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Many traditional unsupervised feature selection algorithms utilize manifold information to mine the local structure of the data. However, the noise existing in the raw data reduces the accuracy of the manifold information of data, which affects the learning effect of the entire algorithm. In order to solve the above problems and more fully find the internal structure inside the data, this paper proposes an adaptive graph regularization and self-expression for noise-aware feature selection (ASNFS). Firstly, the algorithm adopts non-negative matrix factorization to decompose the raw data matrix, and utilizes the low-dimensional matrix generated after decomposition to replace the raw high-dimensional data matrix. This allows the algorithm to reveal some internal structural information of the raw data while reducing the dimensionality of the data. ASNFS also introduces the orthogonal basis clustering with excellent clustering effect, and the interpretability of the algorithm is enhanced. Secondly, in addition to preserving the manifold information in the low-dimensional projection subspace, the algorithm also preserves the manifold information in the non-negative matrix factorization subspace. Meanwhile, the adaptive graph regularization term added to the objective function enables the algorithm to continuously update the similarity matrix. It can effectively remove the noise inside the raw data, and prevent the occurrence of over-fitting phenomenon of the experimental results caused by the fixed similarity matrix. Finally, the similarity matrix retains the local structure information of the data with each iteration, and the results of the feature selection are reused for the construction of the similarity matrix. ASNFS adopts an alternate iterative method to optimize the objective function, which is simple and effective. Then, the algorithm complexity and convergence are analyzed. ASNFS is compared with seven feature selection algorithms on nine datasets, and the experimental results reflect the effectiveness of ASNFS in feature selection. [ABSTRACT FROM AUTHOR]

Most of the existing unsupervised feature selection methods learn the cluster structure through spectral clustering, and then use various regression models to introduce the data matrix into the indicator matrix to obtain feature selection matrix. In these methods, the clustering indicator matrix is usually continuous value, which is not the best choice for the matrix in terms of its supervising role in feature selection. Based on this, unsupervised feature selection via discrete spectral clustering and feature weights (FSDSC) is proposed in this paper. First, FSDSC integrates regression model and spectral clustering in a unified framework for feature selection, and introduces a feature weight matrix, which intuitively expresses the importance of each feature with its diagonal elements. Compared with the common feature selection matrix that requires constraints such as sparse regular items, the appearance of the feature weight matrix reduces the complexity of the model and simplifies the calculation process of feature evaluation. Secondly, for the value of the indicators matrix, the spectral clustering is improved to obtain a discrete clustering indicator matrix, which provides clearer guidance information for feature selection. Finally, in order to avoid trivial solutions, the transformation matrix is constrained by orthogonal constraint. The combination of the orthogonal regression model and spectral clustering enables the algorithm to perform feature selection and manifold information learning at the same time, thereby preserving the local geometric structure of data. Compared with other excellent unsupervised feature selection algorithms, the experimental results prove the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

• This paper proposes a new feature selection method called SLMEA. • The sparse transformation and pseudo label matrix are combined to optimize. • The pseudo label matrix is used to guide the learning of low-dimensional space. • The similarity matrix is constructed adaptively. • The constraint of ℓ 2 , 1 / 2 -norm is applied to the matrix. • The SLMEA can have higher clustering accuracy and normalized mutual information. Traditional feature selection algorithms usually explore the relationship between data and cluster structure in a single space, so the internal relationship obtained is not very rich, and it is not enough to select more valuable features. To solve the above problems, in order to fully mine the intrinsic correlation information in different spaces, so that the relationship between data, features and clustering structure can be explored at the same time, this paper proposes a feature selection method based on sparse and low-dimensional representation with maximum entropy adaptive graph (SLMEA). Firstly, the SLMEA combines the sparse transform representation with pseudo-label matrix learning to optimize, and uses the pseudo-label matrix to guide the learning of sparse low-dimensional space. It can not only explore the relationship between data and pseudo-labels in data space, but also mine the association between features and pseudo-labels in feature space, so as to select more discriminative features. Secondly, based on the maximum entropy theory, the similarity matrix is constructed adaptively, so that the two different manifold structures corresponding to sparse transform representation and pseudo label matrix learning can be adaptively learned and retained in the iterative process. In addition, in order to ensure the sparsity of the transformation matrix, the constraint of ℓ 2 , 1 / 2 -norm is applied to the matrix, which can better deal with the redundant features and obtain more sparse solutions. Finally, the SLMEA uses an alternate iterative update method to optimize the objective function, and carries out extensive experiments on eight mainstream datasets. Compared with seven state-of-the-art algorithms, SLMEA can have higher clustering accuracy and normalized mutual information. [ABSTRACT FROM AUTHOR]

• SLREO performs feature selection in the latent representation space, uses latent representation learning to mine the hidden information between data, and retains the interconnection between data. • SLREO generates pseudo-label information through the OLSDA method embedded in a non-negative manifold structure. • The l 2,1 -norm constraint is imposed on the residual matrix of latent representation learning to ensure the robustness of the clustering indicators. • Unifying the latent representation matrix and the clustering index matrix can preserve the dependencies between data and ensure non-negative of pseudo-labels. • Applying uncorrelated constraint and l 2,1 -norm constraint on the feature transformation matrix can avoid excessive suppression of non-zero rows and the appearance of redundant solutions. And more discriminative features can be selected. Modern unsupervised feature selection methods predominantly obtain the cluster structure and pseudo-labels information through spectral clustering. However, the pseudo-labels obtained by spectral clustering are usually mixed between positive and negative. Moreover, the Laplacian matrix in spectral clustering typically affects feature selection. Additionally, spectral clustering does not consider the interconnection information between data. To address these problems, this paper proposes uncorrelated feature selection via sparse latent representation and extended orthogonal least square discriminant analysis (OLSDA), which we term SLREO). Firstly, SLREO retains the interconnection between data by latent representation learning, and preserves the internal information between the data. In order to remove redundant interconnection information, an l 2,1 -norm constraint is applied to the residual matrix of potential representation learning. Secondly, SLREO obtains non-negative pseudo-labels through orthogonal least square discriminant analysis (OLSDA) of embedded non-negative manifold structure. It not only avoids the appearance of negative pseudo-labels, but also eliminates the effect of the Laplacian matrix on feature selection. The manifold information of the data is also preserved. Furthermore, the matrix of the learned latent representation and OLSDA is used as pseudo-labels information. It not only ensures that the generated pseudo-labels are non-negative, but also makes the pseudo-labels closer to the true class labels. Finally, in order to avoid trivial solutions, an uncorrelated constraint and l 2,1 -norm constraint are imposed on the feature transformation matrix. These constraints ensure row sparsity of the feature transformation matrix, select low-redundant and discriminative features, and improve the effect of feature selection. Experimental results show that the Clustering Accuracy (ACC) and Normalized Mutual Information (NMI) of SLREO are significantly improved, as compared with six other published algorithms, tested on 11 benchmark datasets. [ABSTRACT FROM AUTHOR]

• Calculate the similarity between pseudo-labels to keep complete sample information. • The latent representation space is learned in latent feature space and data space. • The latent representation contains the correlation of pseudo-labels. • Latent feature space provides discriminative information to guide feature selection. • Impose non-negative and l 2,1-2 -norm non-convex constraint on Q. In unsupervised feature selection, the relationship between pseudo-labels is often ignored, and the interconnection information between the data is not fully utilized. In order to solve these problems, this paper proposes a feature selection method via non-convex constraint and latent representation learning with Laplacian embedding (NLRL-LE). NLRL-LE keeps the correlation between the pseudo-labels to make the pseudo-label closer to the true label. And it combines with the interconnection information between data, learns the latent representation matrix to guide feature selection. Specifically, first, NLRL-LE regards each pseudo-label as a latent feature of the sample, constructs a latent feature graph, and retains the inherent attributes of the pseudo-labels. Second, latent representation learning is performed in the space which is made up of the latent feature space and data space. Since the latent feature graph retains the correlation between pseudo-labels, latent representation learning considers the interconnection information between data, and the information contained in the latent representation space is more complete. In addition, in order to make full use of pseudo-labels, the learned latent representation matrix is used as pseudo-label information to provide cluster labels in the latent representation space to guide feature selection. Finally, non-negative and l 2,1-2 -norm non-convex constraint are applied to the feature transformation matrix. The combination of non-negative constraint and non-convex constraint, compared with convex constraint, can ensure the row sparsity of the feature transformation matrix, select low-redundant features, and improve the feature selection effect. The experimental results show that the ACC and NMI of the NLRL-LE are better than the other seven compared algorithms on twelve datasets. [ABSTRACT FROM AUTHOR]

Unsupervised feature selection plays a significant role in data classification and clustering. General regression models cannot directly exploit the information on the feature space and fail to accurately describe the local geometric structure of data during feature selection. To address these problems, this paper proposes the feature selection algorithm, which is based on non-negative spectral feature learning and adaptive rank constraint (NNSAFS). First, the algorithm utilizes the residual term in sparse regression to ensure that the learned low-dimensional subspaces have greater fault tolerance and introduces a feature graph on the sparse transformation matrix to reveal the manifold information on the feature space. This sparse transformation matrix is the projection matrix because the introduction of feature graphs on this matrix can connect manifold learning to feature selection. In addition, traditional spectral clustering algorithms usually construct fixed similarity graphs for clustering analysis. The NNSAFS algorithm imposes a rank constraint on the clustering indicator matrix, which is equivalent to the graph regularization that can recover accurate local structure information. Moreover, the similarity matrix in the regularization term is constructed by using the maximum entropy theory, which can increase the adaptability of manifold learning. Finally, the algorithm imposes the l 1 -norm constraint on the projection matrix, which makes the selected features more conducive to clustering performance. The clustering performance of the NNSAFS algorithm is evaluated against seven other unsupervised feature selection algorithms on nine benchmark datasets. The experimental results show that the features selected by the proposed algorithm are more discriminative and outperform other algorithms in the clustering task. 1 1 The code of the proposed algorithm has been uploaded and available at the following link: https://github.com/Vita427/NNSAFS.git. [ABSTRACT FROM AUTHOR]

Band selection is a research hotspot in hyperspectral image processing. The continuity of the spectral bands causes the adjacent bands to be highly correlated, and correlation among long-range bands is possible with hundreds of spectral bands. Most existing deep learning methods fail to make full use of the inter-band correlation for band selection. In this paper, a novel dual-graph convolutional network based on band attention and a sparse constraint is proposed for band selection. The network consists of two branches. In the attention branch, band-based dual graphs are constructed to encode the contextual correlation of adjacent bands and the structural correlation of long-range bands into non-Euclidean space. Subsequently, the graph convolution-based band attention mechanism is devised to aggregate the band information in the band-based dual graphs and to generate the attention map for all bands. The band attention map is sparsely constrained and embedded as a mask into the trunk branch. In the trunk branch, sample-based dual graphs are constructed to represent the topological information of the samples in the spectral and spatial domains. Furthermore, a dense graph convolutional network is designed to extract and fuse the spatial–spectral and topological features from the shallow to deep layers for classification. A soft-shifting optimization strategy is implemented by defining a new loss from full bands and selected bands to solve the optimization problem caused by the sparse constraint. In this manner, band selection, feature extraction, and classification can be combined into an end-to-end trainable network. The experimental results on representative hyperspectral image datasets demonstrate the superiority of the proposed method over current state-of-the-art band selection methods. • An improved graph convolutional network is proposed for band selection. • Band-based and sample-based graphs are built with spatial and spectral information. • Design soft-shifting optimization strategy to overcome the optimization problem. • Mini batches of labeled and unlabeled samples are used for graph construction. [ABSTRACT FROM AUTHOR]

• A two-stage algorithm for high-dimensional feature selection is proposed. • A advanced hybrid ant colony optimization algorithm is proposed. • Our method has good selection performance with short running time. Ant colony optimization (ACO) is widely used in feature selection owing to its excellent global/local search capabilities and flexible graph representation. However, the current ACO-based feature selection methods are mainly applied to low-dimensional datasets. For thousands of dimensional datasets, the search for the optimal feature subset (OFS) becomes extremely difficult due to the exponential increase of the search space. In this paper, we propose a two-stage hybrid ACO for high-dimensional feature selection (TSHFS-ACO). As an additional stage, it uses the interval strategy to determine the size of OFS for the following OFS search. Compared to the traditional one-stage methods that determine the size of OFS and search for OFS simultaneously, the stage of checking the performance of partial feature number endpoints in advance helps to reduce the complexity of the algorithm and alleviate the algorithm from getting into a local optimum. Moreover, the advanced ACO algorithm embeds the hybrid model, which uses the features' inherent relevance attributes and the classification performance to guide OFS search. The test results on eleven high-dimensional public datasets show that TSHFS-ACO is suitable for high-dimensional feature selection. The obtained OFS has state-of-the-art performance on most datasets. And compared with other ACO-based feature selection methods, TSHFS-ACO has a shorter running time. [ABSTRACT FROM AUTHOR]