619
Hauptverfasser:	Tiantian Xie, Hao Yu, Hewlett, J., Rozycki, P., Wilamowski, B.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York, NY IEEE 01.04.2012 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithm design and analysis Algorithms Applied sciences Artificial intelligence Computation Computer science; control theory; systems Connectionism. Neural networks Exact sciences and technology ISO Jacobian matrices Levenberg-Marquardt algorithm Mathematical analysis Multiplication Networks Neural networks Radial basis function Radial basis function networks second order algorithm Software algorithms Studies Training Vectors Vectors (mathematics) Input output Matrix product Neural network Jacobi matrix Radial basis function Levenberg Marquardt algorithm Classification Matrix calculus radial basis function networks second order algorithm ISO standard Hessian matrices Levenberg-Marquardt algorithm
ISSN:	2162-237X, 2162-2388
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Abstract	This paper proposes an improved second order (ISO) algorithm for training radial basis function (RBF) networks. Besides the traditional parameters, including centers, widths and output weights, the input weights on the connections between input layer and hidden layer are also adjusted during the training process. More accurate results can be obtained by increasing variable dimensions. Initial centers are chosen from training patterns and other parameters are generated randomly in limited range. Taking the advantages of fast convergence and powerful search ability of second order algorithms, the proposed ISO algorithm can normally reach smaller training/testing error with much less number of RBF units. During the computation process, quasi Hessian matrix and gradient vector are accumulated as the sum of related sub matrices and vectors, respectively. Only one Jacobian row is stored and used for multiplication, instead of the entire Jacobian matrix storage and multiplication. Memory reduction benefits the computation speed and allows the training of problems with basically unlimited number of patterns. Several practical discrete and continuous classification problems are applied to test the properties of the proposed ISO training algorithm.
AbstractList	This paper proposes an improved second order (ISO) algorithm for training radial basis function (RBF) networks. Besides the traditional parameters, including centers, widths and output weights, the input weights on the connections between input layer and hidden layer are also adjusted during the training process. More accurate results can be obtained by increasing variable dimensions. Initial centers are chosen from training patterns and other parameters are generated randomly in limited range. Taking the advantages of fast convergence and powerful search ability of second order algorithms, the proposed ISO algorithm can normally reach smaller training/testing error with much less number of RBF units. During the computation process, quasi Hessian matrix and gradient vector are accumulated as the sum of related sub matrices and vectors, respectively. Only one Jacobian row is stored and used for multiplication, instead of the entire Jacobian matrix storage and multiplication. Memory reduction benefits the computation speed and allows the training of problems with basically unlimited number of patterns. Several practical discrete and continuous classification problems are applied to test the properties of the proposed ISO training algorithm.This paper proposes an improved second order (ISO) algorithm for training radial basis function (RBF) networks. Besides the traditional parameters, including centers, widths and output weights, the input weights on the connections between input layer and hidden layer are also adjusted during the training process. More accurate results can be obtained by increasing variable dimensions. Initial centers are chosen from training patterns and other parameters are generated randomly in limited range. Taking the advantages of fast convergence and powerful search ability of second order algorithms, the proposed ISO algorithm can normally reach smaller training/testing error with much less number of RBF units. During the computation process, quasi Hessian matrix and gradient vector are accumulated as the sum of related sub matrices and vectors, respectively. Only one Jacobian row is stored and used for multiplication, instead of the entire Jacobian matrix storage and multiplication. Memory reduction benefits the computation speed and allows the training of problems with basically unlimited number of patterns. Several practical discrete and continuous classification problems are applied to test the properties of the proposed ISO training algorithm. This paper proposes an improved second order (ISO) algorithm for training radial basis function (RBF) networks. Besides the traditional parameters, including centers, widths and output weights, the input weights on the connections between input layer and hidden layer are also adjusted during the training process. More accurate results can be obtained by increasing variable dimensions. Initial centers are chosen from training patterns and other parameters are generated randomly in limited range. Taking the advantages of fast convergence and powerful search ability of second order algorithms, the proposed ISO algorithm can normally reach smaller training/testing error with much less number of RBF units. During the computation process, quasi Hessian matrix and gradient vector are accumulated as the sum of related sub matrices and vectors, respectively. Only one Jacobian row is stored and used for multiplication, instead of the entire Jacobian matrix storage and multiplication. Memory reduction benefits the computation speed and allows the training of problems with basically unlimited number of patterns. Several practical discrete and continuous classification problems are applied to test the properties of the proposed ISO training algorithm.
Author	Hao Yu Wilamowski, B. Hewlett, J. Tiantian Xie Rozycki, P.
Author_xml	– sequence: 1 surname: Tiantian Xie fullname: Tiantian Xie email: tzx0004@tigermail.auburn.edu organization: Dept. of Electr. & Comput. Eng., Auburn Univ., Auburn, AL, USA – sequence: 2 surname: Hao Yu fullname: Hao Yu email: hzy0004@tigermail.auburn.edu organization: Dept. of Electr. & Comput. Eng., Auburn Univ., Auburn, AL, USA – sequence: 3 givenname: J. surname: Hewlett fullname: Hewlett, J. email: jhewlett@uidaho.edu organization: Dept. of Electr. & Comput. Eng., Auburn Univ., Auburn, AL, USA – sequence: 4 givenname: P. surname: Rozycki fullname: Rozycki, P. email: prozycki@wsiz.rzeszow.pl organization: Univ. of Inf. Technol. & Manage., Rzeszow, Poland – sequence: 5 givenname: B. surname: Wilamowski fullname: Wilamowski, B. email: wilam@ieee.org organization: Dept. of Electr. & Comput. Eng., Auburn Univ., Auburn, AL, USA
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References	ref13 ref12 ref15 ref14 blake (ref31) 1998 ref30 ref11 powell (ref2) 1985 ref32 ref10 ref1 ref17 ref16 ref19 ref18 lee (ref7) 2010; 19 ref24 ref23 ref26 cai (ref9) 2010; 57 ref25 ref20 ref22 ref21 ref28 ref27 ref29 ref8 ref4 ref3 ref6 ref5
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SubjectTerms	Algorithm design and analysis Algorithms Applied sciences Artificial intelligence Computation Computer science; control theory; systems Connectionism. Neural networks Exact sciences and technology ISO Jacobian matrices Levenberg-Marquardt algorithm Mathematical analysis Multiplication Networks Neural networks Radial basis function Radial basis function networks second order algorithm Software algorithms Studies Training Vectors Vectors (mathematics)
Title	Fast and Efficient Second-Order Method for Training Radial Basis Function Networks
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