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Support Vector Regression (SVR) formulates is an optimization problem to learn a regression function that maps from input predictor variables to output observed response values. The SVR is useful because it balances model complexity and prediction error, and it has good performance for handling high-dimensional data. In this paper, we use the SVR model to improve the principal component analysis and the factor analysis methods. Simulation experiments are performed to assessment the new method. Some useful applications to real data sets are presented for comparing the competitive SVR models. It is noted that with increasing sample size, the -SVR type under the principal component analysis is the best model. However, under the small sample sizes the SVR type under the factor analysis provided adequate results.

In this investigation, the potential of M5P, Random Tree (RT), Reduced Error Pruning Tree (REP Tree), Random Forest (RF), and Support Vector Regression (SVR) techniques have been evaluated and compared with the multiple linear regression-based model (MLR) to be used for prediction of the compressive strength of bacterial concrete. For this purpose, 128 experimental observations have been collected. The total data set has been divided into two segments such as training (87 observations) and testing (41 observations). The process of data set separation was arbitrary. Cement, Aggregate, Sand, Water to Cement Ratio, Curing time, Percentage of Bacteria, and type of sand were the input variables, whereas the compressive strength of bacterial concrete has been considered as the final target. Seven performance evaluation indices such as Correlation Coefficient (CC), Coefficient of determination (R2), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Bias, Nash-Sutcliffe Efficiency (NSE), and Scatter Index (SI) have been used to evaluate the performance of the developed models. Outcomes of performance evaluation indices recommend that the Polynomial kernel function based SVR model works better than other developed models with CC values as 0.9919, 0.9901, R2 values as 0.9839, 0.9803, NSE values as 0.9832, 0.9800, and lower values of RMSE are 1.5680, 1.9384, MAE is 0.7854, 1.5155, Bias are 0.2353, 0.1350 and SI are 0.0347, 0.0414 for training and testing stages, respectively. The sensitivity investigation shows that the curing time (T) is the vital input variable affecting the prediction of the compressive strength of bacterial concrete, using this data set.

Twin support vector regression (TSVR) is generally employed with -insensitive loss function which is not well capable to handle the noises and outliers. According to the definition, Huber loss function performs as quadratic for small errors and linear for others and shows better performance in comparison to Gaussian loss hence it restrains easily for a different type of noises and outliers. Recently, TSVR with Huber loss (HN-TSVR) has been suggested to handle the noise and outliers. Like TSVR, it is also having the singularity problem which degrades the performance of the model. In this paper, regularized version of HN-TSVR is proposed as regularization based twin support vector regression (RHN-TSVR) to avoid the singularity problem of HN-TSVR by applying the structured risk minimization principle that leads to our model convex and well-posed. This proposed RHN-TSVR model is well capable to handle the noise as well as outliers and avoids the singularity issue. To show the validity and applicability of proposed RHN-TSVR, various experiments perform on several artificial generated datasets having uniform, Gaussian and Laplacian noise as well as on benchmark different real-world datasets and compare with support vector regression, TSVR, -asymmetric Huber SVR, -support vector quantile regression and HN-TSVR. Here, all benchmark real-world datasets are embedded with a different significant level of noise 0%, 5% and 10% on different reported algorithms with the proposed approach. The proposed algorithm RHN-TSVR is showing better prediction ability on artificial datasets as well as real-world datasets with a different significant level of noise compared to other reported models.

Better prediction ability is the main objective of any regression-based model. Large margin Distribution Machine for Regression (LDMR) is an efficient approach where it tries to reduce both loss functions, i.e. ε-insensitive and quadratic loss to diminish the effects of outliers. However, still, it has a significant drawback, i.e. high computational complexity. To achieve the improved generalization of the regression model with less computational cost, we propose an enhanced form of LDMR named as Least Squares Large margin Distribution Machine-based Regression (LS-LDMR) by transforming the inequality conditions alleviate to equality conditions. The elucidation is attained by handling a system of linear equations where we need to measure the inverse of the matrix only. Hence, there is no need to solve the large size of the quadratic programming problem, unlike in the case of other regression-based algorithms as SVR, Twin SVR, and LDMR. The numerical experiment has been performed on the benchmark real-life datasets along with synthetically generated datasets by using the linear and Gaussian kernel. All the experiments of presented LS-LDMR are analyzed with standard SVR, Twin SVR, primal least squares Twin SVR (PLSTSVR), ε-Huber SVR (ε-HSVR), ε-support vector quantile regression (ε-SVQR), minimum deviation regression (MDR), and LDMR, which shows the effectiveness and usability of LS-LDMR. This approach is also statistically validated and verified in terms of various metrics.

Abstract This article focuses on electric load forecasting, which is a challenging task in the energy industry. In this paper, a novel kernel-freeν ν -support vector regression model is proposed for electric load forecasting. The proposed model produces a reduced quadratic surface for nonlinear regression. A feature weighting strategy is adopted to estimate the relevance of the features in the load history. To reduce the effects of outliers in the load history, a weight is assigned to represent the relative importance of each data point. Some computational experiments are conducted on some public benchmark data sets to show the superior performance of the proposed model over some widely used regression models. The results of some extensive computational experiments on the electric load data from the Global Energy Forecasting Competition 2012 and the ISO New England demonstrate better average accuracy of the proposed model.

Rivers face increasing pollution, requiring accurate water quality assessment tools. Existing indices like the Water Quality Index (WQI) often overlook the integration of oxygen-related parameters critical to aquatic health. Here, we develop a machine learning model using Support Vector Regression (SVR) to predict the Water Quality Index (WQI OIs ) by integrating key oxygen-related parameters, including Biological Oxygen Demand (BOD), Chemical Oxygen Demand (COD), Dissolved Oxygen (DO), and the reaeration coefficients (K 1 , K 2 ). Applied to three rivers in Iran, the model demonstrated high accuracy, with a cross-validated R² > 0.95 and root mean squared error (RMSE) of 0.92 for the Haraz River and 1.41 for the Simineh River. Predictions showed strong correlation ( r  = 0.98) with standard indices, and feature importance analysis revealed DO as the most influential parameter. The model’s generalizability was confirmed through validation on independent river datasets, highlighting its robustness across diverse hydrological conditions. This approach offers a scalable, interpretable framework for continuous water quality monitoring, enabling more precise and data-driven management of aquatic ecosystems, particularly in regions with varying environmental factors.

Nitrogen (N) is among the main nutrients widely used in agriculture worldwide; however, its administration and management can be challenging. Excess nitrogen is harmful to plant health and the environment, requiring effective monitoring of leaf nitrogen concentration (LNC) in field crops. Remote sensing stands out as a valuable tool in this context. This study contributed to the monitoring of LNC by implementing a machine learning algorithm based on the processing of reflectance data from Sentinel-2 (S2) satellites obtained via spectral resampling. For this purpose, five independent datasets containing leaf reflectance measurements collected by spectroradiometers were resampled to the spectral resolution of the sensors onboard the S2 satellites. LNC prediction models were developed from the resampled datasets, using Support Vector Regression (SVR) and Random Forest Regression (RFR), with 75% of the data from each set used to train a model and the remaining 25% for validation. The models demonstrated good predictive power, with the Root Mean Squared Error (RMSE) ranging from 0.39 to 0.94%. Furthermore, this study investigated the transferability of the models' predictive power by using 100% of the data from each set for training and validating predictions on the other sets. To improve transferability, the Transfer Component Analysis (TCA) technique was applied to adapt domains between the sets. This analysis revealed favorable results, especially with the TCA-SVR and TCA-RFR combinations, highlighting a greater capacity to extract transferable spectral features between different leaf reflectance datasets. It was concluded that spectral resampling does not hinder the development of effective LNC prediction models. Aligning this resampling with the resolution of Sentinel-2 sensors, resulted in more efficient monitoring of LNC, eliminating the need to individually reference each sampling point. This approach simplified the monitoring process, reduced both time and costs, and was directly beneficial to producers.

Datasets with outliers pose a serious challenge in regression analysis. In this paper, a new regression method called relaxed support vector regression (RSVR) is proposed for such datasets. RSVR is based on the concept of constraint relaxation which leads to increased robustness in datasets with outliers. RSVR is formulated using both linear and quadratic loss functions. Numerical experiments on benchmark datasets and computational comparisons with other popular regression methods depict the behavior of our proposed method. RSVR achieves better overall performance than support vector regression (SVR) in measures such as RMSE and \\[R^2_adj\\] while being on par with other state-of-the-art regression methods such as robust regression (RR). Additionally, RSVR provides robustness for higher dimensional datasets which is a limitation of RR, the robust equivalent of ordinary least squares regression. Moreover, RSVR can be used on datasets that contain varying levels of noise.

In twin support vector regression (TSVR), one can notice that the samples are having the same importance even they are laying above the up-bound and below the down-bound on the estimation function for regression problem. Instead of giving the same emphasis to the samples, a novel approach Asymmetric ν-twin support vector regression (Asy-ν-TSVR) is suggested in this context where samples are having different influences with the estimation function based on samples distribution. Inspired by this concept, in this paper, we propose a new approach as improved regularization based Lagrangian asymmetric ν-twin support vector regression using pinball loss function (LAsy-ν-TSVR) which is more effective and efficient to deal with the outliers and noise. The solution is obtained by solving the simple linearly convergent approach which reduces the computational complexity of the proposed LAsy-ν-TSVR. Also, the structural risk minimization principle is implemented to make the problem strongly convex and more stable by adding the regularization term in their objective functions. The superiority of proposed LAsy-ν-TSVR is justified by performing the various numerical experiments on artificial generated datasets with symmetric and heteroscedastic structure noise as well as standard real-world datasets. The results of LAsy-ν-TSVR compares with support vector regression (SVR), TSVR, TSVR with Huber loss (HN-TSVR) and Asy-ν-TSVR, regularization on Lagrangian TSVR (RLTSVR) for the linear and Gaussian kernel which clearly demonstrates the efficacy and efficiency of the proposed algorithm LAsy-ν-TSVR.

In this work, a novel method called epsilon-nonparallel support vector regression (ε-NPSVR) is proposed. The reasoning behind the nonparallel support vector machine (NPSVM) method for binary classification is extended for predicting numerical outputs. Our proposal constructs two nonparallel hyperplanes in such a way that each one is closer to one of the training patterns, and as far as possible from the other. Two epsilon-insensitive tubes are also built for providing a better alignment for each hyperplane with their respective training pattern, which are obtained by shifting the regression function up and down by two fixed parameters. Our proposal shares the methodological advantages of NPSVM: A kernel-based formulation can be derived directly by applying the duality theory; each twin problem has the same structure of the SVR method, allowing the use of efficient optimization algorithms for fast training; it provides a generalized formulation for twin SVR; and it leads to better performance compared with the original TSVR. This latter advantage is confirmed by our experiments on well-known benchmark datasets for the regression task.