关键词: 多输出回归, 低秩回归, 回归系数矩阵, 特征选择

Abstract: To solve the issue of the existing regression models do not well take advantage of the correlation between inputs and outputs, and among outputs, also between samples, to take the multiple output regression analysis for high-dimensional data, it proposes a novel multiple output regression method called Low-rank Feature Selection for Multiple-output Regression algorithm（for short LFS_MR）. The method can catch the correlation structures of outputs via a low-rank regression model with a low-rank constraint. Specially, it is innovative that the method conducts sample selection via an [L2,p]-norm on this low-rank regression model, which can avoid the interference of noise and outliers reasonably. What’s more, the method conducts feature selection by applying an [L2,p]-norm regularization term to penalty the regression coefficient matrix, which handles with the correlations between inputs and outputs efficiently, and solves the problem of curse of dimensionality for the high-dimensional data. The experimental results on many realistic datasets show that the proposed method can obtain very good results when conduct a multiple output regression analysis for high-dimensional data.

Key words: multiple-output regression, low-rank regression, regression coefficient matrix, feature selection