Search Results (46)

Recently, a growing number of researchers have focused on multi-view subspace clustering (MSC) due to its potential for integrating heterogeneous data. However, current MSC methods remain challenged by limited robustness and insufficient exploitation of cross-view high-order latent information for clustering advancement. To address these challenges, we develop a novel MSC framework termed TMSC-TNNBDR, a tensorized MSC framework that leverages t-SVD based tensor nuclear norm (TNN) regularization and block diagonal representation (BDR) learning to unify view consistency and structural sparsity. Specifically, each subspace representation matrix is constrained by a block diagonal regularizer to enforce cluster structure, while all matrices are aggregated into a tensor to capture high-order interactions. To efficiently optimize the model, we developed an optimization algorithm based on the inexact augmented Lagrange multiplier (ALM). The TMSC-TNNBDR exhibits both optimized block-diagonal structure and low-rank properties, thereby enabling enhanced mining of latent higher-order inter-view correlations while demonstrating greater resilience to noise. To investigate the capability of TMSC-TNNBDR, we conducted several experiments on certain datasets. Benchmarking on circumscribed datasets demonstrates our method’s superior clustering performance over comparative algorithms while maintaining competitive computational overhead. Full article

This paper proposes a new proximal iteratively reweighted nuclear norm method for a class of nonconvex and nonsmooth optimization problems. The primary contribution of this work is the incorporation of line search technique based on dimensionality reduction and extrapolation. This strategy overcomes parameter constraints by enabling adaptive dynamic adjustment of the extrapolation/proximal parameters (α_k, β_k, μ_k). Under the Kurdyka–Łojasiewicz framework for nonconvex and nonsmooth optimization, we prove the global convergence and linear convergence rate of the proposed algorithm. Additionally, through numerical experiments using synthetic and real data in matrix completion problems, we validate the superior performance of the proposed method over well-known methods. Full article

Hyperspectral image (HSI) quality is generally degraded by diverse noise contamination during acquisition, which adversely impacts subsequent processing performance. Current techniques predominantly rely on nuclear norms and low-rank matrix approximation theory to model the inherent property that HSIs lie in a low-dimensional subspace. Recent research has demonstrated that HSI gradient maps also exhibit low-rank priors. The correlated total variation (CTV), which is defined as the nuclear norm of gradient maps, can simultaneously model low-rank and local smoothness priors, and shows better performance than the standard nuclear norm. However, similar to nuclear norms, CTV may excessively penalize large singular values. To overcome these constraints, this study introduces a non-convex correlated total variation (NCTV), which shows the potential to eliminate mixed noise (including Gaussian, impulse, stripe, and dead-line noise) while preserving critical textures and spatial–spectral details. Numerical experiments on both simulated and real HSI datasets demonstrate that the proposed NCTV method achieves better performance in detail retention compared with the state-of-the-art techniques. Full article

A technical challenge for workload prediction in microservice systems is how to capture both the dynamic features of workload and evolving dependencies among microservices. The existing work focused mainly on modeling dynamic features without taking adequate account of evolving dependencies due to their unpredictable temporal dynamics. To fill this gap, as an illustration of bridging theory and real-work solutions by integrating machine learning with data analysis, we propose a novel framework of Temporality-Dependence Dual-Regularized Matrix Factorization (TDDRMF) by combining matrix factorization with regularization on both workload temporality and microservice dependencies. It models the workload matrix as the product of a microservice dependency matrix W and workload feature matrix X applying matrix factorization, and computes X by temporal regularization and W by low-rank norm regularization as a convex relaxation of rank minimization. To further enhance its adaptability to workload variations in real-time environments, we deploy a dynamic error detection and update mechanism. Experiments on the Alibaba dataset show that TDDRMF achieves 18.5% lower RMSE than TAMF in 10-step prediction, improving the existing matrix factorization methods in accuracy. In comparison with ML-based methods, as TDDRMF uses only 5% of their training data, it requires only a small fraction of their training time. Full article

Electricity consumption data form the foundation for the efficient and reliable operation of smart grids and are a critical component for ensuring effective data mining. However, due to factors such as meter failures and extreme weather conditions, anomalies frequently occur in the data, which adversely impact the performance of data-driven applications. Given the near full-rank nature of low-voltage distribution area electricity consumption data, this paper employs clustering to enhance the low-rank property of the data. Addressing common issues such as missing data, sparse noise, and Gaussian noise in electricity consumption data, this paper proposes a multi-norm optimization model based on low-rank matrix theory. Specifically, the truncated nuclear norm is used as an approximation of matrix rank, while the $L_1$-norm and F-norm are employed to constrain sparse noise and Gaussian noise, respectively. The model is solved using the Alternating Direction Method of Multipliers (ADMM), achieving a unified framework for handling missing data and noise processing within the model construction. Comparative experiments on both synthetic and real-world datasets demonstrate that the proposed method can accurately recover measurement data under various noise contamination scenarios and different distributions of missing data. Moreover, it effectively separates principal components of the data from noise contamination. Full article

In this paper, we extend the definition of tensor products from using an invertible matrix to utilising right-invertible matrices, exploring the algebraic properties of these new tensor products. Based on this novel definition, we define the concepts of tensor rank and tensor nuclear norm, ensuring consistency with their matrix counterparts, and derive a singular value thresholding (${\ast }_{L,R}$ SVT) formula to approximately solve the subproblems in the alternating direction method of multipliers (ADMM), which is integral to our proposed tensor robust principal component analysis (${\ast }_{LR}$ TRPCA) algorithm. The computational complexity of the ${\ast }_{LR}$ TRPCA algorithm is $O(k·(n_1{n}_2{n}_3+p·\min (n_1^2{n}_2,n_1{n}_2^2)))$ for k iterations. According to this complexity analysis, by using a right-invertible matrix that selects p rows from the $n_3$ rows of the invertible matrix used in the tensor product with an invertible matrix, the computational load is approximately reduced to $p/n_3$ of what it would be with an invertible matrix, highlighting the efficiency gain in terms of computational resources. We apply this efficient algorithm to grayscale video denoising and motion detection problems, where it demonstrates significant improvements in processing speed while maintaining comparable quality levels to existing methods, thereby providing a promising approach for handling multi-linear data and offering valuable insights for advanced data analysis tasks. Full article

Due to channel noise and random atmospheric turbulence, retrieved satellite images are always distorted and degraded and so require further restoration before use in various applications. The latest quaternion-based weighted nuclear norm minimization (QWNNM) model, which utilizes the idea of low-rank matrix approximation and the quaternion representation of multi-channel satellite images, can achieve image restoration and enhancement. However, the QWNNM model ignores the impact of noise on similarity measurement, lacks the utilization of residual image information, and fixes the number of iterations. In order to address these drawbacks, we propose three adaptive strategies: adaptive noise-resilient block matching, adaptive feedback of residual image, and adaptive iteration stopping criterion in a new adaptive QWNNM model. Both simulation experiments with known noise/blurring and real environment experiments with unknown noise/blurring demonstrated that the effectiveness of adaptive QWNNM models outperformed the original QWNNM model and other state-of-the-art satellite image restoration models in very different technique approaches. Full article

More recently, the ability of the coprime array to yield large array apertures and high degrees of freedom in comparison with the uniform linear array (ULA) has drawn an enormous amount of attention. In light of this, we propose a low-rank matrix completion algorithm via minimization of the ratio of the nuclear norm and the Frobenius norm (N/F) to solve the two-dimensional (2D) direction finding problem for the L-shaped coprime array (LsCA). Specifically, we first interpolate the virtual co-array signal related to the cross-correlation matrix (CCM) and utilize the interpolated virtual signal for Toeplitz matrix reconstruction. Then, the N/F method is employed to perform low-rank matrix completion on the reconstructed matrix. Finally, exploiting the conjugate symmetry characteristics of the completed matrix, we further develop a direction-finding algorithm that enables 2D angle estimation. Remarkably, the 2D angles are able to be automatically paired by the proposed algorithm. Numerical simulation findings demonstrate that the proposed N/F algorithm generates excellent angular resolution and computational complexity. Furthermore, this algorithm yields better estimation accuracy compared to the competing algorithms. Full article

Tensor-based multi-view spectral clustering methods are promising in practical clustering applications. However, most of the existing methods adopt the ${\ell }_{2,1}$ norm to depict the sparsity of the error matrix, and they usually ignore the global structure embedded in each single view, compromising the clustering performance. Here, we design a robust tensor learning method for multi-view spectral clustering (RTL-MSC), which employs the weighted tensor nuclear norm to regularize the essential tensor for exploiting the high-order correlations underlying multiple views and adopts the nuclear norm to constrain each frontal slice of the essential tensor as the block diagonal matrix. Simultaneously, a novel column-wise sparse norm, namely, ${\ell }_{2,p}$, is defined in RTL-MSC to measure the error tensor, making it sparser than the one derived by the ${\ell }_{2,1}$ norm. We design an effective optimization algorithm to solve the proposed model. Experiments on three widely used datasets demonstrate the superiority of our method. Full article

Multi-channel audio signals provide a better auditory sensation to the audience. However, missing data may occur in the collection, transmission, compression, or other processes of audio signals, resulting in audio quality degradation and affecting the auditory experience. As a result, the completeness of the audio signal has become a popular research topic in the field of signal processing. In this paper, the tensor nuclear norm is introduced into the audio signal completion algorithm, and the multi-channel audio signals with missing data are restored by using the completion algorithm based on the tensor nuclear norm. First of all, the multi-channel audio signals are preprocessed and are then transformed from the time domain to the frequency domain. Afterwards, the multi-channel audio with missing data is modeled to construct a third-order multi-channel audio tensor. In the next part, the tensor completion algorithm is used to complete the third-order tensor. The optimal solution of the convex optimization model of the tensor completion is obtained by using the convex relaxation technique and, ultimately, the data recovery of the multi-channel audio with data loss is accomplished. The experimental results of the tensor completion algorithm and the traditional matrix completion algorithm are compared using both objective and subjective indicators. The final result shows that the high-order tensor completion algorithm has a better completion ability and can restore the audio signal better. Full article

The matrix nuclear norm minimization problem has been extensively researched in recent years due to its widespread applications in control design, signal and image restoration, machine learning, big data problems, and more. One popular model is nuclear norm minimization with the $l_2$-norm fidelity term, but it is only effective for those problems with Gaussian noise. A nuclear norm minimization problem with the $l_1$-norm fidelity term has been studied in this paper, which can deal with the problems with not only non-Gaussian noise but also Gaussian noise or their mixture. Moreover, it also keeps the efficiency for the noiseless case. Given the nonsmooth proposed model, we transform it into a separated form by introducing an auxiliary variable and solve it by the semi-proximal alternating direction method of multipliers (sPADMM). Furthermore, we first attempt to solve its dual problem by sPADMM. Then, the convergence guarantees for the aforementioned algorithms are given. Finally, some numerical studies are dedicated to show the robustness of the proposed model and the effectiveness of the presented algorithms. Full article

Camera failure or loss of storage components in imaging equipment may result in the loss of important image information or random pulse noise interference. The low-rank prior is one of the most important priors in image optimization processing. This paper reviews and compares some low-rank constraint models for image matrices. Firstly, an overview of image-inpainting models based on nuclear norm, truncated nuclear norm, weighted nuclear norm, and matrix-factorization-based F norm is presented, and corresponding optimization iterative algorithms are provided. Then, we use different image matrix low-order constraint models to recover satellite images from three types of pulse interference and provide our experimental visual and numerical results. Finally, it can be concluded that the method based on the weighted nuclear norm can achieve the best image restoration effect. The F norm method based on matrix factorization has the shortest computational time and can be used for large-scale low-rank matrix calculations. Compared with nuclear norm-based methods, weighted nuclear norm-based methods and truncated nuclear norm-based methods can significantly improve repair performance. Full article

Array sensor failure poses a serious challenge to robust direction-of-arrival (DOA) estimation in complicated environments. Although existing matrix completion methods can successfully recover the damaged signals of an impaired sensor array, they cannot preserve the multi-way signal characteristics as the dimension of arrays expands. In this paper, we propose a structural-missing tensor completion algorithm for robust DOA estimation with uniform rectangular array (URA), which exhibits a high robustness to non-ideal sensor failure conditions. Specifically, the signals received at the impaired URA are represented as a three-dimensional incomplete tensor, which contains whole fibers or slices of missing elements. Due to this structural-missing pattern, the conventional low-rank tensor completion becomes ineffective. To resolve this issue, a spatio-temporal dimension augmentation method is developed to transform the structural-missing tensor signal into a six-dimensional Hankel tensor with dispersed missing elements. The augmented Hankel tensor can then be completed with a low-rank regularization by solving a Hankel tensor nuclear norm minimization problem. As such, the inverse Hankelization on the completed Hankel tensor recovers the tensor signal of an unimpaired URA. Accordingly, a completed covariance tensor can be derived and decomposed for robust DOA estimation. Simulation results verify the effectiveness of the proposed algorithm. Full article

Methods for detecting small infrared targets in complex scenes are widely utilized across various domains. Traditional methods have drawbacks such as a poor clutter suppression ability and a high number of edge residuals in the detection results in complex scenes. To address these issues, we propose a method based on a joint new norm and self-attention mechanism of low-rank sparse inversion. Firstly, we propose a new tensor nuclear norm based on linear transformation, which globally constrains the low-rank characteristics of the image background and makes full use of the structural information among tensor slices to better approximate the rank of the non-convex tensor, thus achieving effective background suppression. Secondly, we construct a self-attention mechanism in order to constrain the sparse characteristics of the target, which further eliminates any edge residuals in the detection results by transforming the local feature information into a weight matrix to further constrain the target component. Finally, we use the alternating direction multiplier method to decompose the newly reconstructed objective function and introduce a reweighted strategy to accelerate the convergence speed of the model. The average values of the three evaluation metrics, SSIM, BSF, and SNR, for the algorithm proposed in this paper are 0.9997, 467.23, and 11.72, respectively. Meanwhile, the proposed detection method obtains a higher detection rate compared with other algorithms under the same false alarm rate. Full article

In real-world scenarios, images may be affected by additional noise during compression and transmission, which interferes with postprocessing such as image segmentation and feature extraction. Image noise can also be induced by environmental variables and imperfections in the imaging equipment. Robust principal component analysis (RPCA), one of the traditional approaches for denoising images, suffers from a failure to efficiently use the background’s low-rank prior information, which lowers its effectiveness under complex noise backgrounds. In this paper, we propose a robust PCA method based on a nonconvex low-rank approximation and total variational regularization (TV) to model the image denoising problem in order to improve the denoising performance. Firstly, we use a nonconvex $\gamma$-norm to address the issue that the traditional nuclear norm penalizes large singular values excessively. The rank approximation is more accurate than the nuclear norm thanks to the elimination of matrix elements with substantial approximation errors to reduce the sparsity error. The method’s robustness is improved by utilizing the low sensitivity of the $\gamma$-norm to outliers. Secondly, we use the $l_1$-norm to increase the sparsity of the foreground noise. The TV norm is used to improve the smoothness of the graph structure in accordance with the sparsity of the image in the gradient domain. The denoising effectiveness of the model is increased by employing the alternating direction multiplier strategy to locate the global optimal solution. It is important to note that our method does not require any labeled images, and its unsupervised denoising principle enables the generalization of the method to different scenarios for application. Our method can perform denoising experiments on images with different types of noise. Extensive experiments show that our method can fully preserve the edge structure information of the image, preserve important features of the image, and maintain excellent visual effects in terms of brightness smoothing. Full article