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Optimal Linear Combinations of Neural Networks
 NEURAL NETWORKS
, 1994
"... Neural network (NN)based modeling often involves trying multiple networks with different architectures and training parameters in order to achieve acceptable model accuracy. Typically, one of the trained NNs is chosen as best, while the rest are discarded. Hashem and Schmeiser [25] proposed using o ..."
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Cited by 155 (2 self)
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optimal linear combinations of a number of trained neural networks instead of using a single best network. Combining the trained networks may help integrate the knowledge acquired by the component networks and thus improve model accuracy. In this paper, we discuss and extend the idea of optimal linear
Linear combinations in vector space
 Journal of Formalized Mathematics
, 1990
"... Summary. The notion of linear combination of vectors is introduced as a function from the carrier of a vector space to the carrier of the field. Definition of linear combination of set of vectors is also presented. We define addition and subtraction of combinations and multiplication of combination ..."
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Cited by 24 (2 self)
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Summary. The notion of linear combination of vectors is introduced as a function from the carrier of a vector space to the carrier of the field. Definition of linear combination of set of vectors is also presented. We define addition and subtraction of combinations and multiplication of combination
Linear combinations in real linear space
 Journal of Formalized Mathematics
, 1990
"... Summary. The article is continuation of [17]. At the beginning we prove some theorems concerning sums of finite sequence of vectors. We introduce the following notions: sum of finite subset of vectors, linear combination, carrier of linear combination, linear combination of elements of a given set o ..."
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Cited by 34 (5 self)
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Summary. The article is continuation of [17]. At the beginning we prove some theorems concerning sums of finite sequence of vectors. We introduce the following notions: sum of finite subset of vectors, linear combination, carrier of linear combination, linear combination of elements of a given set
Sorting of Linear Combinations of Numbers
, 1999
"... We address here the problem of sorting a set of linear combinations of three arrays of numbers. ..."
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We address here the problem of sorting a set of linear combinations of three arrays of numbers.
ON LINEAR COMBINATIONS OF ORTHOGONAL POLYNOMIALS
"... Abstract. In this expository paper, linear combinations of orthogonal polynomials are considered. Properties like orthogonality and interlacing of zeros are presented. ..."
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Abstract. In this expository paper, linear combinations of orthogonal polynomials are considered. Properties like orthogonality and interlacing of zeros are presented.
Optimal Linear Combinations of
 Neural Networks
, 1997
"... Neural networks based modeling often involves trying multiple networks with different architectures and/or training parameters in order to achieve acceptable model accuracy. Typically, one of the trained NNs is chosen as best, while the rest are discarded. Hashem and Schmeiser [1] propose using opti ..."
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Cited by 1 (0 self)
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optimal linear combinations of a number of trained neural networks instead of using a single best network. In this paper, we discuss and extend the idea of optimal linear combinations of neural networks. Optimal linear combinations are constructed by forming weighted sums of the corresponding outputs
On nonlinear functions of linear combinations
 SIAM Journal of Scientific and Statistical Computing, Vol
, 1984
"... Abstract. Projection pursuit algorithms approximate a function of p variables by a sum of nonlinear functions of linear combinations’ (1) f(Xl,’",xp)’ gi(ailxl+"’+aip). i=1 We develop some approximation theory, give a necessary and sufficient condition for equality in (1), and discuss non ..."
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Cited by 42 (0 self)
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Abstract. Projection pursuit algorithms approximate a function of p variables by a sum of nonlinear functions of linear combinations’ (1) f(Xl,’",xp)’ gi(ailxl+"’+aip). i=1 We develop some approximation theory, give a necessary and sufficient condition for equality in (1), and discuss
Linear combinations of orders
, 2009
"... Abstract. This note explores some properties of a notion of linear combination of partial order relations over a given set. A bilinear form is used to represent compatibility of orders, and we study combinations up to equivalence through this form. A precise description of the quotient ..."
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Abstract. This note explores some properties of a notion of linear combination of partial order relations over a given set. A bilinear form is used to represent compatibility of orders, and we study combinations up to equivalence through this form. A precise description of the quotient
Linear Combinations in Real Linear Space
"... Summary. The article is continuation of [14]. At the beginning we prove some theorems concerning sums of finite sequence of vectors. We introduce the following notions: sum of finite subset of vectors, linear combination, carrier of linear combination, linear combination of elements of a given set o ..."
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Summary. The article is continuation of [14]. At the beginning we prove some theorems concerning sums of finite sequence of vectors. We introduce the following notions: sum of finite subset of vectors, linear combination, carrier of linear combination, linear combination of elements of a given set
Projection Pursuit Regression
 Journal of the American Statistical Association
, 1981
"... A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general smooth functions of linear combinations of the predictor variables in an iterative manner. It is more general than standard stepwise and stagewise regression procedures, ..."
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Cited by 550 (6 self)
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A new method for nonparametric multiple regression is presented. The procedure models the regression surface as a sum of general smooth functions of linear combinations of the predictor variables in an iterative manner. It is more general than standard stepwise and stagewise regression procedures
Results 1  10
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27,507