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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]

Semisupervised band selection (BS) technique plays an important role in processing hyperspectral images (HSIs) because of its superiority of using the limited labeled data and plentiful unlabeled data to select the discriminative and informative feature, which copes with the problem of high-dimensional and scare labeled samples of HSIs. Among semisupervised BS models, graph-based methods are superior to others in many situations and have received more and more attention. However, traditional graph-based models construct a similarity matrix and select valuable bands independently. The similarity matrix remains constant, which will damage the local manifold structure and lead to a suboptimal result. To solve this problem, we propose a semisupervised band selection with an optimal graph (BSOG) approach, which performs BS and local structure learning simultaneously. Instead of fixing the input similarity matrix, the similarity matrix is updated constantly to learn a better local structure. Besides, the learned similarity matrix is adaptive. Then, the optimal band subset can be selected by analyzing the obtained projection matrix $\boldsymbol W$. An efficient and simple optimization algorithm is proposed to solve this model. Experiments on four real HSIs data validate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Linear discriminant analysis (LDA) is one of commonly used supervised subspace learning methods. However, LDA will be powerless faced with the no-label situation. In this paper, the unsupervised LDA (Un-LDA) is proposed and first formulated as a seamlessly unified objective optimization which guarantees convergence during the iteratively alternative solving process. The objective optimization is in both the ratio trace and the trace ratio forms, forming a complete framework of a new approach to jointly clustering and unsupervised subspace learning. The extension of LDA into Un-LDA enables to not only complete unsupervised subspace learning via the explicitly presented subspace projection matrix but also simultaneously finish clustering and even clustering out-of-sample data via the explicitly presented transformation matrix. To overcome the difficulty in solving the non-convex objective optimization, we mathematically prove that the Un-LDA optimization in both forms can be transformed into the simple K-means clustering optimization when the subspace is determined. The Un-LDA optimization is eventually completed by alternatively optimizing the clusters using K-means and the subspace using the supervised LDA methods and iterating this whole process until convergence or stopping criterion. The experiments demonstrate that our proposed Un-LDA algorithms are comparable or even much superior to the counterparts. [ABSTRACT FROM AUTHOR]

Semi-supervised learning models for multiview data are important in image classification tasks, since heterogeneous features are easy to obtain and semi-supervised schemes are economical and effective. To model the view importance, conventional graph-based multiview learning models learn a linear combination of views while assuming a priori weights distribution. In this paper, we present a novel structural regularized semi-supervised model for multiview data, termed Adaptive MUltiview SEmi-supervised model (AMUSE). Our new model learns weights from a priori graph structure, which is more reasonable than weight regularization. Theoretical analysis reveals the significant difference between AMUSE and the prior arts. An efficient optimization algorithm is provided to solve the new model. Experimental results on six real-world data sets demonstrate the effectiveness of the structural regularized weights learning scheme. [ABSTRACT FROM AUTHOR]