Abstract: In order to solve the limitation of traditional feature selection methods for incomplete data, a feature selection method based on auxiliary variable near gradient algorithm is proposed. The missing information was filtered by using the index matrix in the feature selection process, and the outliers with small or even zero weights and important samples with large weights were automatically allocated by using the auxiliary variable near end gradient algorithm to reduce the impact of outliers. Furthermore, an optimization strategy was designed to optimize the proposed objective function, and the convergence of the proposed optimization strategy was proved theoretically and experimentally. The experimental results on real data sets and synthetic incomplete data sets verify the clustering performance of this method in the low dimensional space of high-dimensional data.