Principal Component Regression Model Research Articles

Population stratification correction using Bayesian shrinkage priors for genetic association studies.

Population stratification (PS) is a major source of confounding in population-based genetic association studies of quantitative traits. Principal component regression (PCR) and linear mixed model (LMM) are two commonly used approaches to account for PS in association studies. Previous studies have shown that LMM can be interpreted as including all principal components (PCs) as random-effect covariates. However, including all PCs in LMM may dilute the influence of relevant PCs in some scenarios, while including only a few preselected PCs in PCR may fail to fully capture the genetic diversity. To address these shortcomings, we introduce Bayestrat-a method to detect associated variants with PS correction under the Bayesian LASSO framework. To adjust for PS, Bayestrat accommodates a large number of PCs and utilizes appropriate shrinkage priors to shrink the effects of nonassociated PCs. Simulation results show that Bayestrat consistently controls type I error rates and achieves higher power compared to its non-shrinkage counterparts, especially when the number of PCs included in the model is large. As a demonstration of the utility of Bayestrat, we apply it to the Multi-Ethnic Study of Atherosclerosis (MESA). Variants and genes associated with serum triglyceride or HDL cholesterol are identified in our analyses. The automatic and self-selection features of Bayestrat make it particularly suited in situations with complex underlying PS scenarios, where it is unknown a priori which PCs are potential confounders, yet the number that needs to be considered could be large in order to fully account for PS.

Forecasting Canadian Age-Specific Mortality Rates: Application of Functional Time Series Analysis

In the insurance and pension industries, as well as in designing social security systems, forecasted mortality rates are of major interest. The current research provides statistical methods based on functional time series analysis to improve mortality rate prediction for the Canadian population. The proposed functional time series-based model was applied to the three-mortality series: total, male and female age-specific Canadian mortality rate over the year 1991 to 2019. Descriptive measures were used to estimate the overall temporal patterns and the functional principal component regression model (fPCA) was used to predict the next ten years mortality rate for each series. Functional autoregressive model (fAR (1)) was used to measure the impact of one year age differences on mortality series. For total series, the mortality rates for children have dropped over the whole data period, while the difference between young adults and those over 40 has only been falling since about 2003 and has leveled off in the last decade of the data. A moderate to strong impact of age differences on Canadian age-specific mortality series was observed over the years. Wider application of fPCA to provide more accurate estimates in public health, demography, and age-related policy studies should be considered.

Potato flour content determination of potato–wheat flour mixture based on hyperspectral imaging

SummaryPotato–wheat flour mixture (PWFM) has important significance for the development of potato staple food products. However, conventional chemical methods are unable to detect the content of potato flour. Hyperspectral imaging (HSI) technology combined with chemometrics was investigated to predict the feasibility of potato flour content in PWFM. In this study, seven pretreatment algorithms were performed to process the raw spectral data. The results showed that the standard normalised variables (SNV) to establish a partial least square regression (PLSR) model had the most predictive accuracy with the determination coefficient of prediction () of 0.9729. The characteristic wavelengths of raw spectral information were extracted using three algorithms to reduce the model complexity. Eventually, the extracted characteristic wavelengths of potato flour content combine with SNV to establish PLSR, principal component regression (PCR) and support vector regression (SVR) models. The results revealed that the optimal model was SNV‐competitive adaptive reweighted sampling (CARS)‐PLSR with the values of of 0.9853. These results showed that HSI determination of potato flour content in PWFM was feasible and provided a non‐destructive method.

Principal Component Regression Modeling and Analysis of PM10 and Meteorological Parameters in Sarajevo with and without Temperature Inversion

The specific geographic location of Sarajevo, which is located in a valley surrounded by mountains, provides the opportunity to analyze the relation between the concentration of PM10 and meteorological parameters with and without temperature inversion. The main aim of this paper was to develop forecasting models of the hourly average of PM10 values in the Sarajevo urban area based on meteorological parameters measured in Sarajevo and on the Bjelasnica mountain with and without temperature inversion by using principal component regression (PCR). Also, this research explored and analyzed the differences in the values of the meteorological parameters and PM10 in Sarajevo with and without temperature inversion, and the difference in temperatures between Sarajevo and Bjelasnica with temperature inversion using statistical hypothesis testing with a total of 240 hypothesis tests performed. The measurements of meteorological parameters were taken from 2020 to 2022 for both Sarajevo (630 m) and the Bjelasnica mountain (2067 m), which allowed for the identification of time periods with and without temperature inversion, while measurements of PM10 were taken only in Sarajevo. Data were collected during the heating season (November, December, January, February and March). Since analyses have shown that only January and November had time periods with and without temperature inversion during each hour of the day, a total of seven cases were identified: two cases with and five cases without temperature inversion. For each case, three PCR models were developed using all principal components, backward elimination and eigenvalue principal component elimination criteria (λ<1). A total of 21 models were developed. The performance of the models were evaluated based on the coefficient of determination R2 and the standard error SE. The backward elimination models were shown to have high performances with the highest value of R2= 97.19 and the lowest value of SE=1.32. The study showed that some principal components with eigenvalues λ<1 were significantly related to the independent variable PM10 and thus were retained in the PCR models. In the study, it was shown that backward elimination PCR was an adequate tool to develop PM10 forecasting models with high performances and that it could be useful for authorities for early warnings or other action to protect citizens from very harmful pollution. Hypothesis tests showed different relations of meteorological parameters and PM10 with and without temperature inversion.

Predictive modeling and analysis of key drivers of groundwater nitrate pollution based on machine learning

Nitrate comtamination of shallow groundwater in agricultural intensification regions is a prevalent and global environment issue affecting food security, human health, and the water ecology. Developing a prediction model for groundwater nitrate contamination is crucial for protection of groundwater resources. Machine learning modeling offer potentials to predict contamination, but often fails to adequately screen input features in complex non-linear environments before modeling. Additionally, there is a tendency to overlook the interpretable description of the relationship between major water chemistry parameters and nitrate concentration after modeling, which hinders scientific decision-making by water resource managers. In this study, a dataset consisting of hydrochemical test results from 316 groundwater samples collected between 2011 and 2015 in intensive agricultural areas of Northeast China was collected. Prior to modeling, the dataset was grouped based on land use type, vadose zones types, and thickness. Based on the grouping of data sets, self-organizing map (SOM) and Spearman's coefficients were employed to identity the correlations between water chemical parameters and nitrate concentration (NO3–-N), which provided a logical basis for selecting the key input variables. A radial basis function artificial neural network (RBF ANN) prediction model and principal components regression (PCR) models was constructed using the dataset, and particle swarm optimization algorithm was applied to determine optimal parameter combinations of the RBF ANN. After conducting modeling, the advantages and disadvantages of RBF ANN and principal components regression (PCR) models were thoroughly examined and discussed, and the primary factors that impact nitrate concentrations in groundwater were analyzed using a PCR model. The results revealed that the RBF ANN model showed greater accuracy, while the PCR model offered better interpretability. Therefore, the integration of the two models is advantageous for nitrate prediction research. Human activities, rainfall, land-use types, vadose zones types and thickness are external factors that affecting nitrate concentration, and the difference between nitrification. Denitrification, and dissimilatory nitrate reduction to ammonium (DNRA) is internal driving factors for the change of nitrate concentration in the aquifer, and partially determine differences in the spatial distribution of aquifer nitrate concentrations under various land use types. This study provides a comprehensive approach for predicting nitrate pollution in groundwater under non-linear environmental conditions, supporting decision making in sustainable groundwater development, management, and conservation.

Expeditious and accurate detection of palm oil adulteration in virgin coconut oil by utilizing ATR-FTIR spectroscopy along with chemometrics and regression models

Virgin coconut oil (VCO), being one of the most treasured and healthy edible oil, is at great risk of blending with cheaper oils like palm oil (PO). Fourier transform infrared (FTIR) spectroscopy with an Attenuated total reflection (ATR) accessory was used together with multivariate chemometrics for the classification and evaluation of numerous concentrations of PO (0.5–30% v/v) in VCO. Linear Discriminant Analysis (LDA) showed a 100% correct classification for both the initial and cross-validation groups for all the subsets of PO blends. Principal components regression (PCR) and Partial least squares regression (PLS-R) calibration models were generated and compared for normal, 1st, and 2nd derivatives of the combined informational spectral domain (3010–2800 cm−1 & 1800–700 cm−1) and separate informational domains of the spectra 3010–2800 cm−1 and 1800–700 cm−1 to get the best-fitting models. Regression models for the 2nd derivatives of 1800–700 cm−1 informational spectral domain gave exquisite outcomes of prediction with immense accuracy and precision with the highest R2 of 0.998, and the root mean square error of prediction (RMSEP) of 0.375% v/v for PLS-R and R2 of 0.998 and RMSEP of 0.441% v/v for PCR respectively. The lowest detectable limit of PO in VCO was estimated as 0.5% v/v. Hence, it has been concluded that PO adulteration of up to 0.5% with VCO can be quickly determined by using ATR-FTIR spectroscopy fitted with multivariate chemometrics.

Soil Attributes Mapping with Online Near-Infrared Spectroscopy Requires Spatio-Temporal Local Calibrations

Building machine learning (ML) calibrations using near-infrared (NIR) soil spectroscopy direct in agricultural areas (online NIR), soil attributes can be fine-scale mapped in a faster and more cost-effective manner, guiding management decisions to ensure the maintenance of soil functions. However, a financially and environmentally unattractive density of 3–5 laboratory soil samples per ha is required to build these calibrations. Since no reports have evaluated if they are reusable or if a new calibration is required for each acquisition, this study’s objective was to acquire online NIR spectra in an agricultural field where ML models were previously built and validated, assessing their performance over time. Two spectral acquisitions were held over a fallow tropical field, separated by 21 days. Soil properties (clay, organic matter, cation exchange capacity, pH, phosphorus, potassium, calcium, and magnesium) were predicted using principal components regression models calibrated with day 1 spectra. Day 1 and day 21 predicted values and maps interpolated by ordinary kriging were compared. Spectra characteristics (morphology, features, and intensity) were evaluated. Predicted values from the two days were not correlated, as no causal relationship was found for the only Pearson’s correlation coefficient (r) significative at 99% (p < 0.01) (calcium, with r = 0.22 in the comparison pairing the nearest neighbors from the two days). For clay, organic matter, and cation exchange capacity, despite their robust prediction on day 1, no significative r values were found, ranging from −0.14 to 0.32, when comparing day 1 with day 21. The maps of the two days presented no similar spatial distribution, hindering their use for management decisions. Soil moisture is a suggested source of variation, but the analysis indicated that it was not the only one, requiring further investigation of the effect of soil surface conditions and environmental variables. Although further investigations should be performed, the results presented suggest that online NIR spectra ML models require spatio-temporal local calibrations to perform properly.

Fluoride and nitrate enrichment in coastal aquifers of the Eastern Province, Saudi Arabia: The influencing factors, toxicity, and human health risks

Fluoride and nitrate contamination of groundwater is a major environmental issue in the world's arid and semiarid regions. This issue is severe in both developed and developing countries. This study aimed at assessing the concentration levels, contamination mechanisms, toxicity, and human health risks of NO3− and F− in the groundwater within the coastal aquifers of the eastern part of Saudi Arabia using a standard integrated approach. Most of the tested physicochemical properties of the groundwater exceeded their standard limits. The water quality index and synthetic pollution index evaluated the suitability of the groundwater and showed that all the samples have poor and unsuitable quality for drinking. The toxicity of F− was estimated to be higher than NO3−. Also, the health risk assessment revealed higher risks due to F− than NO3−. Younger populations had higher risks than elderly populations. For both F− and NO3−, the order of health risk was Infants > Children > Adults. Most of the samples posed medium to high chronic risks due to F− and NO3− ingestion. However, negligible health risks were obtained for potential dermal absorption of NO3−. Na–Cl and Ca–Mg–Cl water types predominate in the area. Pearson's correlation analysis, principal component analysis, regression models, and graphical plots were used to determine the possible sources of the water contaminants and their enrichment mechanisms. Geogenic and geochemical processes had greater impact he groundwater chemistry than anthropogenic activities. For the first time, these findings provide public knowledge on the overall water quality of the coastal aquifers and could help the inhabitants, water management authorities, and researchers to identify the groundwater sources that are most desirable for consumption and the human populations that are vulnerable to non-carcinogenic health risks.

Utilization of Chemometric Aided UV- Spectrophotometric Methods for Concurrent Assessment of Emtricitabine, Tenofovir Disoproxil Fumarate, Elvitegravir and Cobicistat in Tablet Formulation.

Emtricitabine (ETC), Tenofovir disoproxil fumarate (TNF), Elvitegravir (EVG), and Cobicistat (CBS) are antiviral drugs used to treat human immunodeficiency virus (HIV) infections. To develop chemometric-aided UV spectrophotometric methods for concurrent estimation of the aforementioned drugs used to treat HIV. This method can be used to reduce the modification of the calibration model by assessing the absorbance at various points in the zero-order spectra within the selected wavelength range. Additionally, it eliminates interfering signals and provides sufficient resolution in multi-component systems. Two Chemo-metric assisted UV-spectrophotometric methods, namely, partial least square (PLS) and principal component regression (PCR) models, were established for the concurrent assessment of EVG, CBS, TNF, and ETC in tablet formulations. The proposed methods were applied to decrease complexity of overlapped spectra and to achieve maximum sensitivity and the lowest error. These approaches were performed in accordance with ICH criteria and compared to the reported HPLC method. The proposed methods were used to assess EVG, CBS, TNF, and ETC in the range of 5-30 µg/mL, 5-30 µg/mL, 5-50 µg/mL and 5-50 µg/mL, respectively, with an excellent correlation coefficient (r ≥ 0.998). The accuracy and precision results were found to be within the acceptable limit. No statistical difference was observed between the proposed and reported studies. The chemometric aided UV-spectrophotometric approaches could be taken into consideration as an alternative of chromatographic procedures in the pharmaceutical industry for routine analysis and testing of readily accessible commercial formulations. Novel chemometric-UV assisted spectrophotometric techniques were developed for assessment of multicomponent antiviral combinations in single tablet formulations. The proposed methods were performed without using harmful solvents, tedious handling, or expensive instruments. The proposed methods were compared statistically with reported HPLC method. Assessment of the EVG, CBS, TNF, and ETC was performed without interference from excipients in their multicomponent formulations.

Micro-Photoluminescence spectroscopy of two distinct types of WS2 monolayers using fs-Ti: Sapphire laser under vacuum and ambient conditions and multivariate calibration models

We utilized Micro-Photoluminescence (μPL) and time-resolved photoluminescence (TRPL) spectroscopies with a femtosecond laser (440 nm) to assess the optical properties of two types of WS2 monolayers (MLs) obtained through mechanical exfoliation of different crystals. Based on cryogenic μPL spectra (4 K), the monolayers were classified as low-defect-concentration (LDC) and high-defect-concentration (HDC). By subjecting the MLs to laser excitation at various photon fluxes under ambient and vacuum conditions at room temperature, we characterized their optical properties. The spectra exhibited two main regions corresponding to optical transitions of neutral excitons (X) and trions (T). Notably, two distinct regimes were observed for quasi-particle decay: X-X annihilation at low photon fluxes and Mott transition at high photon fluxes. The photoluminescence quantum yield (PLQY) was measured under ambient and vacuum conditions, with the presence of physisorbed O2 on the ML surface influencing the results. Additionally, we employed a novel analytical approach combining PL and TRPL spectra with chemometric methods for the regression analysis of the two types of WS2 MLs. Utilizing partial least squares regression and principal component regression models, we estimated the decay times of X and T quasi-particles based on the spectral datasets.

Fetal heart rate changes and labor neuraxial analgesia: a machine learning approach

BackgroundNeuraxial labor analgesia has been associated with fetal heart rate changes. Fetal bradycardia is multifactorial, and predicting it poses a significant challenge to clinicians. Machine learning algorithms may assist the clinician to predict fetal bradycardia and identify predictors associated with its presentation.MethodsA retrospective analysis of 1077 healthy laboring parturients receiving neuraxial analgesia was conducted. We compared a principal components regression model with tree-based random forest, ridge regression, multiple regression, a general additive model, and elastic net in terms of prediction accuracy and interpretability for inference purposes.ResultsMultiple regression identified combined spinal-epidural (CSE) (p = 0.02), interaction between CSE and dose of phenylephrine (p < 0.0001), decelerations (p < 0.001), and the total dose of bupivacaine (p = 0.03) as associated with decrease in fetal heart rate. Random forest exhibited good predictive accuracy (mean standard error of 0.92).ConclusionUse of CSE, presence of decelerations, total dose of bupivacaine, and total dose of vasopressors after CSE are associated with decreases in fetal heart rate in healthy parturients during labor. Prediction of changes in fetal heart rate can be approached with a tree-based random forest model with good accuracy with important variables that are key for the prediction, such as CSE, BMI, duration of stage 1 of labor, and dose of bupivacaine.

Forecasting European Union allowances futures: The role of technical indicators

With the aim of studying the prognostic power of monthly European Carbon futures prices, we employ a wide variety of potential forecasting indicators, including economic variables like uncertainty indicators, energy prices, and stock index data, in addition to exploring the influence of technical indicators on forecasting for the first time. In both in-sample and out-of-sample results, technical indicators display statistically significant ability, exceeding that of economic variables. To gain valuable insight into which indicators are comparatively relevant to the price of EUAs, three types of forecasting methods: univariate predictive regression, dimensionality reduction techniques, and ensemble learning algorithms are applied. Results show that the first diffusion index in the principal component regression and partial least squares model is greatly influenced by the changes of technical indicators, while only having a weak association with economic variables. With respect to ensemble learning algorithms like Xgboost, greater importance is given to technical indicators compared to economic variables when making predictions. Furthermore, technical indicators demonstrate stable economic value to investors in the form of positive CER gains. Our findings present novel evidence for the predictive capacity of technical indicators and can assist policymakers in formulating sustainable and effective energy policies.

Effects of Spatial Characteristics on Non-Standard Employment for Canada’s Immigrant Population

Using microdata from Statistics Canada’s Labour Force Survey (LFS) and Population Census, this paper explores how spatial characteristics are correlated with temporary employment outcomes for Canada’s immigrant population. Results from ordinary least square regression models suggest that census metropolitan areas and census agglomerations (CMAs/CAs) characterized by a high share of racialized immigrants, immigrants in low-income, young, aged immigrants, unemployed immigrants, and immigrants employed in health and service occupations were positively associated with an increase in temporary employment for immigrants. Furthermore, findings from principal component regression models revealed that a combination of spatial characteristics, namely CMAs/CAs characterized by both a high share of unemployed immigrants and immigrants in poverty, had a greater likelihood of immigrants being employed temporarily. The significance of this study lies in the spatial conceptualization of temporary employment for immigrants that could better inform spatially targeted employment policies, especially in the wake of the structural shift in the nature of work brought about by the COVID-19 pandemic.

The Influence of Internet Celebrities on the Purchase Intention of College Students

With the rapid development of Internet technology, Internet celebrity marketing has become an emerging value creation model of the Internet.Nowadays, the Internet celebrities have become an important factor affecting consumers' purchase intention.In order to promote the continuous expansion and development of Internet celebrity marketing.It is necessary to research how the Internet celebrities influence the purchase intention of consumers.This study selected college students in first-tier cities as samples, collected relevant data through online questionnaire, and studied the influence of four characteristics of Internet celebrities on the purchase intention of college students based on principal component regression model and K-means clustering algorithm. Through the principal component regression model, the linear regression equation affecting the purchase intention of college students and the popularity of Internet celebrities have the greatest influence on the purchase intention. At the same time, the k-means clustering algorithm is used to cluster the original indicators, and the conclusion that the popularity of Internet celebrities has the greatest influence on the purchase intention of college students is verified again.

Smart optimization with PPCR modeling in the presence of missing data, time delay and model-plant mismatch

In this paper, a data-driven smart optimization algorithm is presented to identify the optimal operating point of the process and the path from the current operating condition to the optimal operating condition. To model the plant dynamics, a locally weighted semi-supervised probabilistic principal component regression (PPCR) model that is robust to missing data and can handle the time-invariant delay is developed in this paper. Being a locally weighted linear model, a nonlinearity index is utilized to control the accuracy of approximation of the local model. In addition, an updating strategy on the delay range is proposed to reduce the computational effort of real-time modeling. To account for the model–plant mismatch, a penalty term in the form of a robust Gaussian process regression is incorporated into the optimization problem. Finally, to ensure that the algorithm reaches different regions of search space and avoid convergence to local optimum, an exploration step with the aid of acquisition functions is utilized. The performance of the developed approach is illustrated through an experimental case study on a hybrid tank system, and the practical applicability of the algorithm is demonstrated through an industrial example.

Swift and precise detection of argemone oil adulteration in virgin coconut oil by implementing ATR-FTIR spectroscopy integrated with multivariate chemometrics and regression modelling

Virgin coconut oil (VCO), being one of the most priced and healthy edible oil, is at great risk of mixing with cheaper oils like argemone oil (AO). Fourier transform infrared (FTIR) spectroscopy with an Attenuated total reflection (ATR) accessory was used along with multivariate chemometrics and regression modelling for the classification and evaluation of numerous concentrations of AO (0.5–30% v/v) in VCO. LDA showed a 100% correct classification for both the initial and cross-validation groups for all the subsets of AO blends. Principal components regression (PCR) and Partial least squares regression (PLS-R) calibration models were developed and compared for normal, 1st, and 2nd derivatives of the combined informational spectral domain (3010–2800 cm−1 & 1800–700 cm−1) and separate informational regions of the spectra 3010–2800 cm−1 and 1800–700 cm−1 to get the best-fitting models. PCR model for the 1st derivative and PLS-R model for the 2nd derivative spectra of the region of 1800–700 cm−1 gave exquisite outcomes of prediction with immense accuracy and precision with the highest R2 of 0.999, and the root mean square error of prediction (RMSEP) of 0.241% v/v for PCR and R2 of 0.999 and RMSEP of 0.229% v/v for PLS-R respectively. The lowest detectable limit of AO in VCO was estimated as 0.5% v/v.

The effect of air quality parameters on new COVID-19 cases between two different climatic and geographical regions in Turkey.

Different health management strategies may need to be implemented in different regions to cope with diseases. The current work aims to evaluate the relationship between air quality parameters and the number of new COVID-19 cases in two different geographical locations, namely Western Anatolia and Western Black Sea in Turkey. Principal component analysis (PCA) and regression model were utilized to describe the effect of environmental parameters (air quality and meteorological parameters) on the number of new COVID-19 cases. A big difference in the mean values for all air quality parameters has appeared between the two areas. Two regression models were developed and showed a significant relationship between the number of new cases and the selected environmental parameters. The results showed that wind speed, SO2, CO, NOX, and O3 are not influential variable and does not affect the number of new cases of COVID-19 in the Western Black Sea area, while only wind speed, SO2, CO, NOX, and O3 are influential parameters on the number of new cases in Western Anatolia. Although the environmental parameters behave differently in each region, these results revealed that the relationship between the air quality parameters and the number of new cases is significant.

Effects of Meteorological Factors on Apple Yield Based on Multilinear Regression Analysis: A Case Study of Yantai Area, China

Evaluating the impact of different meteorological conditions on apple yield and predicting the future yield in Yantai City is essential for production. Furthermore, it provides a scientific basis for the increase in apple yield. In this study, first, a grey relational analysis (GRA) was used to determine the quantitative relationship between different meteorological factors and meteorological yield which is defined as affected only by meteorological conditions. Then, the comprehensive meteorological factors extracted by a principal component analysis (PCA) were used as inputs for multiple linear regression (MLR). The apple yield accuracy was compared with the lasso regression prediction. Trend analysis showed that the actual apple yield increased annually, but the meteorological yield decreased annually over a long time. Correlation ranking illustrated that the meteorological yield was significantly correlated with the frost-free period, the annual mean temperature, the accumulated temperature above 10 °C, etc. The good consistency between GRA and MLR–PCA showed that the accumulated temperature above 10 °C, the March–October mean temperature, and the June–August mean temperature are key meteorological factors. In addition, it was found that the principal components F2, F4, and F5 were negatively correlated with meteorological yield, while the principal components F1 and F3 were positively correlated with meteorological yield. Moreover, the MLR–PCA model predicted the apple yield in 2020 as 47.256 t·ha−1 with a 7.089% relative error. This work demonstrates that the principal component regression model can effectively extract information about different meteorological factors and improve the model’s accuracy for analyzing key meteorological factors and predicting apple yield.

A comparison study between different kernel functions in the least square support vector regression model for penicillin fermentation process

Soft sensors are becoming increasingly important in our world today as tools for inferring difficult-to-measure process variables to achieve good operational performance and economic benefits. Recent advancement in machine learning provides an opportunity to integrate machine learning models for soft sensing applications, such as Least Square Support Vector Regression (LSSVR) which copes well with nonlinear process data. However, the LSSVR model usually uses the radial basis function (RBF) kernel function for prediction, which has demonstrated its usefulness in numerous applications. Thus, this study extends the use of non-conventional kernel functions in the LSSVR model with a comparative study against widely used partial least square (PLS) and principal component regression (PCR) models, measured with root mean square error (RMSE), mean absolute error (MAE) and error of approximation (Ea) as the performance benchmark. Based on the empirical result from the case study of the penicillin fermentation process, the Ea of the multiquadric kernel (MQ) is lowered by 63.44% as compared to the RBF kernel for the prediction of penicillin concentration. Hence, the MQ kernel LSSVR has outperformed the RBF kernel LSSVR. The study serves as empirical evidence of LSSVR performance as a machine learning model in soft sensing applications and as reference material for further development of non-conventional kernels in LSSVR-based models because many other functions can be used as well in the hope to increase the prediction accuracy.

Chemical and Biological Properties of Agricultural Soils Located along Communication Routes

The aim of the study was to assess the quality of agricultural soils, which accumulate additional amounts of heavy metals from fertilization and modify their bioavailability, with the use of interdependencies between their biological and chemical properties conditioned by the distance from communication routes. Our results indicated that heavy metals had an impact on enzyme activity in soils and their accumulation was significantly related to the distance from the edge of the road, location of sampling sites, date of soil sampling, and years of research. It was found that the greatest amounts of zinc, cadmium, lead, and copper were accumulated at a distance of 5–20 m from the edge of the road. The highest enrichment factor and geoaccumulation index values were recorded for Pb, followed by Zn, Cu, and Cd. Principal component analysis and regression models showed that the activities of phosphatase and dehydrogenases seem to be the best bioindicators of contamination of roadside soils used for agricultural purposes. Since their activity is related to soil’s organic carbon content, inputs of organic fertilizers and crop residues should be ensured in the agroecosystems along roadsides.