This paper studies approximation capability to L^2（Rd） functions of incremental constructive feedforward neural networks （FNN） with random hidden units. Two kinds of therelayered feedforward neural networks are co...This paper studies approximation capability to L^2（Rd） functions of incremental constructive feedforward neural networks （FNN） with random hidden units. Two kinds of therelayered feedforward neural networks are considered： radial basis function （RBF） neural networks and translation and dilation invariant （TDI） neural networks. In comparison with conventional methods that existence approach is mainly used in approximation theories for neural networks, we follow a constructive approach to prove that one may simply randomly choose parameters of hidden units and then adjust the weights between the hidden units and the output unit to make the neural network approximate any function in L2 （Rd） to any accuracy. Our result shows given any non-zero activation function g ： R＋ → R and g（｜｜x｜｜R^d） ∈ L^2（Rd） for RBF hidden units, or any non-zero activation function g（x） ∈ L^2（R^d） for TDI hidden units, the incremental network function fn with randomly generated hidden units converges to any target function in L2 （R^d） with probability one as the number of hidden units n → ∞, if one only properly adjusts the weights between the hidden units and output unit.展开更多
相比于传统的基于梯度的前馈神经网络,随机前馈神经网络具有更好的逼近能力和泛化学习能力,被广泛用于分类等问题中,然而其网络参数完全随机,在实际应用中存在性能不稳定、不可靠的隐患。为此,基于人类学习优化算法提出了一种改进的选...相比于传统的基于梯度的前馈神经网络,随机前馈神经网络具有更好的逼近能力和泛化学习能力,被广泛用于分类等问题中,然而其网络参数完全随机,在实际应用中存在性能不稳定、不可靠的隐患。为此,基于人类学习优化算法提出了一种改进的选择性进化随机网络方法(Improved Selective Evolutionary Random Network,ISERN),协同进行特征选择和网络结构优化以提高网络性能,某远洋船舶海水淡化系统的故障诊断仿真结果表明ISERN方法与其他方法相比具有更好的故障诊断性能,体现出其有效性和优异性。展开更多
基金Supported by the National Nature Science Foundation of China (Grant No10871220)"Mathematics+X" of DLUT (Grant No842328)
文摘This paper studies approximation capability to L^2（Rd） functions of incremental constructive feedforward neural networks （FNN） with random hidden units. Two kinds of therelayered feedforward neural networks are considered： radial basis function （RBF） neural networks and translation and dilation invariant （TDI） neural networks. In comparison with conventional methods that existence approach is mainly used in approximation theories for neural networks, we follow a constructive approach to prove that one may simply randomly choose parameters of hidden units and then adjust the weights between the hidden units and the output unit to make the neural network approximate any function in L2 （Rd） to any accuracy. Our result shows given any non-zero activation function g ： R＋ → R and g（｜｜x｜｜R^d） ∈ L^2（Rd） for RBF hidden units, or any non-zero activation function g（x） ∈ L^2（R^d） for TDI hidden units, the incremental network function fn with randomly generated hidden units converges to any target function in L2 （R^d） with probability one as the number of hidden units n → ∞, if one only properly adjusts the weights between the hidden units and output unit.
文摘相比于传统的基于梯度的前馈神经网络,随机前馈神经网络具有更好的逼近能力和泛化学习能力,被广泛用于分类等问题中,然而其网络参数完全随机,在实际应用中存在性能不稳定、不可靠的隐患。为此,基于人类学习优化算法提出了一种改进的选择性进化随机网络方法(Improved Selective Evolutionary Random Network,ISERN),协同进行特征选择和网络结构优化以提高网络性能,某远洋船舶海水淡化系统的故障诊断仿真结果表明ISERN方法与其他方法相比具有更好的故障诊断性能,体现出其有效性和优异性。
