国家自然科学基金地区项目（61563015，61963015， 61863014），国家自然科学基金重点项目（61733005 ），江西省自然科学基金项目（20171ACB21039，20192BAB207024） ，江西省教育厅科技项目（GJJ150552，GJJ170376）
East China Jiaotong University
Since the semi-supervised feature selection based on Laplacian graph has received extensive attention. However, due to the lack of extrapolation ability of the Laplacian operator, the limited labeled data is still not well utilized and is too sensitive to outliers. Therefore, an adaptive loss semi-supervised sparse feature selection algorithm based on Hessian regularization is proposed, named AHFS. Firstly, Hessian is used to preserve the local manifold structure of data for improving the linear mapping capability. Then, adaptive loss is integrated to improve the robustness of the model to data with small or large loss. Moreover, l2,p-norm is leveraged to constrain the prediction matrix, which not only improves the distinguishing degree of features, but also increases the adaptability of the proposed model. Then, a recursive iterative optimization algorithm is proposed to solve the proposed model. Finally, a systematic experiments are carried out through real public data sets, and the model is analyzed from several aspects to verify the effectiveness and superiority of the proposed method.