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• A novel unsupervised feature selection method is proposed which aims at preserving the local invariance of feature subspace by local linear embedding and manifold regularization simultaneously. • An alternating algorithm based on alternative direction method of multiplier s with computational complexity analysis is designed to handle the resulting optimization problem. • A variety of experiments on several publicly available real world datasets are conducted to demonstrate the effectiveness and superiority of the proposed method. As one of the important dimensionality reduction techniques, unsupervised feature selection (UFS) has enjoyed amounts of popularity over the last few decades, which can not only improve learning performance, but also enhance interpretability and reduce computational costs. The existing UFS methods often model the data in the original feature space, which cannot fully exploit the discriminative information. In this paper, to address this issue, we investigate how to strengthen the relationship between UFS and the feature subspace, so as to select relevant features more straightforwardly and effectively. Methodologically, a novel UFS approach, referred to as Graph Regularized Local Linear Embedding (GLLE), is proposed by integrating local linear embedding (LLE) and manifold regularization constrained in feature subspace into a unified framework. To be more specific, we explicitly define a feature selection matrix composed of 0 and 1, which can realize the process of UFS. For the purpose of modelling the feature selection matrix, we propose to preserve the local linear reconstruction relationship among neighboring data points in the feature subspace, which corresponds to LLE constrained in the feature subspace. To make the feature selection matrix more accurate, we propose to use manifold regularization as an assistant of LLE to find the relevant and representative features such that the selected features can make each sample under the feature subspace be accordance with the manifold assumption. A tailored iterative algorithm based on Alternative Direction Method of Multipliers (ADMM) is designed to solve the proposed optimization problem. Extensive experiments on twelve real-world benchmark datasets are conducted, and the more promising results are achieved compared with the state-of-the-arts approaches. [ABSTRACT FROM AUTHOR]

• Presenting a new multi-label feature selection method that efficiently combines manifold regularization and dependence maximization. • Introducing a HSIC-based measurement to evaluate the dependence between the manifold space and label space. • Developing an iterative optimization method to solve the objective function of our method MRDM with good convergence. • Conducting extensive experiments on various multi-label data sets to demonstrate the superiority of the proposed method. Feature selection is able to select more discriminative features for classification and plays an important role in multi-label learning to alleviate the effect of the curse of dimensionality. Recently, the multi-label feature selection methods based on the sparse regression model have received increasing attentions. However, most of these methods directly project original data space to label space in the regression model, which is inappropriate because the linear assumption between data space and label space doesn't hold in most cases. In the paper, we propose a feature selection method named multi-label feature selection via manifold regularization and dependence maximization (MRDM). In the regression model of MRDM, the original data space is projected to a low-dimensional manifold space, which not only has the same topological structure with the original data, but also has a strong dependence with the class labels. Then, an objective function involving l 2 , 1 -norm regularization is formulated, and an alternating optimization-based iterative algorithm is designed to obtain the sparse coefficients for multi-label feature selection. Extensive experiments on various multi-label data sets demonstrate the superiority of the proposed method compared with some state-of-the-art multi-label feature selection methods. [ABSTRACT FROM AUTHOR]