Clean affinity matrix induced hyper-Laplacian regularization for unsupervised multi-view feature selection

Most previous unsupervised multi-view feature selection (UMFS) methods have achieved appealing performance by exploring the consistency among multiple views. However, they have the following shortcomings: (1) They often fail to consider the potential inconsistency that might be caused by view-specific characteristics from the perspective of sparsity. (2) The previously learned hyper-graph might be affected by noise, thereby reducing the quality of the generated graph. To tackle these issues, this paper proposes a clean affinity matrix induced hyper-Laplacian regularization (CAHR) method for UMFS. Firstly, the initial affinity matrix is decomposed into the consistent and inconsistent parts, then a novel diversity penalty term is introduced to enforce the sparsity of the inconsistent part across views, thereby making the consistent part be cleaner. Secondly, a unified affinity matrix is generated by fusing the consistent factors of the initial affinity matrix in a self-weighted manner, thereby considering the consistency of multi-view data. Based on the unified affinity matrix, a hyper-Laplacian matrix is further constructed, which can maintain high-order manifold structure of data. Finally, a loss function is designed to find the best mapping for feature selection. Comprehensive experiments demonstrate that the proposed method significantly outperforms several state-of-the-art UMFS methods.