Joint Adaptive Graph Learning and Discriminative Analysis for Unsupervised Feature Selection

Unsupervised feature selection plays a dominant role in the process of high-dimensional and unlabeled data. Conventional spectral-based unsupervised feature selection methods always learn the subspace based on the predefined graph which constructed by the original features. Therefore, if the data is corrupted by the noise or redundancy existing in the high-dimensional, then the graph will be incorrect and further degrade the performance of downstream tasks. In this paper, we propose a new unsupervised feature selection method, in which the graph is self-adjusting by the original graph and learned subspace, so as to be the optimal one. Besides, the uncorrelated constraint is added to enhance the discriminability of the model. To optimize the model, we propose an alternative iterative algorithm and provide strict convergence proof. Extensive experiments are conducted to evaluate the performance of our method in comparison with other SOTA methods. The proposed adaptive graph learning strategy can learn a high-quality graph with the information of data structure more accurate. Besides, the uncorrelated constraint extremely ensures the discriminability of selected features.