Multi-view unsupervised feature selection (MUFS), which selects informative features from multi-view unlabeled data, has attracted increasing research interest in recent years. Although great efforts have been devoted to MUFS, several challenges remain: 1) existing methods for incomplete multi-view data are limited to handling missing views and are unable to address the more general scenario of missing variables, where some features have missing values in certain views; 2) most methods address incomplete data by first imputing missing values and then performing feature selection, treating these two processes independently and overlooking their interactions; 3) missing data can result in an inaccurate similarity graph, which reduces the performance of feature selection. To solve this dilemma, we propose a novel MUFS method for incomplete multi-view data with missing variables, termed Tensorized Reliable UnSupervised mulTi-view Feature Selection (TRUST-FS). TRUST-FS introduces a new adaptive-weighted CP decomposition that simultaneously performs feature selection, missing-variable imputation, and view weight learning within a unified tensor factorization framework. By utilizing Subjective Logic to acquire trustworthy cross-view similarity information, TRUST-FS facilitates learning a reliable similarity graph, which subsequently guides feature selection and imputation. Comprehensive experimental results demonstrate the effectiveness and superiority of our method over state-of-the-art methods.

Feature selection, which is a technique to select key features in recommender systems, has received increasing research attention. Recently, Adaptive Feature Selection (AdaFS) has shown remarkable performance by adaptively selecting features for each data instance, considering that the importance of a given feature field can vary significantly across data. However, this method still has limitations in that its selection process could be easily biased to major features that frequently occur. To address these problems, we propose Multi-view Feature Selection (MvFS), which selects informative features for each instance more effectively. Most importantly, MvFS employs a multi-view network consisting of multiple sub-networks, each of which learns to measure the feature importance of a part of data with different feature patterns. By doing so, MvFS mitigates the bias problem towards dominant patterns and promotes a more balanced feature selection process. Moreover, MvFS adopts an effective importance score modeling strategy which is applied independently to each field without incurring dependency among features. Experimental results on real-world datasets demonstrate the effectiveness of MvFS compared to state-of-the-art baselines.

Despite significant progress, previous multi-view unsupervised feature selection methods mostly suffer from two limitations. First, they generally utilize either cluster structure or similarity structure to guide the feature selection, which neglect the possibility of a joint formulation with mutual benefits. Second, they often learn the similarity structure by either global structure learning or local structure learning, which lack the capability of graph learning with both global and local structural awareness. In light of this, this paper presents a joint multi-view unsupervised feature selection and graph learning (JMVFG) approach. Particularly, we formulate the multi-view feature selection with orthogonal decomposition, where each target matrix is decomposed into a view-specific basis matrix and a view-consistent cluster indicator. The cross-space locality preservation is incorporated to bridge the cluster structure learning in the projected space and the similarity learning (i.e., graph learning) in the original space. Further, a unified objective function is presented to enable the simultaneous learning of the cluster structure, the global and local similarity structures, and the multi-view consistency and inconsistency, upon which an alternating optimization algorithm is developed with theoretically proved convergence. Extensive experiments on a variety of real-world multi-view datasets demonstrate the superiority of our approach for both the multi-view feature selection and graph learning tasks. The code is available at https://github.com/huangdonghere/JMVFG.

In this paper, we focus on the unsupervised multi-view feature selection which tries to handle high dimensional data in the field of multi-view learning. Although some graph-based methods have achieved satisfactory performance, they ignore the underlying data structure across different views. Besides, their pre-defined laplacian graphs are sensitive to the noises in the original data space, and fail to get the optimal neighbor assignment. To address the above problems, we propose a novel unsupervised multi-view feature selection model based on graph learning, and the contributions are threefold: (1) during the feature selection procedure, the consensus similarity graph shared by different views is learned. Therefore, the proposed model can reveal the data relationship from the feature subset. (2) a reasonable rank constraint is added to optimize the similarity matrix to obtain more accurate information; (3) an auto-weighted framework is presented to assign view weights adaptively, and an effective alternative iterative algorithm is proposed to optimize the problem. Experiments on various datasets demonstrate the superiority of the proposed method compared with the state-of-the-art methods.

Data integration methods that analyze multiple sources of data simultaneously can often provide more holistic insights than can separate inquiries of each data source. Motivated by the advantages of data integration in the era of "big data", we investigate feature selection for high-dimensional multi-view data with mixed data types (e.g. continuous, binary, count-valued). This heterogeneity of multi-view data poses numerous challenges for existing feature selection methods. However, after critically examining these issues through empirical and theoretically-guided lenses, we develop a practical solution, the Block Randomized Adaptive Iterative Lasso (B-RAIL), which combines the strengths of the randomized Lasso, adaptive weighting schemes, and stability selection. B-RAIL serves as a versatile data integration method for sparse regression and graph selection, and we demonstrate the effectiveness of B-RAIL through extensive simulations and a case study to infer the ovarian cancer gene regulatory network. In this case study, B-RAIL successfully identifies well-known biomarkers associated with ovarian cancer and hints at novel candidates for future ovarian cancer research.