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Training Multilayer Perceptrons Via Minimization of Sum of Ridge Functions
Authors:Wei Wu  Guorui Feng  Xin Li
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
Abstract:Motivated by the problem of training multilayer perceptrons in neural networks, we consider the problem of minimizing E(x)=sum i=1 n f i (xgr i sdotx), where xgr i isinR s , 1leilen, and each f i (xgr i sdotx) 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.
Keywords:multilayer perceptrons  online gradient algorithms  ridge functions
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