A novel regression method: Partial least distance square regression methodology

Abstract

Partial Least Squares (PLS) is a multivariate linear statistical analysis method integrating principal component analysis (PCA), canonical correlation analysis (CCA), and multiple linear regression (MLR) analysis. It can effectively solve the problems of multiple correlation between variables and small sample size. However, PLS also has some imperfections, on the one hand, PLS extracts the latent variables based on the maximization of Pearson correlation coefficient of independent and dependent variables. Here, Pearson correlation coefficient usually cannot measure the nonlinear relationship between variables, so the latent variables cannot ensure the strongest interpretation. On the other hand, PLS applies MLR to the extracted latent variables, which cannot truly reflect the nonlinear relationship of data, so the regression function is usually under-fitting. The above two imperfect designs are the main reasons for the low regression accuracy and prediction performance of PLS for nonlinear data. According to the above problems, this paper proposes a Partial Least Distance Square (PLDS) regression method. PLDS reflects the original data information through distance variance in PCA, employs distance correlation coefficient to measure the correlation between independent and dependent variables in CCA, and performs quasilinear regression and model solution method to obtain the final regression equation in MLR. In order to verify the effectiveness of the proposed method, the UCI datasets and Chinese medicine datasets with dose-effect relationship was used to compare the new method with other classical regression methods. Finally, the experimental results show that PLSD has better prediction performance regardless of whether there is significant nonlinear relationship between variables. In addition, PLDS has high regression accuracy and low computation complexity for high-dimensional and small-sample data.