Although Extreme Learning Machine (ELM) can learn thousands of times faster than traditional slow gradient algorithms for training neural networks, ELM fitting accuracy is limited. This paper develops Functional Extreme Learning Machine (FELM), which is a novel regression and classifier. It takes functional neurons as the basic computing units and uses functional equation-solving theory to guide the modeling process of functional extreme learning machines. The functional neuron function of FELM is not fixed, and its learning process refers to the process of estimating or adjusting the coefficients. It follows the spirit of extreme learning and solves the generalized inverse of the hidden layer neuron output matrix through the principle of minimum error, without iterating to obtain the optimal hidden layer coefficients. To verify the performance of the proposed FELM, it is compared with ELM, OP-ELM, SVM and LSSVM on several synthetic datasets, XOR problem, benchmark regression and classification datasets. The experimental results show that although the proposed FELM has the same learning speed as ELM, its generalization performance and stability are better than ELM.
Keywords: extreme learning machine; functional extreme learning machine; functional neurons; parameter learning algorithm.