Feature selection on incomplete datasets is an exceptionally challenging task. Existing methods address this challenge by first employing imputation methods to complete the incomplete data and then conducting feature selection based on the imputed data. Since imputation and feature selection are entirely independent steps, the importance of features cannot be considered during imputation. However, in real-world scenarios or datasets, different features have varying degrees of importance. To address this, we propose a novel incomplete data feature selection framework that considers feature importance. The framework mainly consists of two alternating iterative stages: the M-stage and the W-stage. In the M-stage, missing values are imputed based on a given feature importance vector and multiple initial imputation results. In the W-stage, an improved reliefF algorithm is employed to learn the feature importance vector based on the imputed data. Specifically, the feature importance vector obtained in the current iteration of the W-stage serves as input for the next iteration of the M-stage. Experimental results on both artificially generated and real incomplete datasets demonstrate that the proposed method outperforms other approaches significantly.
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