Dimensionality Reduction Method Research Articles

A brief review of reduced order models using intrusive and non‐intrusive techniques

AbstractReduced Order Models (ROMs) have gained a great attention by the scientific community in the last years thanks to their capabilities of significantly reducing the computational cost of the numerical simulations, which is a crucial objective in applications like real time control and shape optimization. This contribution aims to provide a brief overview about such a topic. We discuss both a classic intrusive framework based on a Galerkin projection technique and hybrid/non‐intrusive approaches, including Physics Informed Neural Networks (PINN), purely Data‐Driven Neural Networks (NN), Radial Basis Functions (RBF), Dynamic Mode Decomposition (DMD) and Gaussian Process Regression (GPR). We also briefly mention geometrical parametrization and dimensionality reduction methods like Active Subspaces (ASs). Then we test the performance of such approaches in terms of efficiency and accuracy against three academic test cases, the lid driven cavity, the flow past a cylinder and the geometrically parametrized Stanford Bunny. Moreover, we also briefly present some preliminary results related to a more complex case involving an industrial application.

Comparison of dimensionality reduction methods on hyperspectral images for the identification of heathlands and mires

Comparison of dimensionality reduction methods on hyperspectral images for the identification of heathlands and mires

Tracking the topology of neural manifolds across populations

Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising the possibility of studying how these manifolds relate across populations. However, when the manifolds are nonlinear and possibly code for multiple unknown variables, it is challenging to extract robust and falsifiable information about their relationships. We introduce a framework, called the method of analogous cycles, for matching topological features of neural manifolds using only observed dissimilarity matrices within and between neural populations. We demonstrate via analysis of simulations and in vivo experimental data that this method can be used to correctly identify multiple shared circular coordinate systems across both stimuli and inferred neural manifolds. Conversely, the method rejects matching features that are not intrinsic to one of the systems. Further, as this method is deterministic and does not rely on dimensionality reduction or optimization methods, it is amenable to direct mathematical investigation and interpretation in terms of the underlying neural activity. We thus propose the method of analogous cycles as a suitable foundation for a theory of cross-population analysis via neural manifolds.

Peak-Based Machine Learning for Plastic Type Classification in Time-of-Flight Secondary Ion Mass Spectrometry.

Time-of-flight secondary ion mass spectrometry (ToF-SIMS) measurement data and machine learning were used in this work to classify six different types of plastics. In order to take into account the characteristics of the measurement data, the local maxima of the measurement data were first examined in a preprocessing step. Several machine learning methods were then implemented to create a model that could successfully classify the plastics. To visualize the data distribution, we applied a dimensionality reduction method, namely, principal component analysis. Finally, to distinguish between the six types of plastics, we conducted an ensemble analysis using four tree-based algorithms: decision tree, random forest, gradient boosting, and LIGHTGBM. This approach can identify the feature importance of plastic samples and allow the inference of the chemical properties of each plastic type. In this way, ToF-SIMS data could be utilized to successfully classify plastics and enhance explainability.

Simple three-stage control scheme achieving interrupt-free integrated polarization stabilization

It is a long-outstanding challenge to achieve low-complexity interrupt-free integrated polarization stabilization of infinitely changing light. Integrated phase shifters have finite tuning range and experience abrupt switching or reset when reaching the limits of their tuning ranges during the polarization stabilization process. We propose a three-stage interrupt-free integrated polarization stabilization scheme with nested electronic-photonic loops (NEPL) and dimensionality reduction (DR) method. Based on the NEPL structure, only three Mach-Zehnder interferometer (MZI) stages are needed to achieve interrupt-free polarization stabilization scheme. The input state is first constrained into a predetermined range using a nested loops with the first MZI stage and then processed by regular two-stage scheme. Throughout the entire operation, all phase shifters are tuned continuously without any pause, abrupt switching or reset. Furthermore, a DR method is introduced to reduce the control complexity and enhance control speed and accuracy of the regular two-stage scheme. A detailed analysis of the proposed design is provided, and its effectiveness is verified using electronic-photonic co-simulation in the Cadence platform. This scheme consists of only phase shifters, couplers and photodiodes (PDs) with simple electronic controllers, and can be implemented in various material systems and process platforms. To the best of our knowledge, this is the first three-stage interrupt-free polarization stabilization scheme reported in the literature.

Incremental Classification for High-Dimensional EEG Manifold Representation Using Bidirectional Dimensionality Reduction and Prototype Learning.

In brain-computer interface (BCI) systems, symmetric positive definite (SPD) manifold within Riemannian space has been frequently utilized to extract spatial features from electroencephalogram (EEG) signals. However, the intrinsic high dimensionality of SPD matrices introduces too much computational burden to hinder the real-time applications of such BCI, especially in handling dynamic tasks, like incremental learning. Directly reducing the dimensionality of SPD matrices with conventional dimensionality reduction (DR) methods will alter the fundamental properties of SPD matrices. Moreover, current DR methods for incremental learning always necessitate retaining old data to update their representations under new mapping. To this end, a bidirectional two-dimensional principal component analysis for SPD manifold (B2DPCA-SPD) is proposed to reduce the dimensionality of SPD matrices, in such way that the reduced matrices remain on SPD manifold. Afterwards, the B2DPCA-SPD is extended to adapt to incremental learning tasks without saving old data. The incremental B2DPCA-SPD can be seamlessly integrated with the matrix-formed growing neural gas network (MF-GNG) to achieve an incremental EEG classification, where the new low-dimensional representations of the prototypes in old classifiers can be easily recalculated with the updated projection matrix. Extensive experiments are conducted on two public datasets to perform the EEG classification. The results demonstrate that our method significantly reduces computation time by 38.53% and 35.96%, and outperforms conventional methods in classification accuracy by 4.21% to 19.59%.

A new strategy based on multi-source remote sensing data for improving the accuracy of land use/cover change classification.

Land Use/Cover Change (LUCC) plays a crucial role in sustainable land management and regional planning. However, contemporary feature extraction approaches often prove inefficient at capturing critical data features, thereby complicating land cover categorization. In this research, we introduce a new feature extraction algorithm alongside a Segmented and Stratified Principal Component Analysis (SS-PCA) dimensionality reduction method based on correlation grouping. These methods are applied to UAV LiDAR and UAV HSI data collected from land use types (e.g., residential areas, agricultural lands) and specific species (e.g., tree species) in urban, agricultural, and natural environments to reflect the diversity of the study area and to demonstrate the ability of our methods to be applied in different classification scenarios. We utilize LiDAR and HSI data to extract 157 features, including intensity, height, Normalized Digital Surface Model (nDSM), spectral, texture, and index features, to identify the optimal feature subset. Subsequently, the best feature subset is inputted into a random forest classifier to classify the features. Our findings demonstrate that the SS-PCA method successfully enhances downscaled feature bands, reduces hyperspectral data noise, and improves classification accuracy (Overall Accuracy = 91.17%). Additionally, the CFW method effectively screens appropriate features, thereby increasing classification accuracy for LiDAR (Overall Accuracy = 78.10%), HIS (Overall Accuracy = 89.87%), and LiDAR + HIS (Overall Accuracy = 97.17%) data across various areas. Moreover, the integration of LiDAR and HSI data holds promise for significantly improving ground fine classification accuracy while mitigating issues such as the 'salt and pepper noise'. Furthermore, among individual features, the LiDAR intensity feature emerges as critical for enhancing classification accuracy, while among single-class features, the HSI feature proves most influential in improving classification accuracy.

Structure-aware annotation of leucine-rich repeat domains.

Protein domain annotation is typically done by predictive models such as HMMs trained on sequence motifs. However, sequence-based annotation methods are prone to error, particularly in calling domain boundaries and motifs within them. These methods are limited by a lack of structural information accessible to the model. With the advent of deep learning-based protein structure prediction, existing sequenced-based domain annotation methods can be improved by taking into account the geometry of protein structures. We develop dimensionality reduction methods to annotate repeat units of the Leucine Rich Repeat solenoid domain. The methods are able to correct mistakes made by existing machine learning-based annotation tools and enable the automated detection of hairpin loops and structural anomalies in the solenoid. The methods are applied to 127 predicted structures of LRR-containing intracellular innate immune proteins in the model plant Arabidopsis thaliana and validated against a benchmark dataset of 172 manually-annotated LRR domains.

Using a Two-Stage Hybrid Dimensionality Reduction Method on Hyperspectral Data to Predict Chlorophyll Content of Camellia oleifera

Camellia oleifera is an oilseed crop that holds significant economic, ecological, and social value. In the realm of Camellia oleifera cultivation, utilizing hyperspectral analysis techniques to estimate chlorophyll content can enhance our understanding of its physiological parameters and response characteristics. However, hyperspectral datasets contain information from many wavelengths, resulting in high-dimensional data. Therefore, selecting effective wavelengths is crucial for processing hyperspectral data and modeling in retrieval studies. In this study, by using hyperspectral data and chlorophyll content from Camellia oleifera samples, three different dimensionality reduction methods (Taylor-CC, NCC, and PCC) are used in the first round of dimensionality reduction. Combined with these methods, various thresholds and dimensionality reduction methods (with/without further dimensionality reduction) are used in the second round of dimensionality reduction; different sets of core wavelengths with equal size are identified respectively. Using hyperspectral reflectance data at different sets of core wavelengths, multiple machine learning models (Lasso, ANN, and RF) are constructed to predict the chlorophyll content of Camellia oleifera. The purpose of this study is to compare the performance of various dimensionality reduction methods in conjunction with machine learning models for predicting the chlorophyll content of Camellia oleifera. Results show that (1) the Taylor-CC method can effectively select core wavelengths with high sensitivity to chlorophyll variation; (2) the two-stage hybrid dimensionality reduction methods demonstrate superiority in three models; (3) the Taylor-CC + NCC method combined with an ANN achieves the best predictive performance of chlorophyll content. The new two-stage dimensionality reduction method proposed in this study not only improves both the efficiency of hyperspectral data processing and the predictive accuracy of models, but can serve as a complement to the study of Camellia oleifera properties using the Taylor-CC method.

Study on runoff forecasting and error correction driven by atmosphere–ocean-land dataset

Accurate runoff forecasting results can not only provide an important basis for flood control scheduling, but also provide scientific support for water resources optimization, which promotes the maximization of the overall benefits of the basin. To further explore the inherent mechanisms of the atmosphere–ocean-land factors driving runoff changes, this study proposes the factors dimension reduction and interpretation framework based on Pearson, eXtreme Gradient Boosting and SHapley Additive exPlanations (P-XGBoost-SHAP). Base on this, the Gaussian Process Regression (GPR), Long Short-Term Memory neural network (LSTM) and Support Vector Machine (SVM) models are used to construct the atmospheric-ocean-land data-driven runoff prediction model. Meanwhile, for the runoff prediction residuals, this paper proposes an error multi-step correction framework based on ensemble empirical mode decomposition and autoregressive model (EEMD-AR). The case study of Lianghekou hydrological station shows that the factor dimension reduction and interpretation framework can greatly reduce the input dimension of the model, and explain the factors globally and locally by using SHAP Value. Compared with the traditional Random Forest (RF) dimension reduction method, it shows higher prediction accuracy. The Nash-Sutcliffe efficiency coefficient (NSE) can be increased to about 0.93, which is 4.91 % and 1.97 % higher than the series–parallel coupling (AR-Parallel) and empirical mode decomposition-autoregressive (EMD-AR) correction methods, respectively. The accuracy of the runoff forecasting prediction is improved while reducing the input dimension of the model.

Sparse discriminant manifold projections for automatic depression recognition

In recent years, depression has become an increasingly serious problem globally. Previous research have shown that EEG-based depression recognition is a promising technique to serve as auxiliary diagnosis methods that provide assistance to clinicians. Typically, in clinical studies, due to the multichannel nature of EEG, the extracted features usually are high-dimensional and contain many redundant information. Therefore, it is necessary to perform dimensionality reduction before classification to improve the performance of machine learning algorithms. However,existing dimensionality reduction techniques do not design the objective function based on the characteristics of EEG signal and the goal of depression recognition, so they are less suitable for dimensionality reduction of EEG features. To solve this problem, in this paper we propose a novel dimensionality reduction technique called sparse discriminant manifold projections(SDMP) for depression recognition. Specifically, the use of the ℓ2-norm instead of the squared ℓ2-norm as a similarity measure in the objective function reduces sensitivity to noise and outliers. Moreover, the local geometric structure and global discriminative properties of data are integrated, which makes the extracted features more discriminative. Finally, the ℓ2,1-norm regularization is introduced to achieve feature selection. Furthermore, The formulation is extended to the ℓ2,p-norm regularization case, which is more likely to offer better sparsity when 0<p<1. Extensive experiments on EEG data show that the SDMP achieves the competitive performance compared with other state-of-the-art dimensionality reduction methods. It also shows the practical application value of our method in detecting depression.

Genetic ancestry in Puerto Rican afro-descendants illustrates diverse histories of African diasporic populations.

Genetic studies of contemporary Puerto Ricans reflect a demographic history characterized by admixture between Indigenous American, African, and European peoples. While previous studies provide genetic perspectives on the general Puerto Rican population, less is known about the island's sub-populations, specifically Afro-Puerto Ricans. In this study, the genetic ancestry of Afro-Puerto Ricans is characterized and compared to other Caribbean populations. Thirty DNA samples collected among self-identified Puerto Ricans of African descent in Loíza (n = 2), Piñones (n = 13), San Juan (n = 2), Mayagüez (n = 9), and Ponce (n = 4), were genotyped at 750,000 loci on the National Geographic Genochip. We then applied unsupervised clustering and dimensionality-reduction methods to detect continental and subcontinental African and European genetic ancestry patterns. Admixture analyses reveal that on average, the largest genetic ancestry component for Afro-Puerto Ricans is African in origin, followed by European and Indigenous American genetic ancestry components. African biogeographic origins of Afro-Puerto Ricans align most closely with contemporary peoples of Lower Guinea and the Bight of Biafra, while the European genetic ancestry component is most similar to contemporary Iberian, Italian, and Basque populations. These findings contrast with the biogeographic origins of comparative Barbadian and Puerto Rican populations. Our results suggest that while there are similarities with regard to general patterns of genetic ancestry among African descendants in the Caribbean, there is previously unrecognized regional heterogeneity, including among Puerto Rican sub-populations. These results are also consistent with available historical sources, while providing depth absent from the documentary record, particularly with regard to African ancestry.

Predicting susceptibility to COVID-19 infection in patients on maintenance hemodialysis by cross-coupling soluble ACE2 concentration with lymphocyte count: an algorithmic approach

IntroductionPatients on maintenance hemodialysis (MHD) were more vulnerable to and had a higher mortality during the COVID-19 pandemic. As angiotensin converting enzyme 2 (ACE2) and transmembrane protease serine S1 member 2 (TMPRSS2) played crucial roles in viral entry into the human host cells, we therefore investigated in the MHD patients whether their plasma levels were associated with susceptibility to the COVID-19.MethodsBlood samples were collected from the patients in our then COVID-19 free center immediately upon lifting of the stringent quarantine measures in early December of 2022 and infection situation was observed within the following 2 weeks. Plasma levels of the soluble ACE2 (sACE2), ACE (sACE) and TMPRSS2 (sTMPRSS2) were measured with ELISA method. Data were stepwisely tested for independent effect, relevant role and synergistic action on the susceptibility by multiple logistic regression, receiver operating characteristic curve and multiple dimensionality reduction (MDR) method, respectively.ResultsAmong the 174 eligible patients, 95 (54.6%) turned COVID-19 positive with a male to female ratio of 1.57 during the observation period. Comparing with the uninfected, the infected had significantly higher sACE2 and lower sTMPRSS2 levels upon comparable sACE concentration. Besides the sACE2, factors associated with susceptibility were vintage and individual session time of the hemodialysis, smoking and comorbidity of hepatitis, whereas lymphocyte counts showed a tendency (p = 0.052). Patients simultaneously manifesting higher sACE2 level and lower lymphocyte counts had an increased infection risk as confirmed by the MDR method.ConclusionBy sorting out the susceptible ones expeditiously, this algorithmic approach may help the otherwise vulnerable MHD patients weather over future wave of COVID-19 variants or outbreak of other viral diseases.

Rapid detection of oil content in Camellia oleifera kernels based on hyperspectral imaging and machine learning

The oil content (OC) of kernels is one of the primary targets in the breeding of Camellia oleifera. However, the OC determination is labor-consuming and time-costing using traditional methods. In this study, a rapid and efficient OC detecting method was developed based on hyperspectral imaging (HSI). The OCs of 220 C. oleifera clones were first determined using the Soxtec extraction method and hyperspectral images of all samples were obtained. Five spectral preprocessing methods and two dimensionality reduction methods was performed to eliminate hyperspectral noise. Based on the preprocessed spectral and OC data, OC predictive models were developed. The optimal OC prediction model was developed based on the characteristic wavelengths selected by competitive adaptive reweighted sampling from the preprocessed data by Savitzky–Golay smoothing and the first derivative method. The determination coefficient of this model was 0.9383, with a root mean squared error prediction of 1.7921 % and residual predictive deviation of 4.0271. The further validation of this model by the other samples demonstrated it’s robustness and accuracy. The results reveal the potential of HSI in the rapid OC detection in C. oleifera. This will provide reference and guidance for the phenotype collection of C. oleifera.

Research on flood warning model based on dimensionality reduction and integrated neural network

Flood disasters have long-term impacts on human societies and ecosystems, and population growth and urbanization lead to changes in surface conditions that increase the frequency and magnitude of floods. Therefore, understanding and predicting flood probability and constructing a flood warning mechanism are urgent problems. In this paper, a flood warning mechanism based on the probability of flood occurrence is proposed to construct a high-performance and highly interpretable model in a step-by-step manner using machine learning and deep learning methods. First, the correlation level is elucidated by the PCA dimensionality reduction method. Secondly, the K-means clustering method is used to replace the qcut binning method, and the classification model is built by combining the multidimensional data point distribution and classified by polynomial logistic regression. Finally, the integrated neural network model is constructed, the visual model performance is used for full feature optimization, and the performance of the classification model is optimized to achieve the flood prediction effect through the mean square error as the combination of the weights of the integrated model.

Elucidation of endogenous and exogenous chemicals in maternal serum using high-resolution mass spectrometry

The increasing exposure to environmental chemicals calls for comprehensive non-targeted analysis to detect unrecognized substances in human samples. We examined human serum samples to classify compounds as endogenous or exogenous using public databases and to explore the relationships between exposure markers and metabolic patterns. Serum samples from 84 pregnant women at 32 weeks gestation were analyzed using LC-QToFMS. Using the PubChemLite for Exposomics database, we annotated and classified 106 compounds (51 endogenous, 55 exogenous). The compound patterns were analyzed using three dimensional reduction methods: Principal Component Analysis (PCA), regularized Generalized Canonical Correlation Analysis (rGCCA), and Uniform Manifold Approximation and Projection (UMAP). OPTICS clustering applied to these methods revealed two distinct clusters, with 89 % of significant compounds overlapping between clusters. The detected exogenous compounds included dietary substances, phthalates, nitrogenous compounds, and parabens. Pathway enrichment analysis showed that chemical exposure was linked to changes in amino acid metabolism, protein and mineral transport, and energy metabolism. While we found associations between exposure and metabolite changes, we could not establish causality. Our approach of analyzing both exogenous and endogenous chemicals from the same dataset using PubChemLite database presents a new method for exposome research, despite limitations in sample size and peak annotation accuracy. These findings contribute to understanding multiple chemical exposures and their metabolic effects in human biomonitoring.

Industry return volatility and spillover effects in stock market under climate risk perception

ABSTRACT Utilizing alternative dimension reduction methods, this study constructs three Climate Risk Perception Indices (CRPIs) to quantify the impact of investor climate change sentiment on industry return volatility in the Chinese stock market. There are several findings in this study including (1) the CRPIs effectively capture the trend of climate change in China over the past decade. (2) The investor’s attention to climate change positively influences short-term stock market returns, exhibiting seasonal characteristics and industry heterogeneity. (3) The attention serves as an information sender for stocks in Telecommunication, Oil & Petrochemicals, and Environmental Protection. (4) The total spillover effect among climate-sensitive industries is significantly higher during extreme climate events. These conclusions provide empirical evidence for the stock market to respond effectively to climate risks.

Detecting phase transitions based on siamese neural network

Machine learning has been widely applied in physics research. Although unsupervised learning can extract the critical points of phase transitions, the percolation model remains a challenge. Unsupervised learning using the raw configurations of the percolation model fails to capture the critical points. To capture the configuration characteristics of the percolation model, this paper proposes using the maximum cluster as input to the neural network. It is well understood that the order parameter of the percolation model is not simply the particle density, but rather the probability that a given site or bond belongs to the percolating cluster. Additionally, we introduce the use of a Siamese Neural Network (SNN) to detect percolation phase transitions. Unlike unsupervised dimensionality reduction methods or supervised binary classification outputs, the SNN produces a scalar output referred to as similarity. By combining the maximum cluster and the SNN, we not only successfully extract the critical value of the percolation model, but also calculate the correlation exponent via data collapse. We believe that the SNN has great potential in handling phase transition classification problems and can serve as a reference for studying other phase transition systems.

Trace Ratio Based Manifold Learning With Tensor Data

ABSTRACTIn this article, we propose an extension of trace ratio based Manifold learning methods to deal with multidimensional data sets. Based on recent progress on the tensor‐tensor product, we present a generalization of the trace ratio criterion by using the properties of the t‐product. This will conduct us to introduce some new concepts such as Laplacian tensor and we will study formally the trace ratio problem by discussing the conditions for the existence of solutions and optimality. Next, we will present a tensor Newton QR decomposition algorithm for solving the trace ratio problem. Manifold learning methods such as Laplacian eigenmaps, linear discriminant analysis and locally linear embedding will be formulated in a tensor representation and optimized by the proposed algorithm. Finally, we will evaluate the performance of the different studied dimension reduction methods on several synthetic and real world data sets.

A novel inertial parameter identification method for the ship-mounted Stewart platform based on a wave compensation platform

To meet the requirement of time-varying inertial parameter identification of control algorithms for shipborne Stewart wave compensation platforms, this study proposes an innovative inertial parameter identification method based on a non-inertial system. Unlike traditional Stewart identification methods with a fixed frame, the proposed method does not require designing excitation trajectories to consider the condition number of the observation matrix. Namely, the proposed method requires only performing two-dimensional dynamic parameter collection for parameter identification in a six-dimensional non-inertial motion. In addition, a coupling error dimension reduction method is developed to improve the identification accuracy under the condition of coupling motion. Finally, experiments are conducted to verify the effectiveness of the proposed identification method. The experimental results show that under the coupling motion conditions, the coupling errors of the corrected singularity points are reduced by 7.9–28.1% compared to before correction, and the axial force average error correction is below 5.32%.