A variable selection method based on mutual information and variance inflation factor

Feature selection plays a vital role in the quantitative analysis of high-dimensional data to reduce dimensionality. Recently, the variable selection method based on mutual information (MI) has attracted more and more attention in the field of feature selection, where the relevance between the candidate variable and the response is maximized and the redundancy of the selected variables is minimized. However, multicollinearity often is a serious problem in linear models. Collinearity can cause unstable parameter estimation, unreliable models, and weak predictive ability. In order to address this problem, the variance inflation factor (VIF) was introduced for feature selection. Therefore, a variable selection method based on MI combined with VIF was proposed in this paper, called Mutual Information-Variance Inflation Factor (MI-VIF). By calculating the MI between the independent variable and the response variable, the variable with greater MI was selected to maximize the correlation between the independent variable and the response variable. By calculating the VIF between the independent variables, the multicollinearity test was performed. The variables that cause the multicollinearity of the model were eliminated to minimize the collinearity between the independent variables. The proposed method was tested based on two high-dimensional spectral datasets. The regression models (PLSR, MLR) were established based on feature selection through MI-VIF and MI-based methods (MIFS, MMIFS) to compare the prediction accuracy of the models. The results showed that under two datasets, the MI-VIF showed a good prediction performance. Based on the tea dataset, the established MI-VIF-MLR model achieved accuracy with Rp2 of 0.8612 and RMSEP of 0.4096, the MI-VIF-PLSR model achieved accuracy with Rp2 of 0.8614 and RMSEP of 0.4092. Based on the diesel fuels dataset, the established MI-VIF-MLR model achieved accuracy with Rp2 of 0.9707 and RMSEP of 0.6568, the MI-VIF-PLSR model achieved accuracy with Rp2 of 0.9431 and RMSEP of 0.9675. In addition, the MI-VIF was compared with the Successive projections algorithm (SPA), which is a method to reduce the collinearity between variables in the wavelength selection of the near-infrared spectrum. It was found that MI-VIF also had a good predictive effect compared to SPA. It proves that the MI-VIF is an effective variable selection method.