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In this article, we focus on the unsupervised multiview feature selection, which tries to handle high-dimensional data in the field of multiview learning. Although some graph-based methods have achieved satisfactory performance, they ignore the underlying data structure across different views. Besides, their predefined Laplacian graphs are sensitive to the noises in the original data space and fail to obtain the optimal neighbor assignment. To address the above problems, we propose a novel unsupervised multiview feature selection model based on graph learning, and the contributions are three-fold: 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; and 3) an autoweighted 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 to the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Unsupervised feature selection (UFS) aims to remove the redundant information and select the most representative feature subset from the original data, so it occupies a core position for high-dimensional data preprocessing. Many proposed approaches use self-expression to explore the correlation between the data samples or use pseudolabel matrix learning to learn the mapping between the data and labels. Furthermore, the existing methods have tried to add constraints to either of these two modules to reduce the redundancy, but no prior literature embeds them into a joint model to select the most representative features by the computed top ranking scores. To address the aforementioned issue, this article presents a novel UFS method via a convex non-negative matrix factorization with an adaptive graph constraint (CNAFS). Through convex matrix factorization with adaptive graph constraint, it can dig up the correlation between the data and keep the local manifold structure of the data. To our knowledge, it is the first work that integrates pseudo label matrix learning into the self-expression module and optimizes them simultaneously for the UFS solution. Besides, two different manifold regularizations are constructed for the pseudolabel matrix and the encoding matrix to keep the local geometrical structure. Eventually, extensive experiments on the benchmark datasets are conducted to prove the effectiveness of our method. The source code is available at: https://github.com/misteru/CNAFS. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel feature selection approach via explicitly addressing the long-standing subspace sparsity issue. Leveraging $\ell _{2,1}$ -norm regularization for feature selection is the major strategy in existing methods, which, however, confronts sparsity limitation and parameter-tuning trouble. To circumvent this problem, employing the $\ell _{2,0}$ -norm constraint to improve the sparsity of the model has gained more attention recently whereas, optimizing the subspace sparsity constraint is still an unsolved problem, which only can acquire an approximate solution and without convergence proof. To address the above challenges, we innovatively propose a novel subspace sparsity discriminative feature selection (S2DFS) method which leverages a subspace sparsity constraint to avoid tuning parameters. In addition, the trace ratio formulated objective function extremely ensures the discriminability of selected features. Most important, an efficient iterative optimization algorithm is presented to explicitly solve the proposed problem with a closed-form solution and strict convergence proof. To the best of our knowledge, such an optimization algorithm of solving the subspace sparsity issue is first proposed in this article, and a general formulation of the optimization algorithm is provided for improving the extensibility and portability of our method. Extensive experiments conducted on several high-dimensional text and image datasets demonstrate that the proposed method outperforms related state-of-the-art methods in pattern classification and image retrieval tasks. [ABSTRACT FROM AUTHOR]

Due to the exponential growth of multimedia data, multi-modal hashing as a promising technique to make cross-view retrieval scalable is attracting more and more attention. However, most of the existing multi-modal hashing methods either divide the learning process unnaturally into two separate stages or treat the discrete optimization problem simplistically as a continuous one, which leads to suboptimal results. Recently, a few discrete multi-modal hashing methods that try to address such issues have emerged, but they still ignore several important discrete constraints (such as the balance and decorrelation of hash bits). In this paper, we overcome those limitations by proposing a novel method named “Enhanced Discrete Multi-modal Hashing (EDMH)” which learns binary codes and hashing functions simultaneously from the pairwise similarity matrix of data, under the aforementioned discrete constraints. Although the model of EDMH looks a lot more complex than the other models for multi-modal hashing, we are actually able to develop a fast iterative learning algorithm for it, since the subproblems of its optimization all have closed-form solutions after introducing a couple of auxiliary variables. Our experimental results on three real-world datasets have revealed the usefulness of those previously ignored discrete constraints and demonstrated that EDMH not only performs much better than state-of-the-art competitors according to several retrieval metrics but also runs much faster than most of them. [ABSTRACT FROM AUTHOR]