Robust structure-preservation tensorized representation for multi-view unsupervised feature selection

The self-representation methods leverage the linear reconstructability of data points within the same subspace to construct high-quality affinity matrices, showing great potential for improving the performance of multi-view unsupervised feature selection (MUFS). However, existing methods still face some critical challenges. (1) These affinity matrices are inevitably affected by noise in the original data. (2) Enforcing forced non-negativity constraints during their construction may distort the inherent relationships among data points. (3) The optimal structure of the view is not fully exploited. To address these challenges, we propose a novel robust structure-preservation tensorized representation (RSTR) method for MUFS. Specifically, RSTR decomposes each affinity matrix into a clean component and a noise component to mitigate the influence of noise in the original data. Then, the scaled simplex constraint is introduced to ensure the clean affinity matrix more physically meaningful and facilitates the flexible discovery of inherent structures. Moreover, the rank constraint is imposed to identify the optimal structure of each view. Finally, a weighted tensor is constructed from these clean affinity matrices to mine high-order relationships across views. Extensive experiments conducted on eight datasets demonstrate the superiority of RSTR over various state-of-the-art competitors.