Locally Weighted Linear Regression Research Articles

Surface water quality index forecasting using multivariate complementing approach reinforced with locally weighted linear regression model.

River water quality management and monitoring are essential responsibilities for communities near rivers. Government decision-makers should monitor important quality factors like temperature, dissolved oxygen (DO), pH, and biochemical oxygen demand (BOD). Among water quality parameters, the BOD throughout 5 days is an important index that must be detected by devoting a significant amount of time and effort, which is a source of significant concern in both academic and commercial settings. The traditional experimental and statistical methods cannot give enough accuracy or solve the problem for a long time to detect something. This study used a unique hybrid model called MVMD-LWLR, which introduced an innovative method for forecasting BOD in the Klang River, Malaysia. The hybrid model combines a locally weighted linear regression (LWLR) model with a wavelet-based kernel function, along with multivariate variational mode decomposition (MVMD) for the decomposition of input variables. In addition, categorical boosting (Catboost) feature selection was used to discover and extract significant input variables. This combination of MVMD-LWLR and Catboost is the first use of such a complete model for predicting BOD levels in the given river environment. In addition, an optimization process was used to improve the performance of the model. This process utilized the gradient-based optimization (GBO) approach to fine-tune the parameters and better the overall accuracy of predicting BOD levels. To assess the robustness of the proposed method, we compared it to other popular models such as kernel ridge (KRidge) regression, LASSO, elastic net, and gaussian process regression (GPR). Several metrics, comprising root-mean-square error (RMSE), R (correlation coefficient), U95% (uncertainty coefficient at 95% level), and NSE (Nash-Sutcliffe efficiency), as well as visual interpretation, were used to evaluate the predictive efficacy of hybrid models. Extensive testing revealed that, in forecasting the BOD parameter, the MVMD-LWLR model outperformed its competitors. Consequently, for BOD forecasting, the suggested MVMD-LWLR optimized with the GBO algorithm yields encouraging and reliable results, with increased forecasting accuracy and minimal error.

A locally weighted linear ridge regression framework for spatial interpolation of monthly precipitation over an orographically complex area

AbstractThis article aimed to investigate the potential of using three large‐scale precipitation products (PPs), including TRMM, ERA5‐Land, and MSWEP, and two land surface characteristics, including NDVI and Land Surface Temperature (LST), to improve the accuracy of an elevation‐based spatial non‐stationary, Locally Weighted Linear Regression (LWLR) method. A two‐step approach consisting of downscaling and merging was proposed and assessed across an orographically complex region in Iran to construct monthly precipitation maps for the 2001–2015 period. In the first step, three large‐scale PPs were downscaled to 1 km spatial resolution via the Area To Point Kriging (ATPK) method to address the spatial resolution discrepancy between the coarse pixels of PPs and pointwise gauge data. In the second step, five regression models with different combinations of predictors were developed and compared with the benchmark precipitation‐elevation regression model. The L2 regularization method was adopted to overcome the potential multicollinearity issue. The proposed framework could successfully diagnose the multicollinearity issues and dynamically estimate the regularization parameter in space and time. We utilized the holdout method to validate and compare the developed models, in which 50% of gauges were used for fitting the regression functions, and the remaining gauges were assigned to the validation dataset. The validation results showed that the overall monthly accuracy of the benchmark univariate elevation‐based model was improved where the MAE metric was decreased by 16.5%, and CC and KGE were increased by 3.4 and 5.8%, respectively. Also, the rBias was enhanced from −5.72 to 1.24%. Mean monthly precipitation maps of the 2001–2015 period generated by the model with the best combination of predictors and the benchmark model displayed the same spatial pattern consistent with the topography. Further analysis under different validation scenarios revealed that the contribution of PPs and auxiliary variables is the greatest when the training gauge network is sparse. Also, the developed multivariate model has a higher extrapolation ability and is more robust than the benchmark model.

Data-Driven Models for Predicting Solar Radiation in Semi-Arid Regions

Solar energy represents one of the most important renewable energy sources contributing to the energy transition process. Considering that the observation of daily global solar radiation (GSR) is not affordable in some parts of the globe, there is an imperative need to develop alternative ways to predict it. Therefore, the main objective of this study is to evaluate the performance of different hybrid data-driven techniques in predicting daily GSR in semi-arid regions, such as the majority of Spanish territory. Here, four ensemble-based hybrid models were developed by hybridizing Additive Regression (AR) with Random Forest (RF), Locally Weighted Linear Regression (LWLR), Random Subspace (RS), and M5P. The base algorithms of the developed models are scarcely applied in previous studies to predict solar radiation. The testing phase outcomes demonstrated that the AR-RF models outperform all other hybrid models. The provided models were validated by statistical metrics, such as the correlation coefficient (R) and root mean square error (RMSE). The results proved that Scenario #6, utilizing extraterrestrial solar radiation, relative humidity, wind speed, and mean, maximum, and minimum ambient air temperatures as the model inputs, leads to the most accurate predictions among all scenarios (R = 0.968–0.988 and RMSE = 1.274–1.403 MJ/m2⋅d). Also, Scenario #3 stood in the next rank of accuracy for predicting the solar radiation in both validating stations. The AD-RF model was the best predictive, followed by AD-RS and AD-LWLR. Hence, this study recommends new effective methods to predict GSR in semi-arid regions.

Correlation analysis and application investigation of multi-angle simultaneous polarization measurement data and concentration of suspended particulate matter in the atmosphere

Determining the composition, particle size distribution and concentration changes of suspended particulate matter in the atmosphere is important for evaluating the quality of air and its impact on public health. The scattering and absorption of light by suspended particulate matter can change the polarization state of light, which can be used to extract characteristic information of measured particles. Firstly, we use our previously developed multi-angle simultaneous polarization measurement device to monitor the particulate matter around Dianshan Lake, Shanghai, and obtain high-throughput, high-dimensional Stokes data for nearly 1 month. The correlation between the Stokes data measured and the reference concentrations of five suspended particulate matter (Si, K, Fe, Ca, and Zn) was analyzed using the Periodical canonical correlation analysis (PCCA) method. The study shows a strong correlation between the three Stokes vectors and the concentrations of two types of suspended particulate matter in the atmosphere. Moreover, a prediction model for the concentration change of suspended particles was proposed by combining the locally weighted linear regression (LWLR) and the auto regressive moving average (ARMA) model. The prediction results on the concentration change of K and Fe in the atmosphere verified the validity of our method. The research in this work offers the possibility of continuous analysis and prediction of atmospheric suspended particulate matter in real environments.

Predicting Rock Brittleness Using a Robust Evolutionary Programming Paradigm and Regression-Based Feature Selection Model

Brittleness plays an important role in assessing the stability of the surrounding rock mass in deep underground projects. To this end, the present study deals with developing a robust evolutionary programming paradigm known as linear genetic programming (LGP) for estimating the brittleness index (BI). In addition, the bootstrap aggregate (Bagged) regression tree (BRT) and two efficient lazy machine learning approaches, namely local weighted linear regression (LWLR) and KStar approach, were examined to validate the LGP model. To the best of our knowledge, this is the first attempt to estimate the BI through the LGP model. A tunneling project in Pahang state, Malaysia, was investigated, and the requirement datasets were measured to construct the proposed models. According to the results from the testing phase, the LGP model yielded the best statistical indicators (R = 0.9529, RMSE = 0.4838, and IA = 0.9744) for modeling BI, followed by LWLR (R = 0.9490, RMSE = 0.6607, and IA = 0.9400), BRT (R = 0.9433, RMSE = 0.6875, and IA = 0.9324), and KStar (R = 0.9310, RMSE = 0.7933, and IA = 0.9095), respectively. In addition, the sensitivity analysis demonstrated that the dry density factor demonstrated the most effective prediction of BI.

Optimising the Selection of Input Variables to Increase the Predicting Accuracy of Shear Strength for Deep Beams

The deep beam in load transfer is very important as well as difficult to design due to its shear stress problems. Accurate estimation of shear stress would help engineers to get a safer design. One of the major obstacles in building an accurate prediction model is optimising the input variables. Therefore, developing an efficient algorithm to select the optimal input parameters that have the highest information content to represent the target and minimise redundant data is very important. The feature-section algorithm based on the combination of genetic algorithm and information theory (GAITH) was used to select the most important input combinations and introduce them into the prediction models. Four models were used in this study: locally weighted linear regression (LWLR) based on the radial basis kernel function, multiple linear regression (MLR), extreme learning machine (ELM), and random forest (RF). The study found that all applied models were significantly improved by the presence of the GAITH algorithm, except for the MLR model. The LWLR-GAITH model showed 29.15% to 47.88% higher performance accuracy in terms of root mean square error (RMSE) than the other hybrid models during the test phase. Moreover, the results of the standard models (without using the GAITH algorithm) proved the superiority of the LWLR model in reducing the RMSE by 34.51%, 55.17%, and 35.35% compared to RF, MLR, and ELM, respectively. Thus, the inclusion of the LWLR model with GAITH has demonstrated a reliable and applicable computer aid for modelling shear strength in deep beams.

A Local Weighted Linear Regression (LWLR) Ensemble of Surrogate Models Based on Stacking Strategy: Application to Hydrodynamic Response Prediction for Submerged Floating Tunnel (SFT)

Ensemble of metamodels/surrogate models (EM), built based on individual ones, is favoured as an approximation for expensive physical and high-fidelity numerical experiments where individual models with different assumptions on the underlying response functions, datasets, and model structures can be fused more robustly. In this study, a local weighted linear regression (LWLR) approach for constructing the EM, namely the local weighted linear regression ensemble of metamodels (LWLR-EM), is proposed based on the stacking strategy, aiming to address two significant issues in the construction process of EM: 1) it is often unfeasible to obtain sufficient additional points to enhance the performance of EM through high-fidelity numerical simulations and/or physical experiments; 2) underfitting occurs in many cases. To well address these two issues, k-fold cross-validation and local weighted strategies are correspondingly adopted in the metamodel ensembling. Through extensive verification and comparison with existent ensemble methods on typical benchmark test functions, the LWLR-EM is found to perform favourably with competitive accuracy, enhanced robustness, and improved generalization in the prediction task. Thereafter, an engineering practice of submerged floating tunnel (SFT) with five input parameters is considered to further examine the performance of surrogate models. The results show that the proposed LWLR-EM is featured with desirable prediction power and can serve as a competitive alternative in applied ocean engineering.

Assessing machine learning models for streamflow estimation: A case study in Oued Sebaou watershed (Northern Algeria)

This paper proposes rainfall-runoff models based on machine learning to estimate daily streamflows in Oued Sebaou Watershed, a Mediterranean Coastal Basin located in northern Algeria. Therefore, we applied Random Forest (RF), Artificial Neural Networks (ANN) - under different training algorithms -, and Local Weighted Linear Regression (LWLR) using as input combinations of current and past amounts of rainfalls and previous values of streamflow. We selected streamflow and rainfall records to calibrate and validate the stated approaches. The study considered Root Mean Square Error (RMSE) and Correlation Coefficient (R) to evaluate the accuracy of the models. Analyses of the results show that RF provided the best outcomes for both training (RMSE = 4.7458 and R = 0.9834) and validation (RMSE = 2.3617 and R = 0.9719). The ANN calibrated with the Levenberg-Marquardt algorithm presented the second-best result, outperforming its counterparts and LWLR.

An ANN-Based Data Fusion Algorithm for INS/CNS Integrated Navigation System

For INS/CNS integrated navigation system, the performance of data fusion algorithms based on the Kalman filter is seriously degraded when the subsystems have discrepant sampling-frequency. Therefore, a fusion algorithm based on locally weighted linear regression (LWLR), long short-term memory (LSTM), and cubature Kalman filter (CKF) is proposed. First, we construct a deeper coupled INS/CNS system model based on the low-frequency error of the star sensor. Then, during the CNS data sampling interval, LWLR is employed to fit the CNS data, and CKF is used to fuse the fitted CNS data with INS data. And the estimated error calculated using CKF is optimized by LSTM. Finally, the experimental results show that the proposed algorithm suppresses the divergence problem caused by different sampling-frequency and improves the attitude estimation accuracy of the navigation system.

Stacking machine learning models versus a locally weighted linear model to generate high-resolution monthly precipitation over a topographically complex area

This study applied a stacked generalization ensemble approach to generate high-resolution precipitation estimates and compared its performance with an optimized local weighted linear regression (LWLR) algorithm, a well-known local precipitation-elevation interpolation method incorporating physiographical factors. The stacked generalization ensemble consists of multilayer perceptron neural network (MLP), support vector machine (SVM), and random forest (RF) combined through a meta-learning algorithm with/without rescanning input covariates. Sixteen input covariates, including 2 topographic features, 5 cloud properties, 5 environmental variables, 3 precipitation products (PPs), and inverse distance weighted (IDW) estimates as the precipitation background field were fed into the machine learning models. Hold out approach was adopted for performance evaluation in which 50% of the 174 gauges were used for training, and the rest was used for validation. The results indicated that the overall monthly MAE, RMSE, and rBias of the proposed stacking model for the validation dataset were 3.3%, 6.8%, and 50%, respectively, less than that of the RF model, which is the best individual model. Also, the stacking model outperformed LWLR by decreasing monthly MAE, RMSE, and rBias 10.7%, 19.1%, and 28.6%, respectively. Further analysis implied that (1) the stacked model is more robust than LWLR and less dependent on the density of gauges, thus suitable for areas with scarce gauge coverage; (2) comparing the spatial distribution of mean monthly precipitation maps, generated by stacking and LWLR models, stacking algorithm can successfully screen out the bulls' eyes of background IDW precipitation field, and both patterns are consistent with the topography of the area; and (3) the stacking scheme is found to have a better extrapolation ability than LWLR over high elevations.

Prediction of flyrock induced by mine blasting using a novel kernel-based extreme learning machine

Blasting is a common method of breaking rock in surface mines. Although the fragmentation with proper size is the main purpose, other undesirable effects such as flyrock are inevitable. This study is carried out to evaluate the capability of a novel kernel-based extreme learning machine algorithm, called kernel extreme learning machine (KELM), by which the flyrock distance (FRD) is predicted. Furthermore, the other three data-driven models including local weighted linear regression (LWLR), response surface methodology (RSM) and boosted regression tree (BRT) are also developed to validate the main model. A database gathered from three quarry sites in Malaysia is employed to construct the proposed models using 73 sets of spacing, burden, stemming length and powder factor data as inputs and FRD as target. Afterwards, the validity of the models is evaluated by comparing the corresponding values of some statistical metrics and validation tools. Finally, the results verify that the proposed KELM model on account of highest correlation coefficient (R) and lowest root mean square error (RMSE) is more computationally efficient, leading to better predictive capability compared to LWLR, RSM and BRT models for all data sets.

Performance of machine learning methods in predicting water quality index based on irregular data set: application on Illizi region (Algerian southeast)

Groundwater quality appraisal is one of the most crucial tasks to ensure safe drinking water sources. Concurrently, a water quality index (WQI) requires some water quality parameters. Conventionally, WQI computation consumes time and is often found with various errors during subindex calculation. To this end, 8 artificial intelligence algorithms, e.g., multilinear regression (MLR), random forest (RF), M5P tree (M5P), random subspace (RSS), additive regression (AR), artificial neural network (ANN), support vector regression (SVR), and locally weighted linear regression (LWLR), were employed to generate WQI prediction in Illizi region, southeast Algeria. Using the best subset regression, 12 different input combinations were developed and the strategy of work was based on two scenarios. The first scenario aims to reduce the time consumption in WQI computation, where all parameters were used as inputs. The second scenario intends to show the water quality variation in the critical cases when the necessary analyses are unavailable, whereas all inputs were reduced based on sensitivity analysis. The models were appraised using several statistical metrics including correlation coefficient (R), mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE), and root relative square error (RRSE). The results reveal that TDS and TH are the key drivers influencing WQI in the study area. The comparison of performance evaluation metric shows that the MLR model has the higher accuracy compared to other models in the first scenario in terms of 1, 1.4572*10–08, 2.1418*10–08, 1.2573*10–10%, and 3.1708*10–08% for R, MAE, RMSE, RAE, and RRSE, respectively. The second scenario was executed with less error rate by using the RF model with 0.9984, 1.9942, 3.2488, 4.693, and 5.9642 for R, MAE, RMSE, RAE, and RRSE, respectively. The outcomes of this paper would be of interest to water planners in terms of WQI for improving sustainable management plans of groundwater resources.

State-of-health estimation based on real data of electric vehicles concerning user behavior

State of health (SOH) of lithium-ion battery pack directly determines the driving mileage and output power of the electric vehicle. With the development of big data storage and analysis technology, using big data to off-line estimate battery pack SOH is more feasible than before. This paper proposes a SOH estimation method based on real data of electric vehicles concerning user behavior. The charging capacity is calculated by historical charging data, and locally weighted linear regression (LWLR) algorithm is used to qualitatively characterize the capacity decline trend. The health features are extracted from historical operating data, maximal information coefficient (MIC) algorithm is used to measure the correlation between health features and capacity. Then, long and short-term memory (LSTM)-based neural network will further learn the nonlinear degradation relationship between capacity and health features. Bayesian optimization algorithm is used to ensure the generalization of the model when different electric vehicles produce different user behaviors. The estimation method is validated by the 300 days historical dataset from 100 vehicles with different driving behavior. The results indicates that the maximum relative error of estimating SOH is 0.2%.

Application of stacking hybrid machine learning algorithms in delineating multi-type flooding in Bangladesh

Floods are among the most devastating natural hazards in Bangladesh. The country experiences multi-type floods (i.e., fluvial, flash, pluvial, and surge floods) every year. However, areas prone to multi-type floods have not yet been assessed on a national scale. Here, we used locally weighted linear regression (LWLR), random subspace (RSS), reduced error pruning tree (REPTree), random forest (RF), and M5P model tree algorithms in a hybrid ensemble to assess multi-type flood probabilities at a national scale in Bangladesh. We used historical flood data (1988–2020), remote sensing images (e.g., MODIS, Landsat 5–8, and Sentinel-1), and topography, hydrogeology, and environmental datasets to train and validate the proposed algorithms. According to the results, the stacking ensemble machine learning LWLR-RF algorithm performed better than the other algorithms in predicting flood probabilities, with R2 = 0.967–0.999, MAE = 0.022–0.117, RMSE = 0.029–0.148, RAE = 4.48–23.38%, and RRSE = 5.8829.69% for the training and testing datasets. Furthermore, true skill statistics (TSS: 0.929–0.967), corrected classified instances (CCI: 96.45–98.35), area under the curve (AUC: 0.983–0.997), and Gini coefficients (0.966–0.994) were computed to validate the constructed (LWLR-RF) multi-type flood probability maps. The maps constructed via the LWLR-RF algorithm revealed that the proportions of different categories of flooding areas in Bangladesh are fluvial flooding 1.50%, 5.71%, 12.66%, and 13.77% of the total land area; flash floods of 4.16%, 8.90%, 11.11%, and 5.07%; pluvial flooding: 5.72%, 3.25%, 5.07%, and 0.90%; and surge flooding, 1.69%, 1.04%, 0.52%, and 8.64% of the total land area, respectively. These percentages represent low, medium, high, and very high probabilities of flooding. The findings can guide future flood risk management and sustainable land-use planning in the study area.

Measurement of Train Rim Thickness by Machine Learning

The train wheel rim thickness is always manually measured by using handheld devices or in a non-contact way by using laser and image techniques. To reduce the operating costs, this work studied some soft measurement methods with classical machine learning algorithms including neural network (NN), locally weighted linear regression (LWLR), and support vector machine (SVM). By analyzing the correlation between features, it can improve the efficiency of the model. Some approaches were used to optimize the number of hidden layer neurons in NN, parameters in LWLR and SVM. Experiments on real data are conducted, and the results show that the proposed methods can ensure high precision and accuracy, while NN has the highest accuracy.

Kinematic of 4SPRR-SPR parallel robots based on VQTAM

4SPRR-SPR parallel robot is a novel closed-loop mechanism. The research of kinematics is the basis of real-time and robust robot control. This paper aims to proposing a method to address a surrogate model of forward kinematics for PMs (Parallel Mechanisms). Herein, the forward kinematics model is derived by training the VQTAM (Vector-Quantified Temporal Associative Memory) network, which originates from a SOM (Self-Organized Mapping). During the processes of training, testing and estimating this neural network, the priority K-means tree search algorithm is utilized, thus improving the training efficacy. Furthermore, LLR (Local Linear Regression), LWR (Local Weighted Linear Regression) and LLE (Local Linear Embedding) algorithms are respectively combined with VQTAM to get three improvement algorithms, aiming to further optimize the prediction accuracy of the networks. To speed up solving the least squared equation in the three algorithms, SVD (Singular Value Decomposition) is introduced. Finally, Data from inverse kinematics by geometric method is obtained, which is for constructing and validating the VQTAM neural network. Results show that the prediction effect of LLE algorithm is better than others, which could be a potential surrogate model to estimate the output of forward kinematics.

Data-driven early warning model for screenout scenarios in shale gas fracturing operation

In shale gas fracturing operation, proppant screenout is generally recognized as a hazardous operational issue. It affects the performance of hydraulic fracturing horizontal well completion and may lead to downhole accidents. This paper proposes a data-driven early warning method for screenout scenarios based on multi-step forward prediction. Two key contribution of the present work are: development of a prediction model for fracturing pressure by Locally Weighted Linear Regression (LWLR) approach, which parameters are optimised by the integrated PF-ARMA model combining the particle filter (PF) algorithm and the autoregressive moving average (ARMA) model together; proposing a delicate early warning scheme of fracturing screenout event(s) for practical application in the field. The proposed method is tested and fully validated to predict screenout events with satisfying results, which helps to extend the response time for screenout treatment and ensure the long-term safety and integrity of shale gas fracturing operation.

A meticulous intelligent approach to predict thermal conductivity ratio of hybrid nanofluids for heat transfer applications

Accurate estimation of thermal conductivity of hybrid nanofluids is crucial for various engineering and industrial applications. The main objective of this research is to accurately predict the thermal conductivity ratio of hybrid nanofluids in water, ethylene glycol and various volume percentages of ethylene glycol/water as the base fluid. We adopted a novel soft computing technique, namely locally weighted linear regression (LWLR). Furthermore, for better validation, the linear genetic programming (LGP), gene expression programming (GEP) models and numerous empirical correlations were compared with LWLR model. The model outperformed LGP (RMSE = 0.0259, R = 0.964) and GEP (RMSE = 0.0474, R = 0.865) at RMSE = 0.014 and R = 0.988 for the prediction of thermal conductivity of hybrid nanofluids as revealed through performance criteria. Sensitivity analysis showed that the volume fraction, temperature and size of the nanoparticles were the most effective factors among all the inputs in the order of importance. Also, the thermal conductivity of nanoparticle and the mixing ratio of water and ethylene glycol were identified as the least effective factors on the thermal conductivity ratio of hybrid nanofluids assessment.

Predicting the morbidity of chronic obstructive pulmonary disease based on multiple locally weighted linear regression model with K-means clustering

Chronic Obstructive Pulmonary Disease (COPD) is a common chronic respiratory disease related to inflammation affected by harmful gas and particulate matter in the air. Mathematical prediction models between COPD and air pollutants are helpful for early identification, individualized interventions to slow disease progression, and for reduction of medical expenditures. The aim was to build a regression prediction model for the occurrence of COPD acute exacerbation. We collected hospital admissions for COPD in 2015–2018 from ten hospitals in Chongqing, China, used the increment per week as response, and the local sulfur dioxide (SO2), nitrogen dioxide (NO2), carbon monoxide (CO) and particulate matter 2.5 (PM2.5) concentrations as predictor variables to build a multiple prediction model. The Mean Absolute Percentage Error (MAPE) was used to evaluate the efficiency. We found that PM2.5 and SO2 are the most important factors contributing to the improvement of prediction accuracy. Multiple locally weighted linear regression (LWLR) Model based on integrated kernel framework with the K-means algorithm demonstrated minimum prediction error of 9.03 %(k=11).

Learning the Kinematics of a Manipulator Based on VQTAM

The kinematics of a robotic manipulator is critical to the real-time performance and robustness of the robot control system. This paper proposes a surrogate model of inverse kinematics for the serial six-degree of freedom (6-DOF) robotic manipulator, based on its kinematics symmetry. Herein, the inverse kinematics model is derived via the training of the Vector-Quantified Temporal Associative Memory (VQTAM) network, which originates from Self-Organized Mapping (SOM). During the processes of training, testing, and estimating of this neural network, a priority K-means tree search algorithm is utilized, thus improving the training efficacy. Furthermore, Local Linear Regression (LLR), Local Weighted Linear Regression (LWR), and Local Linear Embedding (LLE) algorithms are, respectively, combined with VQTAM to obtain three improvement algorithms, all of which aim to further optimize the prediction accuracy of the networks for subsequent comparison and selection. To speed up the solving of the least squared equation, which is common among the three algorithms, Singular Value Decomposition (SVD) is introduced. Finally, data from forward kinematics, in the form of the exponential product of a motion screw, are obtained, and are used for the construction and validation of the VQTAM neural network. Our results show that the prediction effect of the LLE algorithm is better than others, and that the LLE algorithm is a potential surrogate model to estimate the output of inverse kinematics.