Training Multilayer Perceptrons Via Minimization of Sum of Ridge Functions |
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Authors: | Wei Wu Guorui Feng Xin Li |
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Institution: | (1) Department of Applied Mathematics, Dalian University of Technology, Dalian, 116023, P.R. China;(2) Department of Mathematical Sciences, University of Nevada, Las Vegas, NV 89154-4020, USA |
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Abstract: | Motivated by the problem of training multilayer perceptrons in neural networks, we consider the problem of minimizing E(x)=
i=1
n
f
i
(
i
x), where
i
R
s
, 1in, and each f
i
(
i
x) is a ridge function. We show that when n is small the problem of minimizing E can be treated as one of minimizing univariate functions, and we use the gradient algorithms for minimizing E when n is moderately large. For large n, we present the online gradient algorithms and especially show the monotonicity and weak convergence of the algorithms. |
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Keywords: | multilayer perceptrons online gradient algorithms ridge functions |
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