关键词: 最小绝对收缩和选择算子, 变量选择, 最小角回归, 多元线性回归, 加权

Abstract: Least absolute shrinkage and selection operator (Lasso) has performance superiority in dimension reduction of data and anomaly detection. Concerning the problem that the accuracy is low in anomaly detection based on Lasso, a Least Angle Regression (LARS) algorithm based on multi-dimensional weight was proposed. Firstly, the problem was considered that each regression variable had different weight in the regression model. Namely, the importance of the attribute variable was different in the overall evaluation. So, in calculating angular bisector of LARS algorithm, the united correlation of regression variable and residual vector was introduced to distinguish the effect of different attribute variables on detection results. Then, the three weight estimation methods of Principal Component Analysis (PCA), independent weight evaluation and CRiteria Importance Though Intercriteria Correlation (CRITIC) were added into LARS algorithm respectively. The approach direction and approach variable selection in the solution of LARS were further optimized. Finally, the Pima Indians Diabetes dataset was used to prove the optimal property of the proposed algorithm. The experimental results show that, the LARS algorithm based on multi-dimensional weight has a higher accuracy than the traditional LARS under the same constraint condition with smaller threshold value, and can be more suitable for anomaly detection.

Key words: Least absolute shrinkage and selection operator (Lasso), variable selection, Least Angle Regression (LARS), Multiple Linear Regression (MLR), weighting