网络结构增长的极端学习机算法

Incremental constructive extreme learning machine

针对极端学习机(extreme learning machine,ELM)结构设计问题,基于隐含层激活函数及其导函数提出一种前向神经网络结构增长算法.首先以Sigmoid函数为例给出了一类基函数的派生特性:导函数可以由其原函数表示.其次,利用这种派生特性提出了ELM结构设计方法,该方法自动生成双隐含层前向神经网络,其第1隐含层的结点随机逐一生成.第2隐含层的输出由第1隐含层新添结点的激活函数及其导函数确定,输出层权值由最小二乘法分析获得.最后给出了所提算法收敛性及稳定性的理论证明.对非线性系统辨识及双螺旋分类问题的仿真结果证明了所提算法的有效性.

Focusing on the problem of architectural design of extreme learning machine （ELM）, we propose a novel constructive algorithm by the activation function and its derivatives. Firstly, taking the Sigmoid function as an example, we give in detail the derived characteristics for a class of base functions： derivative functions can be expressed by their primitive functions. By making use of these derived characteristics, we propose a method to design the structure of ELM, which automatically generate feedforward neural networks with double hidden layers. The new units in the first hidden layer are generated randomly one by one; then, the outputs of the second hidden layer （derivation） are calculated by the activation function of the new node in the first layer and its derivatives. The weights of the output layer are calculated analytically by the least squares method. Finally, the analysis of convergence and stability are presented. The effectiveness of the proposed method is demonstrated by simulation results on nonlinear system identification and two-spiral classification problem.