Linear Kernel Research Articles

Reproducing property of bounded linear operators and kernel regularized least square regressions

We consider bounded linear operators from the view of functional reproducing property. For some bounded linear operators associated with orthogonal polynomials we define an inner product space associated with a kernel constructed with orthogonal polynomials, show that it is a functional reproducing kernel Hilbert space (FRKHS) associated with these bounded linear operators and give decay rate for the best FRKHS approximation with a [Formula: see text]-functional associated with the FRKHS. On this basis, we provide a learning rate for kernel regularized regression whose hypothesis space is the defined FRKHS. As applications, we define some concrete FRKHSs associated with polynomial operators such as the Bernstein–Durrmeyer operators, the de la Vallée Poussin operators on both the unit sphere [Formula: see text] and the unit ball [Formula: see text]. We show that these polynomial operators have reproducing property with respect to the corresponding concrete FRKHSs and show the learning rate for the kernel regularized regression. In short, we provide a way of constructing FRKHS operators with Fourier multipliers and show a learning framework from the view of operator approximation.

Machine learning-based electricity theft detection using support vector machines

Electricity theft is a serious issue that many nations face, especially in developing areas where non-technical losses can make up a significant percentage of the overall losses sustained by utilities. Electricity theft detection (ETD) is a very challenging task because it frequently introduces irregularities in customer electricity consumption patterns. In recent times, machine learning (ML) techniques have been investigated as a potential solution for ETD. In this research, author propose electricity theft detection based on four kernel functions of support vector machines (SVM). The proposed method analyzes the electricity consumption patterns and then predicts the category of the user. The kernel functions utilized includes polynomial, sigmoid, radial basis function (RBF) and linear kernel function. For experimentation and model training, a dataset of Pakistani utility company is used, which contains the electricity consumption information. The results highlight SVM method works well for accurate ETD. The detection accuracy of the various kernel functions of SVM is 83%, 79%, 80%, and 76% for RBF, polynomial, sigmoid, and linear kernel functions, respectively, demonstrating the effectiveness of the proposed SVM-based method for theft detection. By leveraging these ML-based methods, utility companies can strengthen their ability to detect and prevent electricity theft, leading to improved revenue management and dependability of services.

Efficacy of Machine Learning Techniques in Diagnosing Urinary Tract Infections: A Study Utilizing a Philippine Clinical Dataset

This research delves into the potential of machine learning models, namely Support Vector Machine (SVM), XGBoost, and LightGBM, to enhance the diagnosis of Urinary Tract Infections (UTIs) based on a comprehensive dataset collected from a local clinic in Northern Mindanao, Philippines, spanning from April 2020 to January 2023. The study integrates clinical variables such as age, gender, and various urine test results including color, transparency, and the presence of substances like glucose, protein, and cells, to determine the most accurate diagnostic model. The dataset presented unique preprocessing challenges, such as converting infant ages into decimal numbers. The SVM with a linear kernel showed remarkable test accuracy of 98.25%, indicating its robustness in handling linear separability in the data. Meanwhile, XGBoost and LightGBM, both with optimal hyperparameter configurations, achieved comparable accuracies of 97.95%. These results underscore the significance of machine learning in medical diagnostics, particularly in settings where swift and reliable decision-making is crucial. Our findings suggest that while ensemble methods like XGBoost and LightGBM are powerful tools for complex datasets, a well-tuned SVM can provide superior accuracy, thus advocating for a data-centric approach in model selection.

Application of the Support Vector Regression Method with the Grid Search Algorithm to Predict Movement Gold Price

Gold is an investment with the smallest risk because it can be sold anytime and anywhere. In Indonesia, gold bullion as an investment product is known for its purity level of 99.99%, namely gold bullion produced by PT. Aneka Tambang (Antam) through its Precious Metals business unit. Apart from its pure production, Antam gold bullion is easier to resell anytime and anywhere because it has an official certificate from the international gold standardisation institution, namely LBMA (London Bullion Market Association), to more easily estimate the value of gold bullion when sold. To overcome this, predictions of future gold prices are needed. In this research, one of the prediction methods is Support Vector Regression with the Grid Search Algorithm. In this method this method will be used to predict the price of gold, which aims to predict and find out the price of gold one year in the future to produce a level accuracy (MAPE) of 5.43% and the prediction of gold prices increasing from 2023-June-01 to 2024-March-23 while experiencing a decline starting in 2024-March-24. Research by examining the relationship between variables, which emphasises data consisting of numbers so that it is analysed based on statistical procedures using the Support Vector Regression method with data sourced from the daily price of gold bullion through PT. Gallery 24 Pawnshops, North Sumatra. Where this method is very well used in predicting by choosing the best kernel used is the linear kernel because, from these three kernels, the best hyperparameters were obtained for predicting gold price movements using a linear kernel with a division for training and testing data of 60: 40. The MAPE value obtained was 5.43.

Machine Learning-Based Predictions of Porosity during Cold Spray Deposition of High Entropy Alloy Coatings

Porosity poses a challenge to the mechanical properties of cold sprayed coatings, especially when it is open or surface-connected, limiting the coatings’ capabilities to act as a barrier. The porosity formation is dependent on the feedstock powder characteristics and the cold spray process parameters. We present a machine learning-based approach to predict porosity based on the above-mentioned factors. Nine different machine learning models based on linear regression (LR), decision trees, random forests, gradient boosting, support vector machine (SVM), and neural networks were explored. Considering the excellent properties of high entropy alloys, Cantor alloy was taken as the consumable. Our dataset, derived from the literature and experiments, identified SVM with a linear kernel and LR as the top-performing models based on the Pearson correlation coefficient (PCC) and root mean square error, where the PCC values exceeded 0.8. The SHapley Additive exPlanations method helped in identifying that the type of gas and powder are the top two factors in pore formation.

Study on detecting main ingredients of silicone rubber based on terahertz spectrum

AbstractThe authors investigated the ingredient detection technique of silicone rubber based on the Terahertz spectrum. For this purpose, 18 diverse high‐temperature vulcanised silicone rubber (HTVSR) formulations were customised, 8 of which are used as calibration set while the rest 10 as prediction set. Based on the Beer‐Lambert Law, the partial‐least‐square (PLS) regression model and the least‐squares support‐vector machines (LS‐SVM) regression model were used to yield the relationships between the absorption spectrums and the content percentages of polydimethylsiloxane (PDMS), alumina trihydrate (ATH), and silica in HTVSR. The results showed that for the formulations tested, the prediction accuracy of all three main ingredients by the PLS regression model could be improved by changing the spectrum range from 0.2–4 to 0.5–2 THz. If the data were pre‐processed by the Savitzky–Golay smoothing method or multiplicative scatter correction method, the prediction accuracy of PDMS could be further enhanced. However, this would lead to a slight decrease in the prediction accuracy of ATH. For the LS‐SVM regression model, the radial basis function (RBF) kernel and the linear kernel were studied. It was found that the prediction accuracy of both kernels was better than that of the PLS regression model. With the LS‐SVM regression model using the RBF kernel, the correlated coefficients of PDMS and ATH in the prediction set could be up to 0.9915 and 0.9742, respectively.

Data-Driven Analytical Model Using Machine Learning Algorithms

The objective of this article is to use machine learning technology, specifically the Support Vector Machine (SVM) approach with a linear kernel, to analyze and predict clean and healthy living behavior (CHLB) in coastal dwellings in Surabaya City. To train the SVM model, researchers collect health and environmental data from the region. As a result, our model predicts house CHLB status with an 83% accuracy rate. The most important variables in this prediction are the amount of community access to appropriate sanitary facilities, the health of households, and the sustainability of public areas that meet health requirements. These findings have crucial implications for attempts to improve CHLB in Surabaya's coastal areas in compliance with the National Medium-Term Development Plan (RPJMN) aims. Furthermore, the findings of this study can be used to build more targeted and long-term health policies in coastal communities.

Augmented support vector regression with an autoregressive process via an iterative procedure

The Support Vector Regression (SVR) technique can approximate intricate systems by addressing learning and estimation challenges within a reproducing kernel Hilbert space, devoid of reliance on specific parameter assumptions. However, when dealing with correlated data like time series, the SVR method often falls short in accounting for underlying temporal structures, leading to limited enhancements in prediction efficiency. We introduce an enhanced SVR method that considers temporal correlations (TemporalSVR) to overcome this constraint. Our proposed method extends kernel functions to include additional linear kernels, facilitating learning temporal patterns. Additionally, we develope an iterative training procedure for the augmented regression model. During model training, we estimate the hyper-parameter in the corresponding loss function using a ‘working’ likelihood approach, enhancing the generalization capabilities of the proposed regression. To demonstrate superior forecasting performance, we conduct extensive numerical simulations on both linear and nonlinear systems and the TemporalSVR achieves improvements ranging from 8% to 114% based on the RMSE ratio from the AR-X model. Furthermore, we investigate the forecasting performance of three basic models (NARX-NN, Statistical SVR, and SVR-ARIMA) and four deep learning (DL) techniques (Transformer, Informer, Reformer, Autormer, and Autoformer) by using a WTI forecasting study. Our proposed TemporalSVR achieves the smallest RMSE at 2.22 and attains the highest success ratio of stock direction prediction at 71.30%. All these numerical results highlight the effectiveness and advantages of our TemporalSVR in handling temporal data and making accurate predictions.

Preliminary Study on the Identification of Aerobic Vaginitis by Artificial Intelligence Analysis System

To develop an artificial intelligence vaginal secretion analysis system based on deep learning and to evaluate the accuracy of automated microscopy in the clinical diagnosis of aerobic vaginitis (AV). In this study, the vaginal secretion samples of 3769 patients receiving treatment at the Department of Obstetrics and Gynecology, West China Second Hospital, Sichuan University between January 2020 and December 2021 were selected. Using the results of manual microscopy as the control, we developed the linear kernel SVM algorithm, an artificial intelligence (AI) automated analysis software, with Python Scikit-learn script. The AI automated analysis software could identify leucocytes with toxic appearance and parabasal epitheliocytes (PBC). The bacterial grading parameters were reset using standard strains of lactobacillus and AV common isolates. The receiver operating characteristic (ROC) curve analysis was used to determine the cut-off value of AV evaluation results for different scoring items were obtained by using the results of manual microscopy as the control. Then, the parameters of automatic AV identification were determined and the automatic AV analysis scoring method was initially established. A total of 3769 vaginal secretion samples were collected. The AI automated analysis system incorporated five parameters and each parameter incorporated three severity scoring levels. We selected 1.5 μm as the cut-off value for the diameter between Lactobacillus and common AV bacterial isolates. The automated identification parameter of Lactobacillus was the ratio of bacteria ≥1.5 μm to those <1.5 μm. The cut-off scores were 2.5 and 0.5, In the parameter of white blood cells (WBC), the cut-off value of the absolute number of WBC was 103 μL－1 and the cut-off value of WBC-to-epithelial cell ratio was 10. The automated identification parameter of toxic WBC was the ratio of toxic WBC toWBC and the cut-off values were 1% and 15%. The parameter of background flora was bacteria<1.5 μm and the cut-off values were 5×103 μL－1 and 3×104 μL－1. The parameter of the parabasal epitheliocytes was the ratio of PBC to epithelial cells and the cut-off values were 1% and 10%. The agreement rate between the results of automated microscopy and those of manual microscopy was 92.5%. Out of 200 samples, automated microscopy and manual microscopy produced consistent scores for 185 samples, while the results for 15 samples were inconsistent. We developed an AI recognition software for AV and established an automated vaginal secretion microscopy scoring system for AV. There was good overall concordance between automated microscopy and manual microscopy. The AI identification software for AV can complete clinical lab examination with rather high objectivity, sensitivity, and efficiency, markedly reducing the workload of manual microscopy.

Bully Comments Classification on TikTok Using Support Vector Machine and Chi-Square Feature Selection

TikTok has been named the world’s most popular social media platform. The high level of TikTok use makes it easier for an irresponsible user to do unethical things such as spreading hateful comments on someone’s account. TikTok developers can prevent bullying by using policies such as word detection and filtering features that indicate comments fall under the category of bullying or non-bullying comments. Therefore, we conducted this study to classify bullying comments using Machine Learning methods for convenience purposes on TikTok usage, a method that we used in this research is the SVM method to classify the data and Chi-Square as the feature selection. Tests were carried out using the Linear, Polynomial, and RBF kernel functions with the C parameter, namely 0,1, 1, and 10 for each kernel. The results of this research show that the Support Vector Machine method with Chi-Square Feature Selection has a better performance. This was proven by the increased accuracy in RBF kernel C=0,1 which was 0,20

Comparison of Discriminant Analysis and Support Vector Machine on Mixed Categorical and Continuous Independent Variables for COVID-19 Patients Data

Purpose: Numerous factors can affect the duration of COVID-19 recovery. One method involves utilizing natural herbal medication. This study seeks to determine the variables influencing the duration of COVID-19 recovery and to compare discriminant analysis and support vector machine models using COVID-19 patient data from West Sumatra.Methods: Two data mining methods, Discriminant Analysis and Support Vector Machine with different types of kernels (linear, polynomial, and radial basis function), were employed to categorize the time of COVID-19 recovery in this work. The study utilized 428 data points, with 75% allocated for training data and 25% for testing data. The independent factors were evaluated by determining the selection variables' information value (IV) to gauge their influence on the dependent variable. Data resampling techniques were employed to tackle the problem of data imbalance. This study employs data resampling techniques, including undersampling, oversampling, and SMOTE. The balancing accuracy of Discriminant Analysis and Support Vector Machine was examined.Result: The Discriminant Analysis with SMOTE achieved a balanced accuracy of 66.50%, outperforming the linear kernel Support Vector Machine with SMOTE, which had a balanced accuracy of 63.20% in this dataset.Novelty: This study assessed the novelty, originality, and value by comparing Discriminant Analysis and SVM algorithms with categorical and continuous independent variables. This research explores techniques for managing imbalanced data using undersampling, oversampling, and SMOTE, with variable selection based on information value assessment.

Activation of epidermal growth factor receptors in triple-negative breast cancer cells by morphine; analysis through Raman spectroscopy and machine learning

Triple negative breast cancer (TNBC) is a very aggressive form of breast cancer, and the analgesic drug morphine has been shown to promote the proliferation of TNBC cells. This article investigates whether morphine causes activation of epidermal growth factor receptors (EGFR), the roles of μ-opioid and EGFR receptors on TNBC cell proliferation and migration. While examining the changes with molecular techniques, we also aimed to investigate the analysis ability of Raman spectroscopy and machine learning-based approach. Effects of morphine on the proliferation and migration of MDA.MB.231 cells were evaluated by MTT and scratch wound-healing tests, respectively. Morphine-induced phosphorylation of the EGFR was analyzed by western blotting in the presence and absence of μ-receptor antagonist naltrexone and the EGFR-tyrosine kinase inhibitor gefitinib. Morphine-induced EGFR phosphorylation and cell migration were significantly inhibited by pretreatments with both naltrexone and gefitinib; however, morphine-increased cell proliferation was inhibited only by naltrexone. While morphine-induced changes were observed in the Raman scatterings of the cells, the inhibitory effect of naltrexone was analyzed with similarity to the control group. Principal component analysis (PCA) of the Raman confirmed the epidermal growth factor (EGF)-like effect of morphine and was inhibited by naltrexone and partly by gefitinib pretreatments. Our in vitro results suggest that combining morphine with an EGFR inhibitor or a peripherally acting opioidergic receptor antagonist may be a good strategy for pain relief without triggering cancer proliferation and migration in TNBC patients. In addition, our results demonstrated the feasibility of the Raman spectroscopy and machine learning-based approach as an effective method to investigate the effects of agents in cancer cells without the need for complex and time-consuming sample preparation. The support vector machine (SVM) with linear kernel automatically classified the effects of drugs on cancer cells with ∼95% accuracy.

The Correlation between Metal Mixed Exposure and Lung Function in Different Ages of the Population.

Herein, we explored the overall association between metal mixtures and lung functions in populations of varying ages and the relationship among the associated components. The 2007-2012 National Health and Nutrition Examination Survey data of 4382 American participants was analyzed, and generalized linear, elastic net, quantile g-computation, and Bayesian kernel machine regression models were used to evaluate the relationship between exposure to the metal mixture and lung function at various ages. The results of barium exposure at distinct stages revealed that children and adolescents exhibited greater lung function changes than those in adults and the elderly. Additionally, compared with children and adolescents, cadmium- and arsenic-containing metabolites contributed to nonconductive lung function changes in adults and the elderly exposed to metal mixtures. The results showed that the effects of exposure to metal mixtures on lung function in children and adolescents were predominantly caused by lead and barium. Altogether, children and adolescents were found to be more susceptible to metal-exposure-mediated lung function changes than adults and the elderly.

Forecasting Gold Prices in Indonesia using Support Vector Regression with the Grid Search Algorithm

Investment is an effort to increase economic growth in Indonesia. A popular investment in the community is gold investment. The value of gold investments tends to increase but is not immune from price fluctuations, therefore it is important to forecast the price of gold in Indonesia. The method that can be used to make this forecast is Support Vector Regression (SVR). SVR is a method that looks for a function that has a deviation of no more than ε to get the target value from all training data. The best SVR model with a linear kernel was obtained from a combination of parameters C=0,0625 and ε=0,001 with a RMSE value of 0,19734 and a value of 0,974112. So, the SVR method is appropriate to use for forecasting gold prices in Indonesia.

Experimental investigation and application of soft computing models for predicting flow energy loss in arc-shaped constrictions

Abstract This investigation focuses on flow energy, a crucial parameter in the design of water structures such as channels. The research endeavors to explore the relative energy loss (ΔEAB/EA) in a constricted flow path of varying widths, employing Support Vector Machine (SVM), Artificial Neural Network (ANN), Gene Expression Programming (GEP), Multiple Adaptive Regression Splines (MARS), M5 and Random Forest (RF) models. Experiments span a Froude number range from 2.85 to 8.85. The experimental findings indicate that the ΔEAB/EA exceeds that observed in a classical hydraulic jump with constriction section. Within the SVM model, the linear kernel emerges as the best predictor of ΔEAB/EA, outperforming polynomial, radial basis function (RBF), and sigmoid kernels. In addition, in the ANN model, the MLP network was more accurate compared to the RBF network. The results indicate that the relationship proposed by the MARS model can play a significant role resulting in high accuracy compared to the non-linear regression relationship in predicting the target parameter. Upon comprehensive evaluation, the ANN method emerges as the most promising among the candidates, yielding superior performance compared to the other models. The testing phase results for the ANN-MLP are noteworthy, with R = 0.997, average RE% = 0.63%, RMSE = 0.0069, BIAS = −0.0004, DR = 0.999, SI = 0.0098 and KGE = 0.995.

Boltzmann stacked classification data mining model for the student performance improvement in academic performance

The term “educational data mining” refers to a field of study where information from academic environments is predicted using data mining, machine learning, and statistics. Education is the act of giving or receiving knowledge to or from someone who is formally studying and developing a natural talent. Over time, scholars have used data mining techniques to uncover hidden information in educational statistics and other external elements. This study suggests a unique method for analysing academic student performance that is based on data mining and machine learning. Here, the input is gathered as a dataset of student academic performance and is processed for normalisation and noise reduction. Then, using the Boltzmann deep learning model coupled with linear kernel principal component analysis, this data’s characteristics were retrieved and chosen. Based on weights, information gain, and the Gini index, the characteristics are assessed and optimised. Following the selection of the pertinent data, conditional random field-based probabilistic clustering model is performed using RNN-based training, and the academic performance of the students is then examined using voting classifiers and sparse features. Experimental results are carried out for students academic performance dataset based on subjects in terms of training accuracy, validation accuracy, mean average precision, mean square error and correlation evaluation. Proposed technique attained accuracy of 96%, precision of 95%, Correlation Evaluation of 92% .

Specific patterns and potential risk factors to predict 3-year risk of death among non-cancer patients with advanced chronic kidney disease by machine learning.

Chronic kidney disease (CKD) is a major public health concern. But there are limited machine learning studies on non-cancer patients with advanced CKD, and the results of machine learning studies on cancer patients with CKD may not apply directly on non-cancer patients. We aimed to conduct a comprehensive investigation of risk factors for a 3-year risk of death among non-cancer advanced CKD patients with an estimated glomerular filtration rate < 60.0 mL/min/1.73m2 by several machine learning algorithms. In this retrospective cohort study, we collected data from in-hospital and emergency care patients from 2 hospitals in Taiwan from 2009 to 2019, including their international classification of disease at admission and laboratory data from the hospital's electronic medical records (EMRs). Several machine learning algorithms were used to analyze the potential impact and degree of influence of each factor on mortality and survival. Data from 2 hospitals in northern Taiwan were collected with 6565 enrolled patients. After data cleaning, 26 risk factors and approximately 3887 advanced CKD patients from Shuang Ho Hospital were used as the training set. The validation set contained 2299 patients from Taipei Medical University Hospital. Predictive variables, such as albumin, PT-INR, and age, were the top 3 significant risk factors with paramount influence on mortality prediction. In the receiver operating characteristic curve, the random forest had the highest values for accuracy above 0.80. MLP, and Adaboost had better performance on sensitivity and F1-score compared to other methods. Additionally, SVM with linear kernel function had the highest specificity of 0.9983, while its sensitivity and F1-score were poor. Logistic regression had the best performance, with an area under the curve of 0.8527. Evaluating Taiwanese advanced CKD patients' EMRs could provide physicians with a good approximation of the patients' 3-year risk of death by machine learning algorithms.

Auditory event-related potential differentiates girls with Rett syndrome from their typically-developing peers with high accuracy: Machine learning study

Rett Syndrome (RTT) is a rare neurodevelopmental disorder caused by mutation in the MECP2 gene. No cures are still available, but several clinical trials are ongoing. Here we examine neurophysiological correlates of auditory processing for ability to differentiate patients with RTT from typically developing (TD) peers applying standard machine learning (ML) methods and pipelines. Capitalized on the available event-related potential (ERP) data recorded in response to tone presented at different rates (stimulus onset asynchrony 900, 1800 and 3600 ms) from 24 patients with RTT and 27 their TD peer. We considered the most common ML models that are widely used for classification tasks. These include both linear models (logistic regression, support-vector machine with linear kernel) and tree-based nonlinear models (random forest, gradient boosting). Based on these methods we were able to differentiate RTT from TD children with high accuracy (with up to 0.94 ROC-AUC score), which was evidently higher at the fastest presentation rate. Importance analysis and perturbation importance pointed out that the most important feature for classification is P2-N2 peak-to-peak amplitude, consistently across the approaches and blocks with different presentation rate. The results suggest the unique pattern of ERP characteristics for RTT and points to features of importance. The results might be relevant for establishing outcome measures for clinical trials.

Detection of Ventricular Fibrillation Using Ensemble Empirical Mode Decomposition of ECG Signals

Ventricular fibrillation (VF) is a critical ventricular arrhythmia with severe consequences. Due to the severity of VF, it urgently requires a rapid and accurate detection of abnormal patterns in ECG signals. Here, we present an efficient method to detect abnormal electrocardiogram (ECG) signals associated with VF by measuring orthogonality between intrinsic mode functions (IMFs) derived from a data-driven decomposition method, namely, ensemble empirical mode decomposition (EEMD). The proposed method incorporates the decomposition of the ECG signal into its IMFs using EEMD, followed by the computation of the angles between subsequent IMFs, especially low-order IMFs, as the features to discriminate normal and abnormal ECG patterns. The proposed method was validated through experiments using a public MIT-BIH ECG dataset for its effectiveness in detecting VF ECG signals compared to conventional methods. The proposed method achieves a sensitivity of 99.22%, a specificity of 99.37%, and an accuracy of 99.28% with a 3 s ECG window and a support vector machine (SVM) with a linear kernel, which performs better than existing VF detection methods. The capability of the proposed method can provide a perspective approach for the real-time and practical computer-aided diagnosis of VF.

Prediction Of Cryptocurrency Prices Using Lstm, Svm And Polynomial Regression

The rapid development of information technology, especially the Internet, has facilitated users with a quick and easy way to seek information. With these convenience offered by internet services, many individuals who initially invested in gold and precious metals are now shifting into digital investments in form of cryptocurrencies. However, investments in crypto coins are filled with uncertainties and fluctuation in daily basis. This risk posed as significant challenges for coin investors that could result in substantial investment losses. The uncertainty of the value of these crypto coins is a critical issue in the field of coin investment. Forecasting, is one of the methods used to predict the future value of these crypto coins. By utilizing the models of Long Short Term Memory, Support Vector Machine, and Polynomial Regression algorithm for forecasting, a performance comparison is conducted to determine which algorithm model is most suitable for predicting crypto currency prices. The mean square error is employed as a benchmark for the comparison. By applying those three constructed algorithm models, the Support Vector Machine uses a linear kernel to produce the smallest mean square error compared to the Long Short Term Memory and Polynomial Regression algorithm models, with a mean square error value of 0.02.