Projection support vector regression algorithms for data regression

Support vector regression (SVR), which has been successfully applied to a variety of real-world problems, simultaneously minimizes the regularization error and empirical risk with a suitable penalty factor. However, it does not embed any prior information of data into the learning process. In this paper, by introducing a new term to seek a projection axis of data points, we present a novel projection SVR (PSVR) algorithm and its least squares version, i.e., least squares PSVR (LS-PSVR). The projection axis not only minimizes the variance of the projected points, but also maximizes the empirical correlation coefficient between the targets and the projected inputs. The finding of axis can be regarded as the structural information of data points, which makes the proposed algorithms be more robust than SVR. The experimental results on several datasets also confirm this conclusion. The idea in this work not only is helpful in understanding the structural information of data, but also can be extended to other regression models.