The regularization feature selection algorithm is not effective in reducing the impact of noisy data. Moreover, the local structure of the sample space is hardly considered. After the samples are mapped to the feature subspace, the relationship between samples is inconsistent with the original space, resulting in unsatisfactory results of the data mining algorithm. This study proposes an anti-noise feature selection method that can effectively solve these two shortcomings of traditional algorithms. This method first uses a self-paced learning training method, which not only greatly reduces the possibility of outliers entering training, but also facilitates the rapid convergence of the model. Then, a regression learner with regular terms is used to select the embedded features, taking into account the "sparse solution" and "solving over-fitting" to make the model more robust. Finally, the technique of locality preserving projections is integrated, and its projection matrix is transformed into the regression parameter matrix of the model, while maintaining the original local structure between the samples while selecting the features. Some experiments are conducted for evaluating the algorithm with a series of benchmark data sets. Experimental results show the effectiveness of the proposed algorithm in term of the aCC and aRMSE.