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Traditional unsupervised feature selection methods usually construct a fixed similarity matrix. This matrix is sensitive to noise and becomes unreliable, which affects the performance of feature selection. The researches have shown that both the global reconstruction information and local structure information are important for feature selection. To solve the above problem effectively and make use of the global and local information of data simultaneously, a novel algorithm is proposed in this paper, called subspace learning for unsupervised feature selection via adaptive structure learning and rank approximation (SLASR). Specifically, SLASR learns the manifold structure adaptively, thus the preserved local geometric structure can be more accurate and more robust to noise. As a result, the learning of the similarity matrix and the low-dimensional embedding is completed in one step, which improves the effect of feature selection. Meanwhile, SLASR adopts the matrix factorization subspace learning framework. By minimizing the reconstruction error of subspace learning residual matrix, the global reconstruction information of data is preserved. Then, to guarantee more accurate manifold structure of the similarity matrix, a rank constraint is used to constrain the Laplacian matrix. Additionally, the l 2,1/2 regularization term is used to constrain the projection matrix to select the most sparse and robust features. Experimental results on twelve benchmark datasets show that SLASR is superior to the six comparison algorithms from the literature. [ABSTRACT FROM AUTHOR]

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]

Non-negative matrix factorization (NMF) can map high-dimensional data into a low-dimensional data space. Feature selection can eliminate the redundant and irrelevant features from the alternative features. In this paper, we propose a feature selection based dual-graph sparse non-negative matrix factorization (DSNMF) which can find an appropriate low dimensional representation of data by NMF and then select more discriminative features to further reduce the dimension of the low dimensional space by feature selection rather than reduce the dimension by only NMF or feature selection in many previous methods. DSNMF combines dual-graph model with non-negative matrix factorization, which can not only simultaneously preserve the geometric structures in both the data space and the feature space, but also make the two non-negative matrix factors update iteratively and interactively. In addition, DSNMF exerts L 2,1 - norm constraint on the non-negative matrix factor of the feature space to make full use of the sparse self-representation information. What's more, we propose a new local discriminative feature selection clustering called feature selection based dual-graph sparse non-negative matrix factorization for local discriminative clustering (DSNMF-LDC) whose clustering effects are better. We give the objective function, the iterative updating rules and the convergence proof. Our empirical study shows that DSNMF-LDC is robust and excellent in comparison to 9 feature selection algorithms and 7 clustering algorithms in clustering accuracy (ACC) and normalized mutual information (NMI). [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]

Feature selection algorithms eliminate irrelevant and redundant features, even the noise, while preserving the most representative features. They can reduce the dimension of the dataset, extract essential features in high dimensional data and improve learning quality. Existing feature selection algorithms are all carried out in data space. However, the information of feature space cannot be fully exploited. To compensate for this drawback, this paper proposes a novel feature selection algorithm for clustering, named self-representation based dual-graph regularized feature selection clustering (DFSC). It adopts the self-representation property that data can be represented by itself. Meanwhile, the local geometrical information of both data space and feature space are preserved simultaneously. By imposing the l 2,1 -norm constraint on the self-representation coefficients matrix in data space, DFSC can effectively select the most representative features for clustering. We give the objective function, develop iterative updating rules and provide the convergence proof. Two kinds of extensive experiments on some datasets demonstrate the effectiveness of DFSC. Extensive comparisons over several state-of-the-art feature selection algorithms illustrate that additionally considering the information of feature space based on self-representation property improves clustering quality. Meanwhile, because the additional feature selection process can select the most important features to preserve the intrinsic structure of dataset, the proposed algorithm achieves better clustering results compared with some co-clustering algorithms. [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]