Partial Least Absolute Deviation Regression And Its Application Based On Extreme Learning Mechanism

With the development of modern social science and technology,the scale of the data generated is gradually expanding,whether it is in the daily life of the people or in the modern industrial production process.The direct use of data for analysis and prediction is becoming more and more important.In terms of multivariate data regression modeling,Partial Least Squares Regression(PLSR)has shown good ability,but in some nonlinear systems or links,its effect is not very satisfactory.Therefore,on this basis,someone proposed a partial least absolute deviation algorithm(PLAD)based on the L₁ norm.This method treats the nonlinear characteristic as an uncertain term.But for nonlinear systems that cannot be locally linearized,the reliability of the model obtained by this method is still not high.In response to this problem,based on the PLAD algorithm,the paper introduces a preprocessing step for the non-linear part of the data,and proposes the following two regression modeling methods for non-linear data:1.The partial least absolute deviation algorithm based on incremental extreme learning machine(IELM-PLAD)is proposed,and the data processing process of incremental extreme learning machine is nested into the framework based on partial least absolute deviation algorithm.And the data is expanded.After obtaining new data,the PLAD method is used to model and predict the data and analyze the results.2.The IELM-PLAD algorithm based on hybrid activation function is proposed.In order to enhance the general applicability of the above method,considering the different characteristics of different activation functions in the framework of the extreme learning machine,the mapping effect on the data is also different.The above method is improved,and a hybrid activation function is proposed.Applied to the data processing part,the PLAD method based on the hybrid incremental extreme learning machine is constructed.Through simulation experiments,the results confirm that the model constructed by the proposed method has good predictive ability,and the predictive accuracy is in line with expectations.