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Unsupervised feature selection aims to select a subset from the original features that are most useful for the downstream tasks without external guidance information. While most unsupervised feature selection methods focus on ranking features based on the intrinsic properties of data, most of them do not pay much attention to the relationships between features, which often leads to redundancy among the selected features. In this paper, we propose a two-stage Second-Order unsupervised Feature selection via knowledge contrastive disTillation (SOFT) model that incorporates the second-order covariance matrix with the first-order data matrix for unsupervised feature selection. In the first stage, we learn a sparse attention matrix that can represent second-order relations between features by contrastively distilling the intrinsic structure. In the second stage, we build a relational graph based on the learned attention matrix and perform graph segmentation. To this end, we conduct feature selection by only selecting one feature from each cluster to decrease the feature redundancy. Experimental results on 12 public datasets show that SOFT outperforms classical and recent state-of-the-art methods, which demonstrates the effectiveness of our proposed method. Moreover, we also provide rich in-depth experiments to further explore several key factors of SOFT.