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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]

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]

In this paper, a novel low-rank structural model is proposed for segmenting data drawn from a high-dimensional space. Our method is based on the fact that all groups clustered from a high-dimensional dataset are distributed in multiple low-rank subspaces. In general, it’s a very difficult task to find the low-rank structures hidden in data. Different from the classical sparse subspace clustering (SSC) and low-rank representation (LRR) which all take two steps including building the affinity matrix and spectral clustering, we introduce a new rank constraint into our model. This constraint allows our model to learn a subspace indicator which can capture different clusters directly from the data without any postprocessing. To further approximate the rank constraint, a piecewise function is utilized as the relaxing item for the proposed model. Besides, under the subspace indicator constraints, the integer programming problem is avoided, which makes our algorithm more efficient and scalable. In addition, we prove the convergence of the proposed algorithm in theory and further discuss the general case in which subspaces don’t pass through the origin. Experiment results on both synthetic and real-world datasets demonstrate that our algorithm significantly outperforms the state-of-the-art methods. [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]

Feature selection is one of the most important techniques to deal with the high-dimensional data for a variety of machine learning and data mining tasks, such clustering, classification, and retrieval, etc. Fuzziness is a widespread nature of data in nature human society. However, most existing feature selection methods ignore the existence of fuzziness in the data, resulting in sub-optimal feature subsets. To address the problem, we propose a novel unsupervised feature selection method, called Unsupervised Discriminative Projection for Feature Selection (UDPFS) to select discriminative features by conducting fuzziness learning and sparse learning, simultaneously. Specifically, we use projection matrix transform data as its low-dimensional representation, which are partitioned into clusters by using membership matrix with sparse constraint. In addition, $\ell _{2, 1}$ ℓ 2 , 1 -norm regularization is applied to the projection matrix. Then, a discriminative projection matrix with row sparse is obtained by perform fuzziness learning and sparse learning, simultaneously. An effective alternative optimization algorithm is proposed to solve the objective function. Evaluate experimental results on several real-world datasets show the effectiveness and superiority of the proposed unsupervised feature selection method. [ABSTRACT FROM AUTHOR]

Data clustering, which is to partition the given data into different groups, has attracted much attention. Recently various effective algorithms have been developed to tackle the task. Among these methods, non-negative matrix factorization (NMF) has been demonstrated to be a powerful tool. However, there are still some problems. First, the standard NMF is sensitive to noises and outliers. Although $\ell _{2,1}$ ℓ 2 , 1 norm based NMF improves the robustness, it is still affected easily by large noises. Second, for most graph regularized NMF, the performance highly depends on the initial similarity graph. Third, many graph-based NMF models perform the graph construction and matrix factorization in two separated steps. Thus the learned graph structure may not be optimal. To overcome the above drawbacks, we propose a robust bi-stochastic graph regularized matrix factorization (RBSMF) framework for data clustering. Specifically, we present a general loss function, which is more robust than the commonly used $L_2$ L 2 and $L_1$ L 1 functions. Besides, instead of keeping the graph fixed, we learn an adaptive similarity graph. Furthermore, the graph updating and matrix factorization are processed simultaneously, which can make the learned graph more appropriate for clustering. Extensive experiments have shown the proposed RBSMF outperforms other state-of-the-art methods. [ABSTRACT FROM AUTHOR]