TIME-FS: Joint Learning of Tensorial Incomplete Multi-View Unsupervised Feature Selection and Missing-View Imputation

Multi-view unsupervised feature selection (MUFS) has received considerable attention in recent years. Existing MUFS methods for processing unlabeled incomplete multi-view data, where some samples are missing in certain views, first impute the missing values and then perform feature selection on the completed dataset. However, treating imputation and feature selection as two separate processes overlooks their potential interactions. The graph-guided local structure gleaned from feature selection can aid in imputation, which in turn can enhance the feature selection performance. Additionally, most similarity graph-based MUFS methods suffer from high computational costs. To address these problems, we propose a novel MUFS method, termed Tensorial Incomplete Multi-view unsupErvised Feature Selection (TIME-FS). TIME-FS unifies missing value recovery, discriminative feature selection, and low-dimensional representation learning within a joint framework through matrix decomposition. Then, TIME-FS conducts CP decomposition on tensor data formed by the low-dimensional representations of different views to learn a consistent anchor graph across views and a view-preference weight matrix, both of which simultaneously guide missing view imputation and feature selection. Furthermore, an efficient algorithm with low time complexity and rapid convergence is proposed to solve TIME-FS. Extensive experimental results demonstrate the effectiveness and efficiency of TIME-FS over state-of-the-art methods.