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Unsupervised feature selection, one of the important dimensionality reduction methods for high-dimensional data, has been paid more and more attention by researchers due to its effectiveness of processing the data without labels. However, most unsupervised feature selection methods do not take into account the fact that real data tends to be mixed with noise or outliers, or only consider the sensitivity of the model to them. In addition, the local manifold structure of data is usually preserved by a simple graph based on fixed k nearest neighbors. On the one hand, the different sample distributions of different data are considered without distinction. On the other hand, simple graph can not well capture the inherent relations between samples when facing multi-modal data. In view of the above problems, a robust unsupervised feature selection algorithm, sparse and minimum-redundant subspace learning with dual regularization (SMRSDR), is proposed in this paper. Specifically, a self-paced learning regularization based on soft weight allocation is introduced into SMRSDR to strictly control the samples' entry into model learning. Normal samples are allowed to enter model learning in order of their importance, while noise or outliers are strictly blocked out of model learning. Besides, considering the difference in sample distribution and the multimodal nature of data, the traditional simple graph Laplacian regularization is replaced by the hypergraph Laplacian regularization based on adaptive nearest neighbors selection. Furthermore, the sparsity and minimum-redundancy constraints are imposed on the subspace learning framework so that the most representative and minimum-redundant features can be selected. Finally, the objective function of SMRSDR is solved by an alternating iterative optimization algorithm. And a series of experiments are performed to comprehensively prove the effectiveness and superiority of SMRSDR. [ABSTRACT FROM AUTHOR]

Existing supervised Multi-Target Feature Selection (MTFS) methods seldom consider the nearest-neighbor relationship and statistical correlation of samples underlying the output space, which leads the result of feature selection to be easily interfered by the output noise, thus making it difficult to achieve satisfactory performance. This paper proposes a novel MTFS method to preserve both the global and local target correlations. Specifically, the low-rank constraint is introduced to achieve multi-layer regression structure to better decouple the inter-input and inter-target relationships. Moreover, the local nearest-neighbor relationships and variable correlations of the sample points in the output space are also explored through adaptive graph and manifold learning, to better utilize the target correlations to improve the MTFS performance. Following the above principle, the resulting objective function and the corresponding optimization algorithm are proposed. Extensive experiments on several public datasets show that the proposed method is superior to other state-of-the-art methods. • A new Embedded MTFS method is proposed to learn the feature redundancy and target correlations in MTR problems. • The nearest-neighbor relationships and target correlations are introduced to achieve superior performance in MTFS tasks. • Extensive experiments on several public datasets show that the proposed method is superior to the compared methods. [ABSTRACT FROM AUTHOR]

In multi-label learning, feature selection is a topical issue for addressing high-dimension data. However, most of existing methods adopt imperfect labels to perform feature selection. Although some graph-based multi-label feature selection methods are proposed to deal with the problem, they adopt the fixed graph Laplacian matrix so that the performances of these models are under-performing. To this end, this paper proposes a Dynamic Subspace dual-graph regularized Multi-label Feature Selection method named DSMFS. DSMFS decomposes the original label space into a low-dimensional subspace, and then both the dynamic label-level subspace graph and the feature-level graph are used to obtain a high-quality label subspace to conduct feature selection process. Seven state-of-the-art methods are compared to the proposed method on twelve multi-label benchmark data sets in the experiments. Experimental results demonstrate the superiority of DSMFS. [ABSTRACT FROM AUTHOR]

Traditional approaches that represent observations in vector or matrix notation easily lead to structure information losses and dependency destruction between elements. Tensors are the generalizations of matrices, providing a natural representation of rich structure in real-world multiway arrays. Although tensor decomposition has been verified and used in classification tasks, the heterogeneity gap among different orders is often neglected. In this paper, we exploited tensor decomposition framework and presented a heterogeneous tensor decomposition for robust classification (HTDRC) approach, which integrates nuclear and ℓ 2 , 1 -norm for intrinsic representation learning. Specifically, to obtain the lowest-rank intrinsic representations of tensorial data from an underlying low-dimensional subspace, HTDRC simultaneously learns a set of orthogonality constrained factor matrices and a low-rank constrained representation matrix. To better guide the decomposition process, a robust discriminant feature selection scheme is utilized by imposing ℓ 2 , 1 -norm penalty on the constructed classification loss and the regularized terms simultaneously. Experiments on four datasets demonstrated the superior performance of our proposed approach. [ABSTRACT FROM AUTHOR]