Missing Value Imputation Based On TS Modeling With Alternate Learning

Data missing is a common problem that often occurs in many fields,such as experimental research and social investigation,which is almost inevitable.This problem not only increases the difficulty of analysis process,but also declines the accuracy and reliability of analysis results.In recent years,how to fill the missing values reasonably and effectively has attracted a lot of attention in the incomplete data analysis.Aiming at the multiple regression relationships among attributes,Takagi-Sugeno(TS)model is carried out for incomplete data modeling and thus to realize missing value imputation.Moreover,an alternating learning strategy is proposed for training the parameters of incomplete data-based model together with imputations.The method divides the dataset into several fuzzy subsets by an incomplete data clustering algorithm,and establishes rule for each subset to describe the regression relationship between its attributes.During the modeling,it utilizes stepwise regression for selecting significant variables as the input of each rule,so as to enhance the fitting ability of TS model.After the model structure being determined,the method initializes missing values with random numbers and starts the alternate learning of parameters and imputations.In the process of alternate learning,model parameters are adjusted first based on the imputed dataset,so as to obtain the more appropriate model outputs for updating imputations.Conversely,the imputed dataset is returned back to the model for calculating more suitable parameters,and the recalculated parameters are utilized for updating imputations again.If the fitting ability of model no longer changes,the alternating learning ends with the output of the latest updated dataset.In this paper,we propose to make regression analyses for incomplete data on the premise of fuzzy partition and impute missing values dynamically in the process of TS modeling.It not only realizes the full utilization of present values,but also achieves a collaborative improvement of accuracy in missing value imputation and incomplete data modeling.The experiment results demonstrate that TS modeling-based methods are more effective in missing value imputation than traditional regression model-based methods,and the fitting ability of TS model can be enhanced by selecting input variables of each rule with stepwise regression.Furthermore,the imputation performance can be further improved on the basis of above optimized model through the alternate learning of parameters and imputations.