Internet of Things (IoT) networks face increasing security threats due to their distributed nature and resource constraints. Although federated learning (FL) has gained prominence as a privacy-preserving framework for distributed IoT environments, current federated principal component analysis (PCA) methods fail to incorporate personalized noise inherent in local data. To address these limitations, we propose an efficient personalized federated PCA (FedEP) method for anomaly detection in IoT networks. The proposed model achieves personalization through introducing local representations with the ℓ1-norm for element-wise sparsity, while maintaining robustness via enforcing local models with the ℓ2,1-norm for row-wise sparsity. To solve this non-convex problem, we develop a manifold optimization algorithm based on the alternating direction method of multipliers (ADMM) with theoretical convergence guarantees. Experimental results confirm that our proposed FedEP outperforms the state-of-the-art FL methods, achieving excellent accuracy in various IoT security scenarios. Our implementation code is accessible at https://github.com/xianchaoxiu/FedEP.

Tensor canonical correlation analysis (TCCA) has garnered significant attention due to its effectiveness in capturing high-order correlations in multi-view learning. However, existing TCCA methods often underemphasize the characterization of individual structures and lack algorithmic convergence guarantees. In order to deal with these challenges, we propose a novel sparse TCCA model called STCCA-L, which integrates sparse regularization of canonical matrices and Laplacian regularization of multi-order graphs into the TCCA framework, thereby effectively exploiting the geometric structure of individual views. To solve this non-convex model, we develop an efficient alternating manifold proximal gradient algorithm based on manifold optimization, which avoids computationally expensive full tensor decomposition and leverages a semi-smooth Newton method for resolving the subproblem. Furthermore, we rigorously prove the convergence of the algorithm and analyze its complexity. Experimental results on eight benchmark datasets demonstrate the superior classification performance of the proposed method. Notably, on the 3Sources dataset, it achieves improvements of at least 4.50% in accuracy and 6.77% in F1 score over competitors. Our code is available at https://github.com/zhudafa/STCCA-L.

To deal with high-dimensional unlabeled datasets in many areas, principal component analysis (PCA) has become a rising technique for unsupervised feature selection (UFS). However, most existing PCA-based methods only consider the structure of datasets by embedding a single sparse regularization or constraint on the transformation matrix. In this paper, we introduce a novel bi-sparse method called BSUFS to improve the performance of UFS. The core idea of BSUFS is to incorporate $\ell _{2,p}$ -norm and $\ell _{q}$ -norm into the classical PCA, which enables our method to select relevant features and filter out irrelevant noises, thereby obtaining discriminative features. Here, the parameters $p$ and $q$ are within the range of [ $0, 1$ ). Therefore, BSUFS not only constructs a unified framework for bi-sparse optimization, but also includes some existing works as special cases. To solve the resulting non-convex model, we propose an efficient proximal alternating minimization (PAM) algorithm using Stiefel manifold optimization and sparse optimization techniques. In addition, the computational complexity analysis is presented. Extensive numerical experiments on synthetic and real-world datasets demonstrate the effectiveness of our proposed BSUFS. The results reveal the advantages of bi-sparse optimization in feature selection and show its potential for other fields in image processing. Our code is available at https://github.com/xianchaoxiu/BSUFS.

The canonical correlation analysis (CCA) has attracted wide attention in fault detection (FD). To improve the detection performance, we propose a new joint sparse constrained CCA (JSCCCA) model that integrates the$\ell _{2,0}$-norm joint sparse constraints into classical CCA. The key idea is that JSCCCA can fully exploit the joint sparse structure to determine the number of extracted variables. We then develop an efficient alternating minimization algorithm using the improved iterative hard thresholding and manifold constrained gradient descent method. More importantly, we establish the convergence guarantee with detailed analysis. Finally, we provide extensive numerical studies on the simulated dataset, the benchmark Tennessee Eastman process, and a practical cylinder-piston process. In some cases, the computing time is reduced by 600 times, and the FD rate is increased by 12.62% compared with classical CCA. The results suggest that the proposed approach is efficient and fast.

The regularized clustering (RC) framework based on the fusion penalty has attracted extensive attention in the last decade because it does not require the prior knowledge of the number of clusters. Although the ground truth connections and weights among samples are beneficial for clustering, the performance of RC could be distorted by the omnipresent spurious connections in real-world data sets. To effectively address the issue, this letter constructs an enhanced regularized clustering model by incorporating a spurious connection detection mechanism into the objective function of the RC framework. The proposed model can effectively reduce the damage caused by spurious connections through adaptively identifying the importance of each connection. Furthermore, an alternating minimization algorithm is developed with detailed convergence analysis. Experimental results validate its effectiveness against several state-of-the-art RC methods

Canonical correlation analysis (CCA) has attracted great interest in multi-view representation. However, most of the CCA methods heavily rely on the matrix structure, which may neglect the prior geometric information in high-order data. To deal with the above issue, we first propose a novel tensor CCA formulation with orthogonality, called TCCA-O, based on the Tucker decomposition to preserve the orthogonality. Then, we incorporate a structured sparse regularization term into the TCCA-O, called TCCA-OS, to improve feature representation. In addition, we develop an efficient alternating direction method of multipliers (ADMM)-based algorithm to solve TCCA-OS and conduct numerical comparisons on four public datasets. The results validate the advantages of the proposed methods in terms of classification accuracy, parameter sensitivity, noise robustness, and model stability. In particular, TCCA-O and TCCA-OS improve the classification accuracy by at least 10.03% and 10.36%, respectively, over the state-of-the-art CCA methods on the Caltech101-7 dataset.

In this article, we propose an efficient fault diagnosis framework to achieve accurate fault isolation. The core is to introduce the$\ell _{2,0}$-norm sparsity constrained optimization to reduce the variable redundancy and determine the variable number, which is different from the existing sparse variants. In order to illustrate the idea, this article takes principal component analysis (PCA) as an essential step. First, a sparsity-aware PCA is constructed by taking advantage of the$\ell _{2,0}$-norm constrained optimization. Afterward, a two-stage monitoring strategy is designed, including fault detection and fault isolation. Once the fault is detected, the sparsity level is then shrunk to achieve accurate fault isolation. Moreover, an alternating direction method of multipliers-based optimization algorithm is developed with detailed implementation. Finally, the detection improvement and accurate isolation performance are validated by two simulated examples, the Tennessee Eastman benchmark process, and a practical cylinder-piston process.

Generalized canonical correlation analysis (GCCA) that aims to deal with multi-view data has attracted extensive attention in signal processing. To improve the representation performance, this letter proposes a new sparsity constrained GCCA (SCGCCA). Technically, it integrates the$\ell _{2,0}$-norm constrained optimization into GCCA, which has not been investigated in the literature. Compared with the existing$\ell _{2,1}$-norm regularized GCCA, the proposed SCGCCA can not only exploit the similarity information belonging to the same features but also determine the number of extracted features. Although it is a nonconvex minimization problem, an efficient alternating minimization algorithm can be designed. Furthermore, a Newton hard thresholding pursuit technique is developed to accelerate the convergence tremendously. Empirical studies suggest both the effectiveness and efficiency of the proposed SCGCCA comparing with the existing GCCA and its variants. In particular, the speed can be increased by 150 times for the simulated dataset.

This article proposes an efficient nonlinear process monitoring method (DCCA-SCO) by integrating canonical correlation analysis (CCA), deep autoencoder neural networks (DAENNs), and sparsity-constrained optimization (SCO). Specifically, DAENNs are first used to learn a nonlinear function automatically, which characterizes intrinsic features of the original process data. Then, the CCA is performed in that low-dimensional representation space to extract the most correlated variables. In addition, the SCO is imposed to reduce the redundancy of the hidden representation. Unlike other deep CCA methods, the DCCA-SCO provides a new nonlinear method that is able to learn a nonlinear mapping with a sparse prior. The validity of the proposed DCCA-SCO is extensively demonstrated on the benchmark Tennessee Eastman (TE) process and the diesel generator process. In particular, compared with the classical CCA, the fault detection rate is increased by 8.00% for the fault IDV(11) in the TE process.

This article proposes a novel modeling method for the stochastic nonlinear degradation process by using the relevance vector machine (RVM), which can describe the nonlinearity of degradation process more flexibly and accurately. Compared with the existing methods, where degradation processes are modeled as the Wiener process with a nonlinear drift function formulized as the power law or exponential law, this kind of modeling method can characterize degradation processes with more nonlinear behavior. Instead of modeling the drift coefficient of the Wiener process directly, the weighted combination of basis functions is utilized to express the increment of the Wiener process and the parameters are calculated by a sparse Bayesian learning algorithm. Based on the proposed model, a numerical approximation formula for the probability density function (PDF) of the remaining useful life (RUL) is derived. Finally, comparison studies, including a numerical simulation and a practical case, are provided to demonstrate the effectiveness and the accuracy of the proposed methods for RUL estimation.