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Feature selection in high-dimensional data is an important part of the data mining process and is widely used in bioinformatics, statistics and image processing fields. Successfully selecting informative features can significantly improve learning accuracy and improve result comprehensibility. However, it is a challenging problem to select features accurately and efficiently from high-dimensional data. In this paper, we propose a Weighted Sparse Regression with Mutual Information (WSRMI) for selecting structural features. Differing from traditional sparse feature selection models that focus solely on either feature correlations or feature importance, the proposed model integrates both aspects through a mutual-information-based weighting mechanism. The proposed model can be effectively applied to regression and binary classification tasks, making it more general and practical for real-world applications. The proposed model is statistically compared with several existing classical models over randomly generated classification and benchmark datasets. Experimental results show that the proposed model is more effective at selecting the informative features with a superior prediction performance than the comparative ones.

Graph-based multi-view clustering methods aim to explore the partition patterns by utilizing a similarity graph. However, many existing methods construct a consensus similarity graph based on the original multi-view space, which may result in the lack of information on the underlying low-dimensional space. Additionally, these methods often fail to effectively handle the noise present in the graph. To address these issues, a novel graph-based multi-view clustering method which combines spectral embedding, non-convex low-rank approximation and noise processing into a unit framework is proposed. In detail, the proposed method constructs a tensor by stacking the inner product of normalized spectral embedding matrices obtained from each similarity matrix. Then, the obtained tensor is decomposed into a low-rank tensor and a noise tensor. The low-rank tensor is constrained via nonconvex low-rank tensor approximation and a novel Cauchy norm with an upper bound is proposed to handle the noise. Finally, we derive the consensus similarity graph from the denoised low-rank tensor. The experiments on five datasets demonstrate that the proposed method outperforms other state-of-the-art methods on five datasets.

Non-negative Matrix Factorization (NMF) has been an ideal tool for machine learning. Non-negative Matrix Tri-Factorization (NMTF) is a generalization of NMF that incorporates a third non-negative factorization matrix, and has shown impressive clustering performance by imposing simultaneous orthogonality constraints on both sample and feature spaces. However, the performance of NMTF dramatically degrades if the data are contaminated with noises and outliers. Furthermore, the high-order geometric information is rarely considered. In this paper, a Robust NMTF with Dual Hyper-graph regularization (namely RDHNMTF) is introduced. Firstly, to enhance the robustness of NMTF, an improvement is made by utilizing the l2,1-norm to evaluate the reconstruction error. Secondly, a dual hyper-graph is established to uncover the higher-order inherent information within sample space and feature spaces for clustering. Furthermore, an alternating iteration algorithm is devised, and its convergence is thoroughly analyzed. Additionally, computational complexity is analyzed among comparison algorithms. The effectiveness of RDHNMTF is verified by benchmarking against ten cutting-edge algorithms across seven datasets corrupted with four types of noise.

Unsupervised feature selection (UFS) methods play a crucial role in improving the efficiency of extracting relevant information and reducing computational complexity in the context of big data analysis. Despite notable advancements in the field of unsupervised feature selection for large-scale datasets, many UFS methods still remain redundant and irrelevant features during the feature selection process. To tackle these challenges, we present a novel unsupervised feature selection method that leverages the generalized regression model with linear discriminant constraints to learn discriminant and effective features from the data. Benefited from this, the relationships and patterns within the high-dimensional data are retained in the reduced-dimensional feature space. We reformulate our proposed method as a multi-variable optimization problem that incorporates equality constraints. To efficiently solve this problem, we develop an algorithm that updates each variable alternately. Extensive experiments on six datasets among nine state-of-the-art methods on the clustering task are conducted to demonstrate the effectiveness of the proposed method.

Incomplete Multi-View Clustering (IMVC) aims to partition data with missing samples into distinct groups. However, most IMVC methods rarely consider the high-order neighborhood information of samples, which represents complex underlying interactions, and often neglect the weights of different views. To address these issues, we propose a High-order Consensus Graph Learning (HoCGL) model. Specifically, we integrate a reconstruction term to recover the incomplete multi-view data. High-order proximity matrices are constructed, and the self-representation similarity matrices and multiple high-order proximity matrices are learned mutually, allowing the similarity matrices to incorporate complex high-order information. Finally, the consensus graph representation is derived from the similarity matrices through a self-weighted strategy. An efficient algorithm is designed to solve the proposed model. The excellent clustering performance of the proposed model is validated by comparing it with eight state-of-the-art models across nine datasets.

Graph non-negative matrix factorization (GNMF) can discover the data’s intrinsic low-dimensional structure embedded in the high-dimensional space. So, it has superior performance for data representation and clustering. Unfortunately, it is sensitive to noise and outliers. In this paper, to improve the robustness of GNMF, l 0 norm is introduced to enhance the sparsity of factorized matrices. As the discontinuity of l 0 norm and minimizing it is a NP-hard problem, five functions approximating l 0 norm are used to transform the problem of the sparse graph non-negative matrix factorization (SGNMF) to a global optimization problem. Finally, the multiplicative updating rules (MUR) are designed to solve the problem and the convergence of algorithm is proven. In the experiment, the accuracy and normalized mutual information of clustering results show the superior performance of SGNMF on five public datasets.

Nonnegative matrix factorization (NMF) is a popular approach to extract intrinsic features from the original data. As the nonconvexity of NMF formulation, it always leads to degrade the performance. To alleviate the defect, in this paper, the self-paced regularization is introduced to find a better factorized matrices by sequentially selecteing data in the learning process. Additionally, to find the low-dimensional manifold embeded in the high-dimensional space, adaptive graph is introduced by using dynamic neighbors assignment. An alternating iterative algorithm is designed to sovle the proposed mathematical factorization formulation. The experimental results are given to show the effectiveness of the proposed approach in comparison with state-of-the-art algorithms on six public datasets.

L0 norm plays a crucial role in sparse optimization, but discontinuities and non-convexity make the minimization of the l0 norm be an NP-hard problem. To alleviate this problem, we design a smoothing function based on the sigmoid function to approximate the l0 norm. To illustrate the physical realizability of the smoothing function and the advanced quality of the approximation, the proposed smoothing function is compared experimentally with several existing smoothing functions. Additionally, we analyze the parameters in the functions to determine the quality of the approximation. We investigate the circuit implementation of the proposed function and five existing smoothing functions; the simulation results show the effectiveness of the designed circuit on the Multisim platform. Experiments on the reconstruction of simulated sparse signals and real image data show that the proposed smoothing function is able to reconstruct sparse signals and images with lower mean square error (MSE) and higher peak signal-to-noise ratio (PSNR), respectively.

This paper proposes a proximal neurodynamic network (PNDN) for solving mixed variational inequalities based on the proximal operator. It is shown that the proposed PNDN is globally exponentially stable under some mild conditions, and a stopping condition is provided for the PNDN. Furthermore, the proposed PNDN is applied in solving variational inequalities and composition optimization with nonsmooth regularization. In addition, the equilibrium point of the proposed proximal gradient neurodynamic network for composition optimization problems is globally exponentially stable via the Polyak-Lojasiewicz condition, a relaxation of strong convexity. Finally, numerical and experimental examples on sparse signal reconstruction and variational arc-flow problems are presented to validate the effectiveness of the proposed neurodynamic network.