Iterative Optimization Algorithm Research Articles

Consensus and discriminative non-negative matrix factorization for multi-view unsupervised feature selection

Multi-view unsupervised feature selection (MUFS) has been proven to be an efficient dimensionality reduction technique for multi-view data. Existing methods have two main challenges: (1) The consistency information from different views is not fully exploited. (2) The cluster structure of the original data is not well utilized. To settle these problems, we propose a novel consensus and discriminative non-negative matrix factorization (CDNMF) for multi-view unsupervised feature selection. Specifically, CDNMF obtains a robust low-dimensional latent space by NMF with an ℓ2,1-norm constraint. To select more discriminative features, we further impose a sparsity constraint on the learned latent features. Moreover, CDNMF performs k-means clustering on all views separately to obtain the pseudo-labels of each view, which are used to guide the learning of consensus information among views. To solve our model, we develop an efficient iterative optimization algorithm. Extensive experimental results on ten benchmark datasets demonstrate that the proposed significantly outperforms several existing feature selection methods in clustering tasks.

Age of Information-Inspired Data Collection and Secure Upload Assisted by the Unmanned Aerial Vehicle and Reconfigurable Intelligent Surface in Maritime Wireless Sensor Networks

This paper proposes an age of information (AoI)-inspired secure transmissions strategy for secure transmission from the maritime wireless sensor network to the onshore base station (BS) with the assistance of the unmanned aerial vehicle (UAV) and reconfigurable intelligent surface (RIS), in which eavesdroppers exist near the BS. In the proposed scheme, the secure transmission process is divided into the data collection period and the data upload period according to the time sequence to minimize the age of information (AoI) for the privacy information. In the data collection period, we design two scheduling schemes by selecting the sensor with the smallest current AoI or the largest difference in the adjacent AoI. In addition, we propose two heuristic algorithms by adopting the particle swarm optimization algorithm (PSO) and genetic algorithm (GA) to solve the above two problems. In the data uploading period, the uploading time minimization problem is converted to the secrecy rate maximization problem. We design an iterative optimization algorithm with auxiliary variables that are introduced to optimize the reflection coefficient of the RIS. Simulation results show that the proposed scheme can reduce the average AoI by about 10 s compared to the current methods.

Discriminative Subspace Learning With Adaptive Graph Regularization

Abstract Many subspace learning methods based on low-rank representation employ the nearest neighborhood graph to preserve the local structure. However, in these methods, the nearest neighborhood graph is a binary matrix, which fails to precisely capture the similarity between distinct samples. Additionally, these methods need to manually select an appropriate number of neighbors, and they cannot adaptively update the similarity graph during projection learning. To tackle these issues, we introduce Discriminative Subspace Learning with Adaptive Graph Regularization (DSL_AGR), an innovative unsupervised subspace learning method that integrates low-rank representation, adaptive graph learning and nonnegative representation into a framework. DSL_AGR introduces a low-rank constraint to capture the global structure of the data and extract more discriminative information. Furthermore, a novel graph regularization term in DSL_AGR is guided by nonnegative representations to enhance the capability of capturing the local structure. Since closed-form solutions for the proposed method are not easily obtained, we devise an iterative optimization algorithm for its resolution. We also analyze the computational complexity and convergence of DSL_AGR. Extensive experiments on real-world datasets demonstrate that the proposed method achieves competitive performance compared with other state-of-the-art methods.

Discriminative embedded multi-view fuzzy C-means clustering for feature-redundant and incomplete data

Multi-view clustering is a widely-used technique that seeks to categorize data obtained from various sources. As a representative method, multi-view fuzzy clustering has attracted growing attention. However, it becomes quite challenging when feature-redundant and incomplete data is presented. Despite the existing studies on dimension reduction and imputation methods, several issues remain unresolved. There is an excessive concern on the imputation, without considering that interpolation methods lead to accuracy degradation. Moreover, most of the methods usually process these two steps separately, resulting in inefficiency. To address these issues, we propose a discriminative embedded incomplete multi-view fuzzy c-means clustering method. We construct the indicator matrix to guide the learning of the common membership function, and design the projection matrix to construct embedding spaces. Subsequently, we develop an iterative optimization algorithm that solves the resultant problem. We demonstrate that the projection matrix can be achieved through the utilization of eigenvalue decomposition. Through extensive experimental studies on various benchmark datasets, the proposed method demonstrates the effectiveness and efficiency compared to the existing state-of-the-art clustering algorithms.

IFKMHC: Implicit Fuzzy K-Means Model for High-Dimensional Data Clustering.

The graph-information-based fuzzy clustering has shown promising results in various datasets. However, its performance is hindered when dealing with high-dimensional data due to challenges related to redundant information and sensitivity to the similarity matrix design. To address these limitations, this article proposes an implicit fuzzy k-means (FKMs) model that enhances graph-based fuzzy clustering for high-dimensional data. Instead of explicitly designing a similarity matrix, our approach leverages the fuzzy partition result obtained from the implicit FKMs model to generate an effective similarity matrix. We employ a projection-based technique to handle redundant information, eliminating the need for specific feature extraction methods. By formulating the fuzzy clustering model solely based on the similarity matrix derived from the membership matrix, we mitigate issues, such as dependence on initial values and random fluctuations in clustering results. This innovative approach significantly improves the competitiveness of graph-enhanced fuzzy clustering for high-dimensional data. We present an efficient iterative optimization algorithm for our model and demonstrate its effectiveness through theoretical analysis and experimental comparisons with other state-of-the-art methods, showcasing its superior performance.

Dual-learning Multi-hop Nonnegative Matrix Factorization for community detection

As an important branch of network science, community detection has garnered significant attention. Among various community detection methods, nonnegative matrix factorization (NMF)-based community detection approaches have become a popular research topic. However, most NMF-based methods overlook the network’s multi-hop information, let alone the community detection results specific to each hop of the network. In this paper, we propose Dual-learning Multi-hop NMF (DL-MHNMF), a method that considers not only the multi-hop connectivity between two nodes but also factors in the shared results across multiple hops and the impact of differences in the specific results at each hop on the shared outcomes. An efficient iterative optimization algorithm with guaranteed theoretical convergence is proposed for solving DL-MHNMF. Methodologically, by iteratively removing the specific results during the optimization process of DL-MHNMF, we achieve enhanced detection accuracy, which is also verified by subsequent experiments. Specifically, we compare fourteen algorithms on eleven publicly available datasets, and experimental results show that our algorithm outperforms most state-of-the-art methods. The source code is availiable at https://github.com/bx20000827/DL-MHNMF.git.

Comprehensive Multiview Representation Learning via Deep Autoencoder-Like Nonnegative Matrix Factorization.

Learning a comprehensive representation from multiview data is crucial in many real-world applications. Multiview representation learning (MRL) based on nonnegative matrix factorization (NMF) has been widely adopted by projecting high-dimensional space into a lower order dimensional space with great interpretability. However, most prior NMF-based MRL techniques are shallow models that ignore hierarchical information. Although deep matrix factorization (DMF)-based methods have been proposed recently, most of them only focus on the consistency of multiple views and have cumbersome clustering steps. To address the above issues, in this article, we propose a novel model termed deep autoencoder-like NMF for MRL (DANMF-MRL), which obtains the representation matrix through the deep encoding stage and decodes it back to the original data. In this way, through a DANMF-based framework, we can simultaneously consider the multiview consistency and complementarity, allowing for a more comprehensive representation. We further propose a one-step DANMF-MRL, which learns the latent representation and final clustering labels matrix in a unified framework. In this approach, the two steps can negotiate with each other to fully exploit the latent clustering structure, avoid previous tedious clustering steps, and achieve optimal clustering performance. Furthermore, two efficient iterative optimization algorithms are developed to solve the proposed models both with theoretical convergence analysis. Extensive experiments on five benchmark datasets demonstrate the superiority of our approaches against other state-of-the-art MRL methods.

Label relaxation and shared information for multi-label feature selection

Due to the rapid growth of labels and high-dimensional data, multi-label feature selection has attracted increasing attention. However, two common issues are ignored by existing multi-label feature selection methods: 1) The pseudo-label matrix is constructed by using logical label matrix directly. 2) There is an imbalance of label density in multi-label data. To tackle the mentioned issues, we innovatively propose a new method named Label relaxation and Shared information for Multi-label Feature Selection (LSMFS). Specifically, LSMFS combines a logical label matrix with a non-negative label relaxation matrix to fit a pseudo-label matrix, which is used for learning the correlations of class labels. LSMFS uses the feature weight matrix to capture a shared information of different related labels, which mitigates the influence of low-density labels on feature selection. The above principles are transformed into the objective function of LSMFS, and an alternate iterative optimization algorithm is developed to solve the objective function. Experiments on multi-label datasets from different domains have demonstrated the effectiveness of the proposed method LSMFS. Code is released at https://github.com/HQUF/LSMFS.

Digital Twins for Discrete Manufacturing Lines: A Review

Along with the development of new-generation information technology, digital twins (DTs) have become the most promising enabling technology for smart manufacturing. This article presents a statistical analysis of the literature related to the applications of DTs for discrete manufacturing lines, researches their development status in the areas of the design and improvement of manufacturing lines, the scheduling and control of manufacturing line, and predicting faults in critical equipment. The deployment frameworks of DTs in different applications are summarized. In addition, this article discusses the three key technologies of high-fidelity modeling, real-time information interaction methods, and iterative optimization algorithms. The current issues, such as fine-grained sculpting of twin models, the adaptivity of the models, delay issues, and the development of efficient modeling tools are raised. This study provides a reference for the design, modification, and optimization of discrete manufacturing lines.

Derivative-Free Iterative One-Step Reconstruction for Multispectral CT.

Image reconstruction in multispectral computed tomography (MSCT) requires solving a challenging nonlinear inverse problem, commonly tackled via iterative optimization algorithms. Existing methods necessitate computing the derivative of the forward map and potentially its regularized inverse. In this work, we present a simple yet highly effective algorithm for MSCT image reconstruction, utilizing iterative update mechanisms that leverage the full forward model in the forward step and a derivative-free adjoint problem. Our approach demonstrates both fast convergence and superior performance compared to existing algorithms, making it an interesting candidate for future work. We also discuss further generalizations of our method and its combination with additional regularization and other data discrepancy terms.

A Novel Algorithm for Solving High-Dimensional Poisson Equations Based on Radial Basis Function Neural Networks

As a widely used equation in electrostatics, the Poisson equation has significant research value in numerical solution. The basic principle of existing methods is to divide the solution domain into various grids and solve the numerical solutions at each grid node. Therefore, the accuracy of the solution is strongly correlated with the grid density divided. Based on this, this paper proposes a grid-free numerical calculation method that requires far fewer model parameters than traditional methods, and can ignore the order of the equation to solve high-dimensional Poisson equations. Given a Poisson equation, which has a certain type of boundary condition. A certain number of coordinate points are selected on the solution space and its boundary to construct a dataset. Using automatic differentiation technique to fit the differential operator in the equation, a loss function is constructed by incorporating the given boundary conditions or initial conditions, and the final numerical solution is obtained through iterative optimization algorithms. In the numerical experiment section, the algorithm proposed in this paper was used to solve the two-dimensional and three-dimensional Poisson equations with given exact solutions. The relative errors between the numerical solution and the true solution were [Formula: see text] and [Formula: see text], which are within the acceptable range. This proves that the proposed algorithm is feasible for solving the two-dimensional and three-dimensional Poisson equations with precise solutions. Secondly, the proposed algorithm is used to solve the four-dimensional Poisson equation with first-type boundary conditions, and the relative error range of the solution was within [0,0.56], which successfully extends the algorithm to solve high-dimensional Poisson equations and verifies its feasibility and efficiency in solving high-dimensional Poisson equations regardless of the dimension restriction.

Semi-supervised multi-label feature selection based on dual dynamic graph

Traditional multi-label feature selection is usually performed under the condition of given label information, but nowadays, labeling multi-label data is a huge project, which is both time-consuming and labor-intensive, but if there is no label information condition, it will lead to poor feature selection, in order to solve this problem, this paper proposes a new semi-supervised multi-label feature selection method, i.e., semi-supervised multi-label feature selection algorithm based on dual dynamic graph. In this paper, a semi-supervised multi-label feature selection algorithm is proposed by constructing a dual dynamic graph. First, the method selects the most discriminative features for dimensionality reduction through the feature selection method of least squares regression, combined with the redundancy penalty of highly correlated features. Second, the label information is added to the construction of sample matrix similarity to learn the similarity. A semi-supervised multi-label feature selection framework is constructed by designing iterative updates of dual dynamic graphs to learn more accurate pseudo-label matrices to guide feature selection. Finally, the paper validates the above model using the alternating iteration optimization algorithm and verifies the effectiveness of the algorithm through experiments.

Congestion-aware Stackelberg pricing game in urban Internet-of-Things networks: A case study

We consider a one-leader multi-follower Stackelberg pricing game in urban Internet-of-Things networks. The leader manages multiple services and sets service prices to maximize profit, while followers seek the most cost-effective services, taking into account service prices, service congestion, and individual locations. Existing approaches often simplify the game process by neglecting followers’ locations, but they are not applicable to real-world complex spatial distributions. In this paper, we focus on the congestion-aware Stackelberg pricing game in urban Internet-of-Things networks, using electric vehicle charging as a case study. The game is reformulated as a mathematical program with equilibrium constraints (MPEC) that considers both congestion effects and followers’ spatial distributions. To solve the MPEC, we introduce the Segmentation-based Pricing with ITERative Optimization (SPITER) algorithm, which converges to a local maximum. Additionally, optimization techniques are developed to improve the performance of solving SPITER in urban environments. We evaluate the performance of SPITER using extensive experiments with two real-life urban datasets, demonstrating the advantages of our model and illustrating SPITER’s effectiveness and convergence.

Self-paced regularized adaptive multi-view unsupervised feature selection

Multi-view unsupervised feature selection (MUFS) is an efficient approach for dimensional reduction of heterogeneous data. However, existing MUFS approaches mostly assign the samples the same weight, thus the diversity of samples is not utilized efficiently. Additionally, due to the presence of various regularizations, the resulting MUFS problems are often non-convex, making it difficult to find the optimal solutions. To address this issue, a novel MUFS method named Self-paced Regularized Adaptive Multi-view Unsupervised Feature Selection (SPAMUFS) is proposed. Specifically, the proposed approach firstly trains the MUFS model with simple samples, and gradually learns complex samples by using self-paced regularizer. l2,p-norm (0<p≤1) is employed to measure the learning error and as the sparse regularization to accommodate various sparsity requirements across different datasets. Moreover, hypergraph Laplacian matrices are constructed for each view to better preserve the local manifold structure and encode high-order relationships within the data space. They are adaptively assigned weights to learn the underlying correlated and diverse information among different views. An iterative optimization algorithm is proposed to solve SPAMUFS and the convergence and computational complexity are also analyzed. The effectiveness of SPAMUFS is substantiated by comparing with eight state-of-the-art algorithms on nine public multi-view datasets.

Robust condition identification against label noise in industrial processes based on trusted connection dictionary learning

In the era of big data, the pervasive use of artificial intelligence (AI) technology has revolutionized various industries. AI-powered systems, particularly those utilizing data-driven interpretable and reliable methods for accurate condition identification, have emerged as a crucial factor in achieving intelligent industrial systems. However, in real industrial sites, the labels of offline data often contain incorrect labels, i.e. label noise, due to human error, sensor failure, and other sources, which reduces the accuracy of the model and affects the performance and safety of the industrial system. To tackle the challenge of precarious performance caused by label noise, this paper proposes a robust method called Trusted Connection Dictionary Learning (TCDL) which effectively mitigates the adverse effects of label noise through interpretable constraints and guarantees the trustworthiness of the model for industrial applications. Specifically, to address the issue of data structure and label inconsistency arising from label noise, this paper presents a dynamic graph model that jointly optimizes data features and label information to obtain consistent representations of them. Subsequently, to effectively fit the labeled data, TCDL leverages the label information from the nearest neighbors through the optimized graph structure and facilitates the self-correction of label noise, leading to robust representations of process features and a reliable condition classifier. Finally, a novel iterative optimization algorithm that combines the Block Coordinate Descent (BCD) method and the Alternating Direction Multiplier Method (ADMM) is also developed to ensure the convergence of the algorithm. Due to simple constraints, it can obtain accurately optimized variables with few iterations. Numerical simulations and industrial experiments demonstrate the superiority of the proposed method compared to some state-of-the-art methods.

Intelligent Reflecting Surface Assisted Secure Computation of Wireless Powered MEC System

The integration of mobile edge computing (MEC) and wireless power transfer (WPT) can effectively improve the computing ability and energy sustainability of energy-constrained wireless devices in the Internet of Things (IoT) networks. Intelligent reflecting surface (IRS) has recently emerged as an effective technique to improve the performance of wireless systems by intelligently reconfiguring wireless environments. This paper studies the exploitation of IRS to improve the secure computation performance of WPT-MEC systems with a passive eavesdropper. A wireless access point (AP) first charge multiple users with the emitted energy signals, and then the users perform local computing and partial offloading to complete their computation tasks with the harvested energy in the presence of an eavesdropper, where the local computing can be executed during the whole process of WPT and offloading. Meanwhile, deploying IRS can improve the energy capture and secure offloading performance of the users. We maximize the secure computation task bits of users by jointly optimizing the AP energy transmit beamforming, the IRS phase shifts, the transmit power, users' offloading time, and the local computation frequency of users, which are tangled with each other. An iterative optimal algorithm is developed to solve this non-convex problem by combining Taylor expansion method, semidefinite relaxation (SDR) algorithm, the Lagrange duality theory and Karush-Kuhn-Tucker (KKT) conditions. The numerical results show that the proposed scheme can effectively increase the secure computation task bits compared with other benchmark schemes, especially for the maximum transmit power of AP, the improvement is above 45 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> .

Research on Computer-aided Adjustment and Optimization of Train Service Plan based on Passenger Flow Assignment

Abstract According to the complex characteristics of the mutual influence of passenger flows between different train adjustment schemes, a computer-aided train service plan adjustment optimization model based on passenger flow assignment is proposed with the goal of minimizing the remaining passenger turnover. The actual operating effects of trains and the impact between different adjustment measures and between trains are also considered. A computer iterative optimization algorithm with 2 stages based on the greedy principle is designed. The computer processing is divided into two stages: train adjustment plan selection and passenger flow information analysis. The selection of adjustment schemes is feedback-corrected based on the results of passenger flow assignment. Finally, taking the train operation plan of the Beijing-Shanghai high-speed railway as the research object, an example is demonstrated, and the results show that the model and algorithm can effectively obtain the optimal train adjustment scheme under the current conditions.

A new optimal iterative algorithm for solving nonlinear equations

The aim of this paper is to propose a new iterative algorithm (scheme or method) for solving algebraic and transcendental equations considering fixed point and an initial guess value on the x-axis. The concepts of slope of a line and Taylor series are used in the derivation. The algorithm has second-order convergence and requires two function evaluations in each step, which shows that it is optimal with computational efficiency index 1.414 and informational efficiency 1. The validity of the algorithm is examined by solving some examples and their comparisons with the Newton’s method.

Exploring Molecular Energy Landscapes by Coupling the DFTB Potential with a Tree-Based Stochastic Algorithm: Investigation of the Conformational Diversity of Phthalates.

Exploring the global energy landscape of relatively large molecules at the quantum level is a challenging problem. In this work, we report the coupling of a nonredundant conformational space exploration method, namely, the robotics-inspired iterative global exploration and local optimization (IGLOO) algorithm, with the quantum-chemical density functional tight binding (DFTB) potential. The application of this fast and efficient computational approach to three close-sized molecules of the phthalate family (DBP, BBP, and DEHP) showed that they present different conformational landscapes. These differences have been rationalized by making use of descriptors based on distances and dihedral angles. Coulomb interactions, steric hindrance, and dispersive interactions have been found to drive the geometric properties. A strong correlation has been evidenced between the two dihedral angles describing the side-chain orientation of the phthalate molecules. Our approach identifies low-energy minima without prior knowledge of the potential energy surface, paving the way for future investigations into transition paths and states.

Iterative multi-objective design of hydrogen embrittlement resistant high-strength steels using Bayesian optimization

The infiltration of hydrogen can weaken the strength and toughness of materials, especially in high-strength steel. Considering the inherent trade-off between strength and toughness in steel design, balancing these two factors with the material's hydrogen embrittlement sensitivity has become a huge challenge in steel design. The long cycle nature of hydrogen embrittlement testing makes the iteration of traditional trial and error methods infeasible for steel development. This work adopts active learning algorithms based on Bayesian and Pareto optimization to iteratively optimize the chemical composition and processing technology of high-strength steel, in order to simultaneously improve its hydrogen filled tensile strength (UTS_H) and hydrogen filled total elongation (TEL_H). After two rounds of iterative optimization, the iterative optimization algorithm significantly improved the strength prediction of materials after hydrogen charging. The machine learning model found 16 types of steel from over 15 million unknown materials. Eight materials showed better comprehensive performance than known data, with one material having a tensile strength exceeding 1800 MPa and an elongation of 12.6%. Subsequent experiments showed that the optimization algorithm demonstrated an understanding of the impact of austenite content on hydrogen embrittlement sensitivity in multiple experiments, and designed high-strength steel resistant to hydrogen embrittlement through the austenite content of martensitic steel.