Dimensionality Reduction Model Research Articles

Carbon meets credit: enhancing corporate ratings using principal component analysis and Gaussian mixture models

This study integrates environmental factors, such as carbon emissions and climate-related risks, with traditional financial metrics to enhance corporate credit rating predictions for approximately 2,000 publicly listed Chinese firms. Utilizing Principal Component Analysis (PCA) for dimensionality reduction and Gaussian Mixture Models (GMM) for probabilistic clustering, the approach effectively addresses multicollinearity and captures nuanced financial-environmental relationships. The PCA-GMM framework not only improves predictive accuracy over traditional methods but also maintains high interpretability, making it suitable for complex risk profiles. Empirical results demonstrate that firms with lower carbon emissions and robust financial health receive higher credit ratings, providing valuable insights for investors and policymakers. This model supports sustainable economic growth in alignment with China’s dual carbon goals by highlighting the critical interplay between financial performance and environmental responsibility.

An adaptive learning method for long-term gesture recognition based on surface electromyography.

The surface electromyography (EMG) signal reflects the user's intended actions and has become the important signal source for human-computer interaction. However, classification models trained on EMG signals from the same day cannot be applied for different days due to the time-varying characteristics of the EMG signal and the influence of electrodes shift caused by device wearing for different days, which hinders the application of commercial prosthetics. This type of gesture recogni-tion for different days is usually referred to as long-term gesture recognition.
Approach. To address this issue, we propose a long-term gesture recognition method by optimizing feature extraction, dimensionality reduction, and classification model calibration in EMG signal recognition. Our method extracts differential common spa-tial patterns (CSP) features and then conduct dimensionality reduction with non-negative matrix factorization (NMF), effectively reducing the influence of the non-stationarity of the EMG signals. Based on clustering and classification self-training(CCST) scheme, we select samples with high confidence from unlabeled sam-ples to adaptively updates the model before daily formal use. 
Main results. We verify the feasibility of our method on a dataset consisting of 30 days of gesture data. The proposed gesture recognition scheme achieves accuracy over 90%, similar to the performance of daily calibration with labeled data. However, our method needs only one repetition of unlabeled gestures samples to update the classifi-cation model before daily formal use. 
Significance. From the results we can conclude that the proposed method can not only ensure superior performance, but also greatly facilitate the daily use, which is especially suitable for long-term application.&#xD.

Statistical Analysis of Complex Shape Graphs.

This paper provides developments in statistical shape analysis of shape graphs, and demonstrates them using such complex objects as Retinal Blood Vessel (RBV) networks and neurons. The shape graphs are represented by sets of nodes and edges (articulated curves) connecting some nodes. The goals are to utilize nodes (locations, connectivity) and edges (edge weights and shapes) to: (1) characterize shapes, (2) quantify shape differences, and (3) model statistical variability. We develop a mathematical representation, elastic Riemannian metrics, and associated tools for shape graphs. Specifically, we derive tools for shape graph registration, geodesics, statistical summaries, shape modeling, and shape synthesis. Geodesics are convenient for visualizing optimal deformations, and PCA helps in dimension reduction and statistical modeling. One key challenge lies in comparing shape graphs with vastly different complexities (in number of nodes and edges). This paper introduces a novel multi-scale representation to handle this challenge. Using the notions of (1) "effective resistance" to cluster nodes and (2) elastic shape averaging of edge curves, it reduces graph complexity while retaining overall structures. This allows shape comparisons by bringing graphs to similar complexities. We demonstrate these ideas on 2D RBV networks from the STARE and DRIVE databases and 3D neurons from the NeuroMorpho database.

Joint Sparse Local Linear Discriminant Analysis for Feature Dimensionality Reduction of Hyperspectral Images

Although linear discriminant analysis (LDA)-based subspace learning has been widely applied to hyperspectral image (HSI) classification, the existing LDA-based subspace learning methods exhibit several limitations: (1) They are often sensitive to noise and demonstrate weak robustness; (2) these methods ignore the local information inherent in data; and (3) the number of extracted features is restricted by the number of classes. To address these drawbacks, this paper proposes a novel joint sparse local linear discriminant analysis (JSLLDA) method by integrating embedding regression and locality-preserving regularization into the LDA model for feature dimensionality reduction of HSIs. In JSLLDA, a row-sparse projection matrix can be learned, to uncover the joint sparse structure information of data by imposing a L2,1-norm constraint. The L2,1-norm is also employed to measure the embedding regression reconstruction error, thereby mitigating the effects of noise and occlusions. A locality preservation term is incorporated to fully leverage the local geometric structural information of the data, enhancing the discriminability of the learned projection. Furthermore, an orthogonal matrix is introduced to alleviate the limitation on the number of acquired features. Finally, extensive experiments conducted on three hyperspectral image (HSI) datasets demonstrated that the performance of JSLLDA surpassed that of some related state-of-the-art dimensionality reduction methods.

Abstract 4121812: Longitudinal Trajectory-Based Classification of Heart Failure with preserved Ejection Fraction: A Machine Learning Approach

Background: Heart failure (HF) with preserved ejection fraction (HFpEF) is a complex syndrome characterized by heterogeneous pathophysiology and dynamic changes in cardiac structure and function. Current research predominantly focuses on left ventricular ejection fraction (LVEF) or left ventricular structures with predefined categories. This study hypothesized that applying unsupervised methodologies to longitudinal echocardiography will reveal distinct trajectory patterns in cardiac structure and function related to clinical outcomes in HFpEF patients. Methods: This retrospective cohort study, conducted at UC Davis Medical Center (2014 to 2022), consisted of adult patients with HFpEF. The inclusion criteria included ICD HF codes, a left ventricular ejection fraction (LVEF) ≥50%, and a Brain natriuretic peptide (BNP) ≥100 pg/ml or N-terminal-pro BNP (NT-proBNP) ≥225 pg/ml. Longitudinal data were analyzed using unsupervised machine learning, including UMAP for dimensionality reduction and Gaussian Mixture Models for clustering. Primary and secondary outcomes included all-cause mortality and changes in BNP levels, respectively. Results: The study included 1,626 patients. The cohort had a median age of 69 years, was 57.5% female, and 51.8% white. Three distinct echocardiographic trajectory patterns emerged (p<.05) among the HFpEF cohort. Trajectory #1 (n=568) exhibited a high-stable pattern with the highest mortality rates, Trajectory #2 (n=512) showed a high-decreasing pattern with high mortality rates, and Trajectory #3 (n=546) had a low-increasing pattern with the lowest mortality rates. Trajectories varied significantly in baseline characteristics and longitudinal echocardiographic changes, with Trajectory #3 having a lower baseline left ventricular mass index (p<.001) and a higher mean arterial pressure ( p =.001) compared to the other trajectories. Kaplan-Meier survival analysis indicated significant differences in survival among the trajectories ( p =.004). Conclusion: The study utilized unsupervised analysis of longitudinal echocardiographic data to identify three distinct HFpEF trajectories, each associated with unique clinical features and outcomes. These findings underscore the heterogeneity of HFpEF and highlight the potential trajectory-based patient stratification to improve targeted intervention strategies. Future validation in larger, multicenter cohorts is warranted to enhance HFpEF management and patient prognosis.

A tied-weight autoencoder for the linear dimensionality reduction of sample data

Dimensionality reduction is a method used in machine learning and data science to reduce the dimensions in a dataset. While linear methods are generally less effective at dimensionality reduction than nonlinear methods, they can provide a linear relationship between the original data and the dimensionality-reduced representation, leading to better interpretability. In this research, we present a tied-weight autoencoder as a dimensionality reduction model with the merit of both linear and nonlinear methods. Although the tied-weight autoencoder is a nonlinear dimensionality reduction model, we approximate it to function as a linear model. This is achieved by removing the hidden layer units that are largely inactivated by the input data, while preserving the model’s effectiveness. We evaluate the proposed model by comparing its performance with other linear and nonlinear models using benchmark datasets. Our results show that the proposed model performs comparably to the nonlinear model of a similar autoencoder structure to the proposed model. More importantly, we show that the proposed model outperforms the linear models in various metrics, including the mean square error, data reconstruction, and the classification of low-dimensional projections of the input data. Thus, our study provides general recommendations for best practices in dimensionality reduction.

Bayesian clustering of high-dimensional data via latent repulsive mixtures

SUMMARY Model-based clustering of moderate or large dimensional data is notoriously difficult. We propose a model for simultaneous dimensionality reduction and clustering by assuming a mixture model for a set of latent scores, which are then linked to the observations via a Gaussian latent factor model. This approach was recently investigated by Chandra et al. (2023). The authors use a factor-analytic representation and assume a mixture model for the latent factors. However, performance can deteriorate in the presence of model misspecification. Assuming a repulsive point process prior for the component-specific means of the mixture for the latent scores is shown to yield a more robust model that outperforms the standard mixture model for the latent factors in several simulated scenarios. The repulsive point process must be anisotropic to favour well-separated clusters of data, and its density should be tractable for efficient posterior inference. We address these issues by proposing a general construction for anisotropic determinantal point processes. We illustrate our model in simulations as well as a plant species co-occurrence dataset.

Soft sensor model for endpoint carbon content and temperature in BOF steelmaking based on just-in-time learning with multilayer structure preservation and sparse information enhancement

Ensuring precise prediction of the endpoint carbon content and temperature is paramount in controlling the endpoint of the basic oxygen furnace (BOF) steelmaking process. However, due to the frequent fluctuations in real-time blowing conditions, the conventional just-in-time learning soft sensor approach encounters challenges in effectively anticipating the blowing endpoint. To address these aforementioned issues, this research introduces a novel approach known as the pattern-oriented multilayer structure preservation and sparse information enhancement model (POMLSP-SIE). This approach involves dynamically generating a dataset with the same distribution based on the characteristics of the query sample pattern. It is combined with a multi-pathway dimension reduction model to preserve multi-view spatial geometry information while reducing data dimension. The low-dimensional embedding serves as dictionaries containing various hierarchical structural characteristics. Significant information within these dictionaries is sparsely represented to amplify its influence during the regression prediction process while diminishing the impact of less relevant information. This refinement aims to rectify the problem of static regression models being weak to adapt to changing working conditions, ultimately enhancing prediction performance. The effectiveness of the proposed method is substantiated through an experimental study utilising real converter steelmaking process data, thereby confirming its practical applicability.

A novel dimension reduction model based on POD and two-grid Crank–Nicolson mixed finite element methods for 3D nonlinear elastodynamic sine–Gordon problem

Earthquake, petroleum and gas extraction, and underground nuclear test all could cause nonlinear tectonic deformation. It is of great significance to effectively predict and evaluate the disasters and impacts of these geological structure deformation. In this end, a three-dimension (3D) nonlinear elastodynamic sine–Gordon model that can be used to describe nonlinear tectonic deformation including 3D displacement vector, 3 × 3 symmetric stress tensor matrix, nonlinear sin term, and singular initial value functions is first proposed. Then, a new time semi-discrete mixed Crank–Nicolson (TSDMCN) scheme for the 3D nonlinear elastodynamic sine–Gordon model is developed, and the existence, stability, and error estimates of the TSDMCN solutions are proved. Next, a new two-grid mixed finite element Crank–Nicolson (TGMFECN) method with unconditional stability for the 3D nonlinear elastodynamic sine–Gordon model is developed, and the existence, stability, and error estimates of the TGMFECN solutions are proved. Thenceforth, it is the most important thing is that a novel reduced-dimensional iterative TGMFECN (RDITGMFECN) method in matrix form is established by resorting to proper orthogonal decomposition only to lower the unknown TGMFECN solution coefficient vectors and keep TGMFECN basis functions unchanged, which can ensure that the RDITGMFECN method has the same accuracy as the usual TGMFECN method, but can greatly lower the dimension of the unknown TGMFECN solution coefficient vectors so as to mitigate calculated workload, save CPU operating-time, improve computing efficiency, and improve real-time calculating accuracy. In theory, the existence, stability, and error estimates of RDITGMFECN solutions are demonstrated by matrix analysis such that the theoretical analysis becomes very intuitive and easy to be understood by the public, which is a new attempt of theoretical analysis. In application, two numerical examples are used to simulate the 3D nonlinear tectonic deformation caused by earthquake and to verify the correctness of our theoretical results and the effectiveness of the RDITGMFECN method.

Dynamical mode recognition of coupled flame oscillators by supervised and unsupervised learning approaches

Combustion instability in gas turbines and rocket engines, as one of the most challenging problems in combustion research, arises from the complex interactions among flames influenced by chemical reactions, heat and mass transfer, and acoustics. Identifying and understanding combustion instability is essential for ensuring the safe and reliable operation of many combustion systems, where exploring and classifying the dynamical behaviors of complex flame systems is a core task. To facilitate fundamental studies, the present work concerned dynamical mode recognition of coupled flame oscillators made of flickering buoyant diffusion flames, which have gained increasing attention in recent years but are not sufficiently understood. The time series data of flame oscillators were generated through fully validated reacting flow simulations. Due to the limitations of expertise-based models, a data-driven approach was adopted. In this study, a nonlinear dimensional reduction model of variational autoencoder (VAE) was used to project the high dimensional data onto a 2-dimensional latent space. Based on phase trajectories in the latent space, both supervised and unsupervised classifiers were proposed for datasets with and without well-known labeling, respectively. For labeled datasets, we established the Wasserstein-distance-based classifier (WDC) for mode recognition; for unlabeled datasets, we developed a novel unsupervised classifier (GMM-DTW) combining dynamic time warping (DTW) and Gaussian mixture model (GMM). Through comparing with conventional approaches for dimensionality reduction and classification, the proposed supervised and unsupervised VAE-based approaches exhibit a prominent performance across seven assessment metrics for distinguishing dynamical modes, implying their potential extension to dynamical mode recognition in complex combustion problems.

Preterm Birth in African American Women: A Multi-Omic Pilot Study in Early Pregnancy.

Preterm birth (PTB; <37weeks completed gestation) is a devastating problem affecting over 13 million live births worldwide. In the U.S., African Americans experience significantly higher rates of PTB compared to non-Hispanic Whites. PTB disparities have been linked to social determinants of health (e.g., socioeconomic status, discrimination). However, the biological underpinnings related to these associations are unclear. DNA methylation (DNAm) is subject to environmental influences, and DNAm modifications are known to affect gene expression. Using a multi-omic approach, we examined differences in combined DNA methylation (DNAm) and messenger RNA (mRNA) transcriptomic data from 20 pregnant African American women (12 PTB; 8 term birth) early in pregnancy (8-18weeks gestation). We found that the HLA-DQB2 gene was both differentially methylated (cg12296550; p = .02) and differentially expressed (p = .014; log2FC = 2.5) between women with PTB and term birth. Gene expression analysis showed HLA-DQB2 and HLA-DRB4 (p = .028; log2FC = -3.6) were the two most highly expressed genes. HLA-DQB2 expressed higher in PTB and HLA-DRB4 expressed higher in term birth. However, no genes remained significant (p < .05) after Bonferroni correction. HLA-DRB4 and AKR1C1 were identified as a potential biomarkers in dimensionality reduction models and are also important to immune function and allogenic breakdown. Altered gene expression may lead to inflammatory imbalances or allogenic intolerance resulting in PTB. This study provides proof-of-concept evidence for the feasibility and importance of future multi-omics studies with larger populations to further explore the genes and pathways identified here.

An extended two-parameter mixed-dimensional model of fractured porous media incorporating entrance flow and boundary-layer transition effects

We develop an enhanced reduced model for single-phase flow in fractured porous media capable of incorporating more realistic interface conditions at the fracture terminations. In addition to the traditional dimensional model reduction, where the elements of the discrete fracture network are treated as lower dimensional manifolds embedded in the porous matrix, we explore the microscale behavior of the boundary layer flow at the entrances of a fracture bounded by two parallel plates to construct a new set of interface conditions of Robin-type, giving rise to localized pressure jumps at the fracture edges. Within this enriched description, sharper reduced flow and tracer transport mixed-dimensional models are constructed in the asymptotic limit ruled by two small parameters related to the ratio between fracture aperture and entrance developing length and a macroscopic length scale. The discrete flow/transport mixed-dimensional model is discretized by a new discontinuous Galerkin(dG)-based formulation. An adequate version of the Galerkin-Newton method is developed for the numerical treatment of the non-linear Robin interface condition. Considering several fracture arrangements, numerical results illustrate the sharper description of the model proposed herein in predicting flow and tracer transport patterns in fractured media.

Data-Efficient Dimensionality Reduction and Surrogate Modeling of High-Dimensional Stress Fields

Abstract Tensor datatypes representing field variables like stress, displacement, velocity, etc., have increasingly become a common occurrence in data-driven modeling and analysis of simulations. Numerous methods [such as convolutional neural networks (CNNs)] exist to address the meta-modeling of field data from simulations. As the complexity of the simulation increases, so does the cost of acquisition, leading to limited data scenarios. Modeling of tensor datatypes under limited data scenarios remains a hindrance for engineering applications. In this article, we introduce a direct image-to-image modeling framework of convolutional autoencoders enhanced by information bottleneck loss function to tackle the tensor data types with limited data. The information bottleneck method penalizes the nuisance information in the latent space while maximizing relevant information making it robust for limited data scenarios. The entire neural network framework is further combined with robust hyperparameter optimization. We perform numerical studies to compare the predictive performance of the proposed method with a dimensionality reduction-based surrogate modeling framework on a representative linear elastic ellipsoidal void problem with uniaxial loading. The data structure focuses on the low-data regime (fewer than 100 data points) and includes the parameterized geometry of the ellipsoidal void as the input and the predicted stress field as the output. The results of the numerical studies show that the information bottleneck approach yields improved overall accuracy and more precise prediction of the extremes of the stress field. Additionally, an in-depth analysis is carried out to elucidate the information compression behavior of the proposed framework.

Cross-sectional zero-dimension temperature model for thin-walled circular tubes in space environment

A sufficiently accurate, yet computationally efficient prediction of temperature field is essential for design of spacecraft structures. This paper presents a model dimension reduction method for thermal analysis of thin-walled circular tubes in space environment, which takes into account radiation heat transfer among the internal surfaces besides heat conduction along the circumferential direction and radiative emission from the external surface. Temperature distribution on the tube cross section is approximated by a series of harmonic functions, so that a one-dimensional problem is reduced to that of zero dimension. The relation between average and perturbation temperatures that depend only on time is broadened to fully coupled one. By comparison to the previous model and the plane finite element model, the accuracy and economy of the new model are illustrated. The results show that internal radiation exchange plays an important role in thermal analysis of thin-walled circular tubes used extensively in spacecraft appendages. Furthermore, differences between present and previous models are analyzed and a two-way analysis of variance is performed to determine the effect of various physical and geometric parameters on the temperature distribution and response of the tubes. The work can be further developed to analyze thermally induced deformation and vibration of spacecraft structures.

Deep learning to capture leaf shape in plant images: Validation by geometric morphometrics.

Plant leaves play a pivotal role in automated species identification using deep learning (DL). However, achieving reproducible capture of leaf variation remains challenging due to the inherent "black box" problem of DL models. To evaluate the effectiveness of DL in capturing leaf shape, we used geometric morphometrics (GM), an emerging component of eXplainable Artificial Intelligence (XAI) toolkits. We photographed Ranunculus auricomus leaves directly in situ and after herbarization. From these corresponding leaf images, we automatically extracted DL features using a neural network and digitized leaf shapes using GM. The association between the extracted DL features and GM shapes was then evaluated using dimension reduction and covariation models. DL features facilitated the clustering of leaf images by source populations in both in situ and herbarized leaf image datasets, and certain DL features were significantly associated with biological leaf shape variation as inferred by GM. DL features also enabled leaf classification into morpho-phylogenomic groups within the intricate R. auricomus species complex. We demonstrated that simple in situ leaf imaging and DL reproducibly captured leaf shape variation at the population level, while combining this approach with GM provided key insights into the shape information extracted from images by computer vision, a necessary prerequisite for reliable automated plant phenotyping.

Detection method for chloride ion penetration distribution in concrete based on hyperspectral images and LSTM.

The infiltration of chloride ions corrodes steel reinforcement and causes concrete to crack, reducing the overall bearing capacity and compromising the structure's service life and safety. Timely acquisition of chloride ion distribution is essential for accurately assessing the performance of concrete structures. We present a method for detecting the distribution of chloride ion penetration based on hyperspectral images and long short-term memory (LSTM). First, hyperspectral images of the chloride-ion-permeated split surfaces of the concrete are obtained, and a total of 1000 average spectral data points across 5 categories are collected. The Savitzky-Golay (S-G) data preprocessing algorithm is then applied to reduce spectral noise. Then, we employed a joint Competitive Adaptive Re-weighted Sampling-Principal Component Analysis (CARS-PCA) dimensionality reduction method to identify spectral feature bands highly correlated with concrete chloride distribution. Finally, the LSTM method is utilized to achieve precise classification of the various components of concrete and to accurately identify the distribution of chloride ions. The CARS-PCA dimensionality reduction model, when integrated with an LSTM network, yields superior performance models with an equivalent number of features. This combination achieves a classification accuracy of 93%, reflecting an average improvement of 4.71% over other classification algorithms.

A wee exploration of techniques for risk assessments of extreme events

AbstractAssessing the behaviour of extreme events in univariate and multivariate settings entails many challenges, from the need to capture different sources of non-stationarity to adequately extrapolate into the tail of the distribution and compute probabilities of extreme events associated with high-dimensional vectors. Motivated by these common issues, we use a combination of methods from extreme-value theory, dimensionality reduction, non-parametric statistics, copula theory, and bootstrap model averaging to provide estimates of risk measures associated with environmental extremes. The work is tailored to the four data challenges presented in the EVA (2023) Conference Data Challenge competition, and the methods introduced here represent the approach taken by the Wee Extremes group.

Utilizing X-ray diffraction in conjunction with competitive adaptive reweighted sampling (CARS) and principal component analysis for the discrimination of medicinal pearl powder and nacre powder.

Nacre powder, often utilized to counterfeit medicinal pearl powder due to their similar chemical composition and appearance, poses a challenge in product authentication. This study introduces a rapid and efficient method for distinguishing between medicinal pearl powder and nacre powder using X-ray diffraction in conjunction with principal component analysis (PCA). The X-ray diffraction pattern underwent preprocessing techniques including smoothing denoising (Savitzky-Golay filter, 5-point) and second-order derivative analysis. Subsequently, PCA was employed for dimensionality reduction modeling. The CARS method was applied to select optimal variables for model refinement, determining the data preprocessing approach and key modeling variables. This method demonstrates the capability to accurately differentiate between pearl powder, nacre powder, and even counterfeit samples containing up to 90% pearl powder. With a high accuracy rate, swift operational speed, and potential for automation, this approach shows promise for practical implementation in the realm of pearl powder quality control.

Reproduction of a Digital Avatar using AI Smart Glasses

In response to the rapid development of artificial intelligence, this article is committed to researching the creation of AI glasses that combine augmented reality technology and artificial intelligence big model reasoning ability. The study uses a dimensionality reduction model to record human experiences in multidimensional space, continuously feeds behavioral habits through machine learning, and constructs a virtual digital human that conforms to the characteristics of digital avatars.

A Framework for Prediction of Type II Diabetes through Ensemble Stacking Model

In order to prevent long term complications of diabetes its early diagnosis is crucial. With Increasing advances in Artifical Intelligence (AI) and Machine Learning(ML) researchers are increasingly focusing on using them for early diagnosis of diseases.AI and ML has significant potential for early prediction of type 2 diabetes. In this article we have described a ML based framework for prediction of type 2 diabetes -Improved Ensemble Learning with Dimensionality Reduction Model (IELDR) and discussed its result. An IELDR algorithm is an Auto encoder-based feature extraction method with ensemble learning. The experiments were carried out using the LS_diabetes dataset. LS_diabetes dataset containing 374 records with 35 features related to lifestyle and stress. Accuracy, precision, specificity, sensitivity, f1 score, roc and Mathew correlation coefficient (MCC) were measured. After this results were tested and validated using Diabetes_2019 dataset and PIMA diabetes dataset. The IELDR model showed results in terms accuracy, precision, specificity, sensitivity, f1 score, roc and Mathew correlation coefficient (MCC) of 98.67%, 95.24%, 100%, 98.18%, 97.56%, 99.09% and 0.97 respectively. In comparison with PIMA diabetes dataset, LS_diabetes dataset showed an accuracy, precision, sensitivity, specificity, f1-score,roc and mcc value by 17.96%,13.15% 40.22%,5.59%,28.38%,22.09% and 0.4 respectively. The IELDR model achieved the best result on the LS_diabetes dataset showed an accuracy, sensitivity, roc and mcc value improved by 1.82%, 1.58%, 3.01%and 0.04 % compared to the Diabetes_2019 dataset .This proposed IELDR system predicts the risk of type 2 diabetes in a healthy person based on the person’s current lifestyle pattern. This system can be helpful for early prediction of type2 diabetes.