Dimensionality Reduction Method Research Articles

Random field of homogeneous and multi-material structures by the smoothed finite element method and Karhunen–Loève expansion

A random field of homogeneous and multi-material structures with uncertain scenarios is addressed by constructed the generalized stochastic cell-based smoothed finite element model. Smoothed finite element method (S-FEM) is “Jacobian-free”, which is not only overcomes the limitations of “overly-stiff” and low accuracy of the standard FEM, but also demonstrates strong resistance to mesh distortion. This paper proposes an efficient non-intrusive stochastic smoothed finite element method (SS-FEM) based on cell-based smoothing domains (SD) for the stochastic analysis of elastic problems, which describe much more realistically real physical systems under uncertain scenarios. This SS-FEM starts from the Gaussian random field based on representation related to the spatial variability in material parameters based on the Karhunen-Loève (KL) expansion, and then establishes the basic formulation that considers the effects of uncertainties. A generalized solving framework based on numerical integration is further developed. The non-intrusive dimension reduction method is also adopted to obtain the statistical moments and probability density function. The proposed SS-FEM can capture the structural stochastic responses under uncertainty condition by combining gradient smoothing technology and uncertainty quantification. A number of engineering examples are compared with the solution of Monte Carlo simulation to demonstrate both the accuracy and the efficiency of the proposed method.

Efficient Local Coherent Structure Learning via Self-Evolution Bipartite Graph.

Dimensionality reduction (DR) targets to learn low-dimensional representations for improving discriminability of data, which is essential for many downstream machine learning tasks, such as image classification, information clustering, etc. Non-Gaussian issue as a long-standing challenge brings many obstacles to the applications of DR methods that established on Gaussian assumption. The mainstream way to address above issue is to explore the local structure of data via graph learning technique, the methods based on which however suffer from a common weakness, that is, exploring locality through pairwise points causes the optimal graph and subspace are difficult to be found, degrades the performance of downstream tasks, and also increases the computation complexity. In this article, we first propose a novel self-evolution bipartite graph (SEBG) that uses anchor points as the landmark of subclasses, and learns anchor-based rather than pairwise relationships for improving the efficiency of locality exploration. In addition, we develop an efficient local coherent structure learning (ELCS) algorithm based on SEBG, which possesses the ability of updating the edges of graph in learned subspace automatically. Finally, we also provide a multivariable iterative optimization algorithm to solve proposed problem with strict theoretical proofs. Extensive experiments have verified the superiorities of the proposed method compared to related SOTA methods in terms of performance and efficiency on several real-world benchmarks and large-scale image datasets with deep features.

Comparative Analysis of Manifold Learning-Based Dimension Reduction Methods: A Mathematical Perspective

Manifold learning-based approaches have emerged as prominent techniques for dimensionality reduction. Among these methods, t-Distributed Stochastic Neighbor Embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP) stand out as two of the most widely used and effective approaches. While both methods share similar underlying procedures, empirical observations indicate two distinctive properties: global data structure preservation and computational efficiency. However, the underlying mathematical principles behind these distinctions remain elusive. To address this gap, this study presents a comparative analysis of the subprocesses involved in these methods, aiming to elucidate the mathematical mechanisms underlying the observed distinctions. By meticulously examining the equation formulations, the mathematical mechanisms contributing to global data structure preservation and computational efficiency are elucidated. To validate the theoretical analysis, data are collected through a laboratory experiment, and an open-source dataset is utilized for validation across different datasets. The consistent alignment of results obtained from both balanced and unbalanced datasets robustly confirms the study’s findings. The insights gained from this study provide a deeper understanding of the mathematical underpinnings of t-SNE and UMAP, enabling more informed and effective use of these dimensionality reduction techniques in various applications, such as anomaly detection, natural language processing, and bioinformatics.

On the Use of Dimension-Reduction Methods in Fatigue Analysis of Flexible Risers Subjected to Bimodal Seas

Abstract Fatigue analyses of flexible pipes through the application of long-term response statistics, when considering bimodal seas, are particularly challenging due to the excessive computational costs involved, since they require, generally, to solve numerically a four-dimensional integral associated with time-domain finite element-based analyses of the flexible pipe. This paper investigates different dimension-reduction methods (DRMs) as effective approaches to compute fatigue damage of these structures. The performance of the DRMs was compared with that of the Monte Carlo simulation method (MCSM). Two case studies are presented: a 4 in., and a 7 in., flexible riser connected to a semi-submersible, and a spread-moored floating production storage and offloading unit platform, respectively. The studies demonstrated that some DRMs presented accurate results, exhibiting high efficacy with errors below 3%. Furthermore, the bivariate dimension-reduction method required only 18% of the computational cost associated with the standard Gauss–Hermite quadrature in space R4 (without any reduction), or much less when compared to the MCSM.

A mathematical programming approach to export pathway planning of distributed hydrogen production in offshore wind farm

Hydrogen production is a vital development trend to improve the economics and penetration rate of offshore wind farms (OWFs), and distributed hydrogen production (DHP) is a preferred solution for deep and far sea OWFs without expensive submarine cables and offshore substations. The export pathway of OWF-DHP consists of collection pipelines, transmission pipelines, and offshore compressor stations. In this paper, mathematical programming is introduced to explore the export pathway planning problem of OWF-DHP. Firstly, the area of OWF is discretized into multiple grids with the center of the grids being the candidate locations of the offshore compressor station. Then, a binary integer quadratic programming problem is established to optimize both the offshore compressor station location and pipeline construction with different topologies. Further, the mathematical model is solved by the branch and cut algorithm integrated with the proposed dimension reduction methods. Finally, the effectiveness of the proposed export pathway planning approach is verified by the actual data of Baltic Eagle OWF in Germany, which would support the construction of the OWF-DHP project.

Novel optimal sensor placement method towards the high-precision digital twin for complex curved structures

The complex shape of the structure and the new needs for high-precision in digital twin modeling pose challenges for sensor placement optimization. A novel optimal sensor placement towards the high-precision digital twin (OSP-HDT) method is proposed for complex curved structures. It comprises three key aspects. Firstly, leveraging the spatial dimensionality reduction method, the complex curved surface is simplified into a planar representation. Subsequently, candidate sensor placement points can be easily identified by dividing the background mesh in the plane and screening them within the curved surface. These candidate points are then binary encoded to facilitate the subsequent optimization. Secondly, the method collects result data from the finite element model, treating it as virtual sensor data. Using this data, a surrogate model is constructed and then the objective function is formulated based on both the global and local critical areas precision of the surrogate model. Thirdly, the sensor placement optimization model is constructed, followed by optimization design using the efficient multi-objective covariance matrix adaptive evolutionary strategy. Through the steps above, the optimal sensor placement can be identified. To validate the proposed OSP-HDT method, an experiment is conducted on an S-shaped variable cross-section stiffened shell, with the construction of the corresponding digital twin. Compared to the uniform placement with an equivalent number of sensors, the OSP-HDT method demonstrated a significant 9.0% improvement in global precision and a remarkable 62.1% enhancement in local precision of critical areas. Furthermore, when compared to the random sensor placement strategies, the OSP-HDT method exhibited a 20.5% increase in global precision, together with a 44.2% increase in the local precision. Notably, even when compared to the full sensor placement, the OSP-HDT method can maintain comparable local precision, while significantly reducing the number of sensors by 77.6%. The above comparison indicates that the proposed OSP-HDT method can build a digital twin model with higher global and local precision for complex structures.

What charge-off rates are predictable by macroeconomic latent factors?

Charge-offs provide critical insights into the risk level of loan portfolios within the banking system, signaling potential systemic risks that could lead to deep recessions. Utilizing consolidated financial statements, we have compiled the net charge-off rate (COR) data from the 10 largest U.S. bank holding companies (BHCs) for disaggregated loans, including business loans, real estate loans, and consumer loans, as well as the average COR for each loan category among these top 10 banks. We propose factor-augmented forecasting models for CORs that incorporate latent common factor estimates, including targeted factors, via an array of data dimensionality reduction methods for a large panel of macroeconomic predictors. Our models have demonstrated superior performance compared with benchmark forecasting models, particularly well for business loan and real estate loan CORs, while predicting consumer loan CORs remains challenging especially at short horizons. Notably, real activity factors improve the out-of-sample predictability over the benchmarks for business loan CORs even when financial sector factors are excluded.

A dimension reduction method of two‐grid finite element solution coefficient vectors for the Allen–Cahn equation

This paper mainly focuses on the dimension reduction of unknown finite element (FE) solution coefficient vectors in two‐grid Crank–Nicolson FE (TGCNFE) method for the nonlinear Allen–Cahn equation. For this purpose, a new TGCNFE method for the nonlinear Allen–Cahn equation is first developed and the unconditional stability and errors of TGCNFE solutions are analyzed. Thereafter, the most important thing is to lower the dimension of the unknown FE solution coefficient vectors by a proper orthogonal decomposition, to establish a new reduced‐dimension extrapolated TGCNFE (RDETGCNFE) method, and to analyze the unconditional stability and errors of RDETGCNFE solutions. Moreover, the correctness of our theoretical results is validated by some numerical experiments.

Mass Spectrometry Imaging Combined with Sparse Autoencoder Method Reveals Altered Phosphorylcholine Distribution in Imipramine Treated Wild-Type Mice Brains.

Mass spectrometry imaging (MSI) is essential for visualizing drug distribution, metabolites, and significant biomolecules in pharmacokinetic studies. This study mainly focuses on imipramine, a tricyclic antidepressant that affects endogenous metabolite concentrations. The aim was to use atmospheric pressure matrix-assisted laser desorption/ionization (AP-MALDI)-MSI combined with different dimensionality reduction methods to examine the distribution and impact of imipramine on endogenous metabolites in the brains of treated wild-type mice. Brain sections from both control and imipramine-treated mice underwent AP-MALDI-MSI. Dimensionality reduction methods, including principal component analysis, multivariate curve resolution, and sparse autoencoder (SAE), were employed to extract valuable information from the MSI data. Only the SAE method identified phosphorylcholine (ChoP) as a potential marker distinguishing between the control and treated mice brains. Additionally, a significant decrease in ChoP accumulation was observed in the cerebellum, hypothalamus, thalamus, midbrain, caudate putamen, and striatum ventral regions of the treated mice brains. The application of dimensionality reduction methods, particularly the SAE method, to the AP-MALDI-MSI data is a novel approach for peak selection in AP-MALDI-MSI data analysis. This study revealed a significant decrease in ChoP in imipramine-treated mice brains.

A Comparative Study of Different Dimensionality Reduction Algorithms for Hyperspectral Prediction of Salt Information in Saline–Alkali Soils of Songnen Plain, China

Hyperspectral technology is widely recognized as an effective method for monitoring soil salinity. However, the traditional sieved samples often cannot reflect the true condition of the soil surface. In particular, there is a lack of research on the spectral response of cracked salt-affected soils despite the common occurrence of cohesive saline soil shrinkage and cracking during water evaporation. To address this research, a laboratory was designed to simulate the desiccation cracking progress of 57 soda saline–alkali soil samples with different salinity levels in the Songnen Plain of China. After completion of the drying process, spectroscopic analysis was conducted on the surface of all the cracked soil samples. Moreover, this study aimed to evaluate the predictive ability of multiple linear regression models (MLR) for four main salt parameters. The hyperspectral reflectance data was analyzed using three different band screening methods, namely random forest (RF), principal component analysis (PCA), and Pearson correlation analysis (R). The findings revealed a significant correlation between desiccation cracking and soil salinity, suggesting that salinity is the primary factor influencing surface cracking of saline–alkali soil in the Songnen Plain. The results of the modeling analysis also indicated that, regardless of the spectral dimensionality reduction method employed, salinity exhibited the highest prediction accuracy for soil salinity, followed by electrical conductivity (EC) and sodium (Na+), while the pH model exhibited the weakest predictive performance. In addition, the usage of RF for band selection has the best effect compared with PCA and Pearson methods, which allows salt information of soda saline–alkali soils in Songnen Plain to be predicted precisely.

Enhancing Intrusion Detection with Dimensionality Reduction Methods Using Machine Learning

Enhancing Intrusion Detection with Dimensionality Reduction Methods Using Machine Learning

Neural Network forAutomatic Encryption Using Key Component Analysis to Detect Network Intrusion inCloud Computing

Cloud computing is one of the networks that has attracted more people's attention than other networks in today's world, and the reason for this is that it stores data in itself. This network consists of different computers that are scattered in different places and each user will be able to be a member in this space by registering in it. Among the many important issues related to the environment is the issue of security, which has become a very complex challenge. In order to secure networks, tools have beencreated, and one of these tools is the use of artificial intelligence methods to establish security in this environment. In most of the researches carried out in this field, either the duration of the algorithm execution was very long or the researches did not have enough accuracy, so article, we tried to detect the penetration in cloud computing. This was done in two different scenarios for feature selection and reduction. In one scenario, we reduced the dimensions using the fundamental analysis method, and in the other scenario, we did this using the bat meta-heuristic algorithm. In both scenarios, we used self-encrypting neural network for classification, and the structure of this network was the same in both scenarios. The reason for using these two scenarios was that we want to compare the accuracy obtained and the execution time of the algorithm for the dimensionality reduction method with principal component analysis and meta-heuristic algorithm. , the obtained results showed that the accuracy of the dimension reduction method with the meta-heuristic algorithm was more accurate than the principal component analysis method, but its execution time was approximately 13 minutes more than the principal component analysis method.

Biophysical essentials – A full stack open-source software framework for conserved and advanced analysis of patch-clamp recordings

Background and ObjectivesPatch-Clamp recordings allow for in depth electrophysiological characterization of single cells, their general biophysical properties as well as characteristics of voltage- and ligand-gated ionic currents. Different acquisition modes, such as whole-cell patch-clamp recordings in the current or voltage clamp configuration, capacitance measurements or single channel recordings from cultured cells as well as acute brain slices are routinely performed for these purposes. Nevertheless, multipurpose transparent and adaptable software tools to perform reproducible state-of-the-art analysis of multiple experiment types and to manage larger sets of experimental data are currently unavailable. MethodsBiophysical Essentials (BPE) was developed as an open-source full stack python software for transparent and reproducible analysis of electrophysiological recordings. For validation, BPE results were compared with manually analyzed single-cell patch-clamp data acquired from a human in vitro nociceptor-model and mouse dorsal root ganglia neurons. ResultsWhile initially designed to improve time consuming and repetitive analysis steps, BPE was further optimized as a technical software solution for entire workflow processing including data acquisition, data preprocessing, normalization and visualization and of single recordings up to stacked calculations and statistics of multiple experiments. BPE can operate with different file formats from different amplifier systems and producers. An in-process database logs all analysis steps reproducible review and serves as a central storage point for recordings. Statistical testing as well as advanced analysis functions like Boltzmann-fitting and dimensional reduction methods further support the researchers' needs in projects involving electrophysiology techniques. ConclusionsBPE extends beyond available patch-clamp specific, open source – and commercial analysis tools in particular because of reproducible and sharable analysis workflows. BPE enables full analysis from raw data acquisition to publication ready result visualizations – all within one single program. Thereby, BPE significantly enhances transparency in the analytical process of patch-clamp data analysis. BPEs function scope is completely accessible through an easy-to-use graphical user interface eliminating the need for programing language proficiency as required by many community patch-clamp analysis frameworks and algorithms.

Classification Model for Real-Time Monitoring of Machining Status of Turned Workpieces

The occurrence of tool chatter can have a detrimental impact on the quality of the workpiece. In order to improve surface quality, machining stability, and reduce tool wear cycles, it is essential to monitor the workpiece machining process in real time during the turning process. This paper presents a tool chatter state recognition model based on a denoising autoencoder (DAE) for feature dimensionality reduction and a bidirectional long short-term memory (BiLSTM) network. This study examines the feature dimensionality reduction method of the DAE, whereby the reduced-dimensional data are concatenated and input into the BiLSTM model for training. This approach reduces the learning difficulty of the network and enhances its anti-interference capability. Turning experiments were conducted on a SK50P lathe to collect the dataset for model performance validation. The experimental results and analysis indicate that the proposed DAE-BiLSTM model outperforms other models in terms of prediction and classification accuracy in distinguishing between stable machining, over-machining, and severe chatter stages in turning chatter state recognition. The overall classification accuracy reached 96.28%.

On the long-term fatigue analysis of marine structures

This paper investigates the performance of several procedures available in literature used to evaluate the multi-dimensional integral associated with long-term fatigue assessment of marine structures. Direct integration methods, Monte Carlo-based approaches and Dimension-Reduction methods are investigated. The focus is on solving the four-dimensional integral for wave-induced fatigue cases when wind-sea and swell waves are simultaneously considered in the analysis. Although the procedures investigated can be used either for time-domain or frequency-domain fatigue approaches, all fatigue analyses performed in this work are restricted to the frequency-domain and are based on idealized stress transfer functions that attempt to mimic the complex behavior of some marine structures. To evaluate the performance of these methodologies, different transfer functions of unimodal and bimodal types are studied. The long-term fatigue damages are calculated using all the investigated methods, and their accuracies and efficiencies are compared. It is found that the efficiency of Monte Carlo Simulation-based methods is problem-dependent and may require many numerical simulations to achieve good accuracy for some cases. Additionally, the Dimension-Reduction methods can lead to highly suitable results with a very low number of integration points and, among all methods investigated, the BDRM (Bivariate Dimension-Reduction Method) stands out due to its excellent performance.

An optimization framework with dimensionality reduction using Markov Chain Monte Carlo and genetic algorithms for groundwater potential assessment

Limited samples and high-dimensional feature spaces often hinder the accuracy of machine learning (ML) models in regional groundwater potential assessment (GPA). This study proposes a novel framework, the GPA with Dimensionality Optimization (GPADO), that optimizes feature dimension reduction to enhance prediction performance. Taking the Jianghan Basin as an example, data on nine continuous variables and five categorical variables influencing the region's GPA were gathered, expanding the feature set to 37 through One-hot encoding for categorical variables. Three scenarios were devised to assess prediction outcomes following various dimensionality reduction approaches. Comparative analysis revealed that a hybrid dimension reduction method, incorporating both continuous and categorical variables, yielded the highest validation set accuracy. Consequently, genetic algorithm and Markov Chain Monte Carlo methods were employed to determine the optimal solution and uncertainties associated with four unknown parameters: the chosen dimension reduction method for continuous and categorical variables, and the number of dimensions retained. Results indicated that utilizing singular value decomposition to reduce categorical variables to three dimensions, coupled with principal component analysis reducing continuous variables to three dimensions, produced the highest model validation accuracy of 0.834 within the GPADO framework. This optimal configuration facilitated automated ML training, resulting in a final validation set accuracy of 0.851 and a test set accuracy of 0.836. The resulting model provided a more precise spatial distribution of groundwater potential and demonstrated the GPADO framework's effectiveness in improving GPA accuracy, particularly in data-scarce regions. The GPADO framework offers a valuable approach for enhancing GPA studies.

Multi-label feature selection based on nonlinear mapping

Feature selection is one of the important pre-processing methods for dimensionality reduction in multi-label learning tasks, which has attracted extensive attention in recent years. Most of the existing approaches transform feature data into the label space during the feature-label mapping process by assuming linear relationship between the feature and label spaces. However, the linearity assumption does not hold in most cases, especially for high-dimensional spaces. This work proposes a novel dimension reduction model for multi-label data by using nonlinear mapping (NMFS). The model introduces a point-to-point sigmoid function to describe the intrinsic relationship from data space to label space. The proposed method improves the generalization ability of feature selection by limiting the range of data transformation to the interval [0,1] which is consistent with the predicted values of the labels. The feature weight matrix is constrained by the l2,1-norm to ensure its sparsity, which forms the basis of feature selection. The variables in the NMFS model are iteratively updated using the gradient momentum optimization strategy, and a sparse weight-coefficient matrix is obtained for multi-label feature ordering. Experimental results on 14 multi-label data sets verify the effectiveness of the proposed method, and show the proposed method is superior to the most advanced multi-label feature selection methods.

PARE: A framework for removal of confounding effects from any distance-based dimension reduction method.

Dimension reduction tools preserving similarity and graph structure such as t-SNE and UMAP can capture complex biological patterns in high-dimensional data. However, these tools typically are not designed to separate effects of interest from unwanted effects due to confounders. We introduce the partial embedding (PARE) framework, which enables removal of confounders from any distance-based dimension reduction method. We then develop partial t-SNE and partial UMAP and apply these methods to genomic and neuroimaging data. For lower-dimensional visualization, our results show that the PARE framework can remove batch effects in single-cell sequencing data as well as separate clinical and technical variability in neuroimaging measures. We demonstrate that the PARE framework extends dimension reduction methods to highlight biological patterns of interest while effectively removing confounding effects.

An adaptive dimension-reduction Chebyshev metamodel

An adaptive dimension-reduction Chebyshev metamodel (ADC) is proposed to balance the accuracy and efficiency of dimension-reduction Chebyshev metamodels. A univariate dimension-reduction Chebyshev metamodel (UDC) is constructed by the dimension-reduction method and the Chebyshev metamodel. Based on the UDC, the bivariate terms largely impacting the metamodel are selected using an adaptive selection method, and are combined with the UDC to construct the ADC. The ADC has higher accuracy than the UDC because more calculated sample points are added. Compared with the bivariate dimension-reduction Chebyshev metamodel, the ADC needs fewer sample points and has higher efficiency. The result of numerical examples illustrate that ADC has higher accuracy compared with other commonly-used metamodels and is more suitable for approximating high-dimensional complex models.

Impact of Dimensionality Reduction Method in Brain Tumor Classification Using Transfer Learning

Impact of Dimensionality Reduction Method in Brain Tumor Classification Using Transfer Learning