Functional Extreme Learning Machine

Extreme learning machine(ELM)has been widely used in many fields because of its high learning accuracy,easy to use and fast training speed,and has become a research hotspot in the field of artificial neural network.Although the research has made great progress,the ELM theory still exists:(1)The number of hidden layer neurons of ELM cannot be obtained by an effective algorithm.(2)ELM has randomly given left weights and hidden layer thresholds,which makes the model prone to problems such as low generalization performance and unsatisfactory stability,which greatly limits the application range of ELM.In view of some shortcomings of the above ELM theory,the results of this paper are as follows:(1)Based on the functional neuron(FN)model,a new functional extreme learning machine(FELM)theory is proposed by using the functional equation solving theory to guide the modeling process of functional extreme learning machine.The functional neurons of the learning machine are not fixed and learnable.They are usually linear combinations of any linearly independent basic functions.There are coefficients in the linear combination,and the network parameters are composed of the coefficients of each neuron.Unlike ELM,FELM has neither biases nor weights in the connection between neurons,so it achieves the purpose of network learning by adjusting the coefficients of the basic functions in neurons.(2)The FELM uses the functional equation solving theory to simplify its model.The simplified model is equivalent to the initial model,and the number of neurons in the model is determined.There is no need to find the optimal number of hidden layer nodes according to the problem to be solved.The learning machine has no random parameters,and its network parameters are obtained without iteration.Two fast parameter learning algorithms are proposed,which are simple,no iteration and high precision.One is based on the generalized inverse theory of matrix,and the other is based on linear equations.(3)The selection of the basic functions in the FELM neuron functions are based on human experience.If the selection is improper,the generalization ability and stability of the network will be greatly affected.A parameter reduction method is proposed to quickly improve the generalization ability and stability of the network.