Maximization Algorithm Research Articles

A new multivariate gamma process model for degradation analysis

AbstractIn reliability engineering, it is frequently encountered that multiple performance characteristics (PCs) deteriorate simultaneously. The associated degradation processes are usually dependent and exhibit some heterogeneity from unit to unit, which makes the multivariate degradation modeling and reliability evaluation more challenging. To this end, we propose a new multivariate gamma process model. This model introduces a multivariate random vector, whose joint distribution is constructed by marginal gamma distributions and a copula function, to describe the unit‐to‐unit variability and the dependence among PCs. Meanwhile, it does not require all PCs to be inspected at the same time points in contrast to the traditional copula‐based degradation models. In addition, two reliability evaluation methods are developed. Model parameters are estimated by the stochastic expectation maximization algorithm, and a three‐step procedure is provided to initialize this algorithm. Subsequently, numerical simulations are implemented to verify the proposed methods. Finally, two examples are provided for illustration, and it is shown that the proposed model and methods scale well to the degradation data with different numbers of PCs. What is more, comparisons with several benchmark models are performed, and the superiority of the proposed model is well demonstrated.

Optimal Allocation of Distributed Generation Using Lightning Search Algorithm for Profit Maximization in a Distribution System

Optimal Allocation of Distributed Generation Using Lightning Search Algorithm for Profit Maximization in a Distribution System

Scalable Distributed Algorithms for Size-Constrained Submodular Maximization in the MapReduce and Adaptive Complexity Models

Scalable Distributed Algorithms for Size-Constrained Submodular Maximization in the MapReduce and Adaptive Complexity Models

Carrier phase error overbounding using Gaussian mixture model for high-precision air navigation integrity monitoring

Carrier phase measurements play a pivotal role in enabling high-precision positioning within future air traffic systems and autonomous vehicles. Current aviation navigation integrity monitoring, primarily using pseudorange measurements, cannot meet system positioning accuracy and integrity requirements, leading to limitations and false alarm risks, especially in complex urban canyons with signal reflections. This work presents a carrier phase-based positioning integrity monitoring algorithm, utilizing the expectation–maximization algorithm to compute parameters for the Gaussian mixture model (GMM) and nonparametric bootstrapping to construct an overbounding model of carrier phase residuals. It establishes a precise protection level (PL) calculation method, which is validated with static and flight data, demonstrating accurate overbounding of carrier phase residuals using GMM. Protection levels during testing remain below the alarm limit and exceed system positioning error, ensuring normal system operation without false or missed alarms, confirming the effectiveness of the established carrier phase error overbounding model.

State Evaluation of Electrical Equipment in Substations Based on Data Mining

This paper explores the combination of a data mining-based state evaluation method for electrical equipment in substations, analyzing the effectiveness and accuracy. First, a Gaussian mixture model is applied to fit all raw data of electrical equipment. The Expectation Maximization algorithm summarizes the data distribution characteristics and identifies outliers. The a priori algorithm is then employed for data mining to derive frequent itemsets and association rules between equipment quality and measurement data. For new equipment samples, conditional probabilities of each feature are independently calculated and combined to classify and evaluate equipment quality. The results suggest that equipment reliability in smart substations can be inferred from historical and real-time operational data using improved association rule algorithms and Naive Bayes classifiers. Finally, the proposed method was applied to analyze statistical data from a 110 kV substation of a power supply company. The states prediction accuracy exceeded 95% when compared with actual equipment quality. The effectiveness evaluation metrics demonstrated that this method outperforms single-category algorithms in terms of accuracy and discrimination ability.

How Gaussian mixture modelling can help to verify reference intervals from laboratory data with a high proportion of pathological values

Abstract Objectives Although there are several indirect methods that can be used to verify reference limits, they have a common weakness in that they assume a low proportion of pathological values. This paper investigates whether a Gaussian decomposition algorithm can identify the non-pathological fraction even if it is not the main subset of mixed data. Methods All investigations are carried out in the R programming environment. The mclust package is used for Gaussian mixture modelling via the expectation maximization (EM) algorithm. For right-skewed distributions, logarithms of the original values are taken to approximate the Gaussian model. We use the Bayesian information criterion (BIC) for evaluation of the results. The reflimR and refineR packages serve as comparison procedures. Results We generate synthetic data mixtures with known normal distributions to demonstrate the feasibility and reliability of our approach. Application of the algorithm to real data from a Nigerian and a German population produces results, which help to interpret reference intervals of reflimR and refineR that are obviously too wide. In the first example, the mclust analysis of hemoglobin in Nigerian women supports the medical hypothesis that an anemia rate of more than 50 % leads to falsely low reference limits. Our algorithm proposes various scenarios based on the BIC values, one of which suggests reference limits that are close to published data for Nigeria but significantly lower than those established for the Caucasian population. In the second example, the standard statistical analysis of creatine kinase in German patients with predominantly cardiac diseases yields a reference interval that is clearly too wide. With mclust we identify overlapping fractions that explain this false result. Conclusions Gaussian mixture modelling does not replace standard methods for reference interval estimation but is a valuable adjunct when these methods produce discrepant or implausible results.

A multivariate student-t process model for dependent tail-weighted degradation data

Traditionally, the Gaussian assumption, implied by the Wiener process, is widely admitted for modeling degradation processes. However, when degradation data exhibit heavy tails, this assumption is not suitable. To overcome this limitation, this article proposes a novel class of tail-weighted multivariate degradation model, which is built upon Student-t process. The model is able to account for both between-unit variability and process dependency, while allowing the adjustment of tail heaviness through tuning the parameter of the degree of freedom. For reliability assessment, we derive the system reliability function and present an efficient Monte Carlo method for its evaluation. Further, we introduce an expectation–maximization algorithm for parameter estimation and design a bootstrap method for interval estimation. Comprehensive simulation studies are conducted to validate the effectiveness of the inference method. Finally, the proposed methodology is applied to analyze two real-world degradation datasets.

A dynamic generative model can extract interpretable oscillatory components from multichannel neurophysiological recordings.

Modern neurophysiological recordings are performed using multichannel sensor arrays that are able to record activity in an increasingly high number of channels numbering in the 100s to 1000s. Often, underlying lower-dimensional patterns of activity are responsible for the observed dynamics, but these representations are difficult to reliably identify using existing methods that attempt to summarize multivariate relationships in a post hoc manner from univariate analyses or using current blind source separation methods. While such methods can reveal appealing patterns of activity, determining the number of components to include, assessing their statistical significance, and interpreting them requires extensive manual intervention and subjective judgment in practice. These difficulties with component selection and interpretation occur in large part because these methods lack a generative model for the underlying spatio-temporal dynamics. Here, we describe a novel component analysis method anchored by a generative model where each source is described by a bio-physically inspired state-space representation. The parameters governing this representation readily capture the oscillatory temporal dynamics of the components, so we refer to it as oscillation component analysis. These parameters - the oscillatory properties, the component mixing weights at the sensors, and the number of oscillations - all are inferred in a data-driven fashion within a Bayesian framework employing an instance of the expectation maximization algorithm. We analyze high-dimensional electroencephalography and magnetoencephalography recordings from human studies to illustrate the potential utility of this method for neuroscience data.

A unified framework of semi-supervised community detection integrating network topology and node content

Detecting the community structure within networks is important because it aids in the analysis of complex networks. However, the existence of diverse complex structures in the network topology can limit the topological information’s ability to represent communities. For instance, the accuracy of many traditional methods based on topology alone decreases sharply when a link is missing or noisy. To solve the above-mentioned issues simultaneously, we propose a unified framework of semi-supervised community detection integrating content information. Three models are proposed, instead of a special model-handling problem. The framework used performs the same interpretation for a target problem. The inputs contain the adjacent and node content matrix. The proposed models describe the network topology using a non-negative matrix factorization (NMF) algorithm–based generative model or modularity maximization algorithm. Additionally, we use the equivalence theory of the pLSI, and NMF models the content information based on NMF. Community membership is also used as the relationship between communities and node contents. The models uniformly integrate content information and network topology. Further, a constraint matrix that depicts must-links is built by calculating the similarity of neighbors between any two nodes. Must-link pairs can represent the network topology’s prior information. The models’ community memberships are adjusted by using a strong constraint based on the connected component of this matrix. The models also introduce prior information into the topological and content information in the mentioned models. We compared the proposed models with the state-of-the-art community detection models on artificial networks and five real networks. The experimental results show that the proposed models outperformed the models combining topology and content and semi-supervised models. Fusing the topology with the content and the prior information in the models was also effective for community detection. Thus, the models under the framework are more advantageous than other semi-supervised models when incorporating the same amount of prior information into the models. The semi-supervised framework used also has a certain level of competitiveness in detecting communities.

Bayesian improved cross entropy method with categorical mixture models for network reliability assessment

We employ the Bayesian improved cross entropy (BiCE) method for rare event estimation in static networks and choose the categorical mixture (CM) as the parametric family to capture the dependence among network components. The proposed method is termed BiCE-CM. At each iteration of BiCE-CM, the mixture parameters are updated through the weighted maximum a posteriori (MAP) estimate, which mitigates the overfitting issue of the standard improved cross entropy (iCE) method through a novel balanced prior, and we propose a generalized version of the expectation–maximization (EM) algorithm to approximate this weighted MAP estimate. The resulting importance sampling distribution is proved to be unbiased. For choosing a proper number of components K in the mixture, we compute the Bayesian information criterion (BIC) of each candidate K as a by-product of the generalized EM algorithm. The performance of the proposed method is investigated through a simple illustration, a benchmark study, and a practical application. In all these numerical examples, the BiCE-CM method results in an efficient and accurate estimator that significantly outperforms the standard iCE method and the BiCE method with the independent categorical distribution.

Spatially explicit supply chain for nationwide CO2-to-fuel infrastructure: Data-driven optimization with Gaussian mixture model -based region screening and clustering

This study proposes a novel machine learning-based method for designing spatially explicit supply chains for establishing a nationwide CO2 utilization strategy. The proposed method is capable of considering not only technical feature for CO2-to-fuel conversion, but also the geographical features for facility allocation by integrating spatial data and various sociological information. To develop the proposed method, map polygonization and the ray-casting algorithm for precise spatial data generation are implemented, which identifies and screens out geographically and socially unfavorable terrains for facility allocation. The scenario evaluation method, which includes the Gaussian mixture model-based expectation–maximization algorithm and supply chain economics, such as transportation price and facility capital investment, are considered to calculate a large set of supply chain scenarios. As a case study, the proposed method is applied to determine the optimal supply chain configuration to secure economic feasibility in the Korean CO2 capture and utilization project. The results identify the hydrogen price as the most critical factor in the supply chain economy and show the potential profitability in 2043–2045. This study can promote the nationwide CO2 reduction strategy and the development of a sustainable energy supply system.

Covariate-dependent spatio-temporal covariance models

Geostatistical regression models are widely used in environmental and geophysical sciences to characterize the mean and dependence structures for spatio-temporal data. Traditionally, these models account for covariates solely in the mean structure, neglecting their potential impact on the spatio-temporal covariance structure. This paper addresses a significant gap in the literature by proposing a novel covariate-dependent covariance model within the spatio-temporal random-effects model framework. Our approach integrates covariates into the covariance function through a Cholesky-type decomposition, ensuring compliance with the positive-definite condition. We employ maximum likelihood for parameter estimation, complemented by an efficient expectation conditional maximization algorithm. Simulation studies demonstrate the superior performance of our method compared to conventional techniques that ignore covariates in spatial covariances. We further apply our model to a PM2.5 dataset from Taiwan, highlighting wind speed’s pivotal role in influencing the spatio-temporal covariance structure. Additionally, we incorporate wind speed and sunshine duration into the covariance function for analyzing Taiwan ozone data, revealing a more intricate relationship between covariance and these meteorological variables.

Minimum cost consensus model with variable cost for multi-criteria large-scale group decision-making considering the tolerance of decision-makers

The objective of multicriteria large-scale group decision-making (LSGDM) is to obtain a decision result that gains acceptance from the majority of decision-makers (DMs). The consensus reaching process (CRP) plays a crucial role in guiding DMs to continuously adjust their opinions through feedback adjustment mechanisms to form a widely accepted decision result. In practical decision-making, adjusting opinions incurs costs and involves limited resources. Simultaneously, DMs have tolerance for modifying their opinions. To this end, this paper proposes a minimum cost consensus model (MCCM) with variable cost to reach consensus efficiently within limited resources and DMs’ tolerance. Firstly, a method to measure the combined similarity among DMs is proposed. Then, an extended local fitness maximization (ELFM) algorithm suitable for multicriteria LSGDM problems is proposed for clustering. Furthermore, an objective method of determining the unit adjustment costs for DMs in the MCCM is provided. For the CRP that considers the tolerance of DMs, this paper introduces the MCCM with variable cost to obtain the adjustment opinions of DMs. During the selection process, we utilize the stochastic multicriteria acceptability analysis (SMAA) method to evaluate alternatives and selection. Finally, the feasibility of the proposed method is verified through an illustrative example, and its advantages are emphasized through comparative analysis.

Influence Maximization Based on Adaptive Graph Convolution Neural Network in Social Networks

The influence maximization problem is a hot issue in the research on social networks due to its wide application. The problem aims to find a small subset of influential nodes to maximize the influence spread. To tackle the challenge of striking a balance between efficiency and effectiveness in traditional influence maximization algorithms, deep learning-based influence maximization algorithms have been introduced and have achieved advancement. However, these algorithms still encounter two key problems: (1) Traditional deep learning models are not well-equipped to capture the latent topological information of networks with varying sizes and structures. (2) Many deep learning-based methods use the influence spread of individual nodes as labels to train a model, which can result in an overlap of influence among the seed nodes selected by the model. In this paper, we reframe the influence maximization problem as a regression task and introduce an innovative approach to influence maximization. The method adopts an adaptive graph convolution neural network which can explore the latent topology information of the network and can greatly improve the performance of the algorithm. In our approach, firstly, we integrate several network-level attributes and some centrality metrics into a vector as the presentation vector of nodes in the social network. Next, we propose a new label generation method to measure the influence of nodes by neighborhood discount strategy, which takes full account of the influence overlapping problem. Subsequently, labels and presentation vectors are fed into an adaptive graph convolution neural network model. Finally, we use the well-trained model to predict the importance of nodes and select top-K nodes as a seed set. Abundant experiments conducted on various real-world datasets have confirmed that the performance of our proposed algorithm surpasses that of several current state-of-the-art algorithms.

Energy-efficient maximization algorithm for energy harvesting under imperfect channel information

In this paper, we propose a novel energy-efficient resource optimization scheme in non-orthogonal multiple access (NOMA) networks with simultaneous wireless information and power transfer (SWIPT). In this system, we consider practical imperfect channel information that accounts for random channel delays and channel estimation errors. Additionally, the small cell users (SCUs) in a heterogeneous network (HetNet) can harvest energy from the small base station (SBS) signal by energy harvesting. Based on the non-linear energy harvesting (NEH) model, the problem of maximizing energy efficiency with imperfect channel state information (CSI) is formulated. Since the formulated problem is a probabilistic mixed non-convex optimization problem, a two-stage algorithm is developed to jointly optimize sub-channel matching and power allocation. In particular, the problem is first transformed into a non-probabilistic problem through the relaxation method. For the sub-channels matching problem, a low-complexity many-to-many matching algorithm is designed to achieve dynamic matching based on the preference lists. For the power allocation problem, the closed-form transmission power of SCUs can be derived by the Dinkelbach method and Lagrangian dual approach. Simulation results show that the proposed scheme can achieve higher energy efficiency than existing linear energy harvesting (LEH)-NOMA and NEH-OFDMA schemes, with improvements of 37.99% and 84.69%, respectively.

Graph learning from incomplete graph signals: From batch to online methods

Inferring graph topologies from data is crucial in many graph-related applications. Existing works typically assume that signals are observed at all nodes, which may not hold due to application-specific constraints. The problem becomes more challenging when data are sequentially available and no delay is tolerated. To address these issues, we propose an approach for learning graphs from incomplete data. First, the problem of learning graphs with missing data is formulated as maximizing the posterior distribution with hidden variables from a Bayesian perspective. Then, we propose an expectation maximization (EM) algorithm to solve the induced problem, in which graph learning and graph signal recovery are jointly performed. Furthermore, we extend the proposed EM algorithm to an online version to accommodate the delay-sensitive situations of sequential data. Theoretically, we analyze the dynamic regret of the proposed online algorithm, illustrating the effectiveness of our algorithm in tracking graphs from partial observations in an online manner. Finally, extensive experiments on synthetic and real data are conducted, and the results corroborate that our approach can learn graphs effectively from incomplete data in both batch and online situations.

A novel finite mixture model based on generalized scale mixtures of generalized normal distributions with application to stock dataset

This paper introduces a novel family of distributions known as generalized scale mixtures of generalized normal distributions (GSMGN). These distributions incorporate two additional shape parameters that serve to regulate the shape and tails of the distribution. A finite mixture model based on this family is presented to address clustering heterogeneous data in the presence of leptokurtic and heavy-tailed outcomes. The estimation of the parameters of this model are obtained by developing an ECM-PLA ensemble algorithm which combine the profile likelihood approach (PLA) and the classical Expectation Conditional Maximization (ECM) algorithm, and the observed information matrix is obtained. The applicability of this new family and the numerical performance of the proposed methodology is discussed through simulated and real data examples.

Throughput maximization algorithm for RIS-aided cognitive backscatter communication networks

Throughput maximization algorithm for RIS-aided cognitive backscatter communication networks

Area extraction and growth monitoring of sugarcane from multi-source remote sensing images under a polarimetric SAR data compensation based on buildings

ABSTRACT Aiming at the issue of low accuracy in crop mapping and growth monitoring caused by imprecise calibration of radar time-series data, this paper proposed a Synthetic Aperture Radar (SAR) spatio-temporal error compensation method. By constructing a compensation reference image using the buildings with stable backscattering coefficients in the study area, the error correction of time-series SAR data was realized based on the compensation model. The compensated SAR data were used to establish the Sugarcane Growth Index (SGI) according to the growth curve of sugarcane. The sugarcane area was extracted after combining the compensated SGI and optical image, and the accuracy of F1 on sugarcane distribution extraction was 92.12%. There was an improvement of 4.11% compared with no compensation method. On this basis, the newly planted and ratoon sugarcane were further classified by the expectation maximization algorithm based on the compensated SAR image at the seedling stage. The newly planted sugarcane and the ratoon sugarcane could be accurately distinguished with area extraction accuracy of 82.06% and 80.59%, respectively. Moreover, the compensated SAR data of time series during the tillering to maturity stages were used to estimate the sugarcane height, yielding an R 2 value of 0.717 using a quadratic polynomial model. The Spatio-temporal error compensation method for distributed targets proposed in this study can reduce the loss of SAR data across various times and regions, and achieve accurate results of sugarcane distribution extraction and plant height estimation.

Analyzing risk influencing factors of ship collision accidents: A data-driven Bayesian network model integrating physical knowledge

The interaction and propagation effects among risk-influencing factors (RIFs) often lead to maritime accidents. Therefore, to support maritime risk management in decision-making, it is imperative to conduct a quantitative risk assessment (QRA) of these accidents, which requires a methodology capable of capturing causal relationships in limited cases. To achieve this goal, this study proposes a data-driven Bayesian network (BN) model that integrates physical knowledge with the QRA. Based on the collected data, a combination of domain knowledge, structure learning, and parameter learning is employed to construct the model. In the data-driven phase, three structural learning algorithms including Bayesian search (BS), Greedy thick thinning (GTT), and Peter-Clark (PC) algorithms, were used in combination with the expectation maximization algorithm of parameter learning. Then, using four indices calculated by the confusion matrix, the most fitting algorithm for structure learning was chosen, and the confusion matrix was obtained by five-fold cross-validation. Finally, network propagation impact (NPI) is introduced to prioritize RIFs. Preventive measures and emergency plans are formulated based on the network resilience metric (NRM) and network vulnerability metric (NVM). This approach leverages the objectivity of a data-driven BN and integrates domain expertise to enhance model validity. A case study of collisions was conducted to demonstrate the applicability of the model. The data were sourced from 327 collision accident reports provided by the China Maritime Safety Administration, and the PC algorithm was chosen. Findings indicate that the “Management system”, “Supervision”, and “Crew training” RIFs are prioritized for preventive measures, whereas “Communication” receives more resources for emergency handling. The results suggest the formulation of risk management strategies for practitioners to improve maritime safety.