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Article

The Prediction of Pectin Viscosity Using Machine Learning Based on Physical Characteristics—Case Study: Aglupectin HS-MR

by
Przemysław Siejak
1,
Krzysztof Przybył
2,*,
Łukasz Masewicz
1,
Katarzyna Walkowiak
1,*,
Ryszard Rezler
1 and
Hanna Maria Baranowska
1
1
Department of Physics and Biophysics, Faculty of Food Science and Nutrition, Poznań University of Life Sciences, Wojska Polskiego 38/42, 60-637 Poznań, Poland
2
Department of Dairy and Process Engineering, Faculty of Food Science and Nutrition, Poznań University of Life Sciences, 31 Wojska Polskiego St., 60-624 Poznań, Poland
*
Authors to whom correspondence should be addressed.
Sustainability 2024, 16(14), 5877; https://doi.org/10.3390/su16145877
Submission received: 29 March 2024 / Revised: 17 June 2024 / Accepted: 9 July 2024 / Published: 10 July 2024
(This article belongs to the Section Sustainable Food)
Browse Figures
Review Reports Versions Notes

Abstract

:
In the era of technology development, the optimization of production processes, quality control and at the same time increasing production efficiency without wasting food, artificial intelligence is becoming an alternative tool supporting many decision-making processes. The work used modern machine learning and physical analysis tools to evaluate food products (pectins). Various predictive models have been presented to estimate the viscosity of pectin. Based on the physical analyses, the characteristics of the food product were isolated, including L*a*b* color, concentration, conductance and pH. Prediction was determined using the determination index and loss function for individual machine learning algorithms. As a result of the work, it turned out that the most effective estimation of pectin viscosity was using Decision Tree (R2 = 0.999) and Random Forest (R2 = 0.998). In the future, the prediction of pectin properties in terms of viscosity recognition may be significantly perceived, especially in the food and pharmaceutical industries. Predicting the natural pectin substrate may contribute to improving quality, increasing efficiency and at the same time reducing losses of the obtained final product.

1. Introduction

Recently, the food industry has been using plant origin compounds and natural polysaccharides [1,2,3]. Following increasing consumer awareness, the food industry is placing more emphasis on using the least processed, non-chemically modified, natural materials with healthy benefits for our organism to make its products. Pectins are heteropolysaccharides which occur naturally in fruits (apple, currant, gooseberry or citrus), where they play the role of a structure-forming raw material, and they are responsible for regulating water management [4,5,6]. These polysaccharides are a very important component of the human diet, because they function as dietary fiber [7,8,9]. They are used in the treatment of obesity and diseases associated with disorders of fat metabolism. In addition, they are also used to lower cholesterol, prevent constipation and cause blood sugar levels to drop. When pectins are used as a supplement to food, they can form its texture, taste and affect the dietary qualities of the resulting product. Pectin preparations can also act as thickening, gelling and stabilizing substances and as carriers for other substances. The adhesive properties of pectin depend on the type of pectin and environmental conditions (pH). Independent of the concentration of sugars in neutral and acidic solutions, pectins form brittle gels. In contrast, the gelling rate of pectin preparations is affected by their degree of esterification. The rate of the gelling increases with increasing temperature, decreasing the pH value of the environment and increasing the consistency of the extract.
Research into the effective prediction of physical properties and behavior of food products, optimization of the production processes, recognition of dependencies between various attributes in predicting, among others, pectin viscosity and quality control when obtaining these food products are key aspects for ensuring the efficiency of unit processes in the food industry. This was confirmed by studies on the prediction of pectin viscosity by atomic force microscopy, among others, and measurements of the viscosity of pectin solutions showing the high stability of pectin solutions [10]. Moreover, it demonstrated that rheological changes of potato pectin depend on factors such as concentration, pH value, temperature and metal ions [11]. As a result of technological advances in artificial intelligence (AI), processes for predicting or analyzing relationships between attributes (physical properties) are now becoming as efficient and effective as traditional methods [12,13,14].
Nowadays, machine and deep learning are used in many fields, including image analysis using convolutional neural networks (CNNs) [15,16,17], natural language processing (NLP) [18], classification [19], prediction [20], ask automation and solving other data problems (big data) [21,22].
The study also applies advanced machine learning approaches and physical analysis techniques that will allow for the faster yet effective prediction of food products. It is suggested that the machine learning algorithms will allow for the tracing of a dataset of physical properties and making decisions in the aspect of pectin viscosity prediction.
The aim of the research work was to develop an innovative method for predicting pectin viscosity based on selected physical properties using machine learning algorithms. Artificial intelligence methods were applied with the help of selected regression models. Considering the optimization of production processes and maintaining the quality control of pectin-containing products, the proposed model can be useful in industry, especially in the food as well as pharmaceutical industries. Machine learning and deep learning can help improve quality standards by predicting the relationship between physical properties, in this case viscosity assessment, in order to obtain the optimal final product, i.e., pectin.

2. Materials and Methods

The research material was pectin, exactly, Aglupectin HS-MR in powdered form, which was obtained in cooperation with JRS SILVATEAM INGREDIENTS. Aglupectin HS-MR (pectin) was used for research without further processing.
As part of the study, the basic physical and rheological parameters of pectin in aqueous environments of different pH were determined. In the first step, pectin solutions were prepared in aqueous buffers in the pH range from 3.00 to 8.00 in increments of 1 (citrate-phosphate buffers). In addition, in order to obtain information over the fullest possible range of variation in pectin concentrations typically used in the food industry, tests were performed over a range of concentrations from 1 to 8% (w/w) for each pH value (48 systems in total). In this, an adequate proportion of pectin was weighed out and supplemented with buffer, until a total weight of 120 g was obtained. Pectins are compounds that are difficult to dissolve in aqueous environments, and their dissolution efficiency varies strongly with pH. The preparation procedure consisted of swelling pectin in buffer for 1 day, followed by post-slow dissolution while stirring (mechanical stirrer 140 rpm) and simultaneous gradual heating. The temperature that was used to cook the pectin systems was 50 ± 1 °C for the first hour of dissolution, after which the temperature was raised to 75 ± 1 °C and the process continued at this temperature with constant stirring. The process was stopped when the pectin was visually detected to be completely dissolved (1–2 h after the temperature reached 75 °C, depending on the pH of the buffer and the desired concentration). The solution thus prepared was left under room conditions for 1 day. Measurements were taken immediately after 24 h of preparation. All measurements were performed at room temperature.

2.1. Conductance, Concentration and pH

The concentration was measured with a portable density meter Mettler—Tolledo Densito (Greifensee, Switzerland), using the syringe method. Inside the syringe, about 5 mL of the test sample was placed, then using the syringe plunger, the sample was introduced into the instrument and the measurement was made. After each cycle, the measuring chamber was rinsed with distilled water. The measurement of each solution was performed five times.
The conductivity measurements were made with a Mettler—Tolledo Seven Compact Duo S213 (Switzerland) conductivity meter, using an InLab 731-ISM conductivity probe. Ph measurement was performed with the same instrument, using an InLab Expert PRO ISM probe. Each measurement was repeated five times.

2.2. Color Measurement

In order to determine L*a*b* color parameters, an NH 310 colorimeter (Shenzhen ThreeNH Technology Co., Ltd., Shiyan, China) with a liquid measuring attachment was used. The preparation procedure required preparing the test sample by pouring 35 mL of the test sample into a cuvette. Then, it was locked in a special holder. The color measurement for each test sample was repeated 10 times. As a result of the measurements, mean values and standard deviation (SD) were determined for each sample.

2.3. Viscosity Measurement

In order to obtain information about the basic rheological parameters, the method of dynamic mechanical analysis was used using the DMTW rheological analyzer (COBRABiD, Poznan, Poland) operating in an inverted torsional pendulum system, according to the procedure presented by Rezler et al. [23]. The device used made it possible to evaluate rheological parameters, including elastic modulus, loss modulus and dynamic viscosity values based on free vibration damping decrement measurements. The measurement geometry used was of the plate-cone type (f = 0.03 m, α = 6°). The frequency of the forcing mechanical field was 2.6 Hz. The oscillation frequency of 2.6 Hz used makes it possible to determine the rheological properties of the tested systems (weakly cross-linked) over the entire range of concentrations used. The strain was 0.8%. The measurement of each sample was performed five times. According to the results obtained, the mean viscosity value and the standard deviation (SD) were determined. Due to the characteristics of the samples and the purpose of this work, only the dynamic viscosity values were analyzed. Moreover, a simple analysis of the viscosity dependence on the concentration for each pH value was performed using three different simple mathematical models, power (η = aCb), exponential (η = a exp(bC) and polynomial (η = 1 + aC + bC2), which are typical for different hydrocolloids (η represents viscosity, a and b are coefficients and C is concentration) [24].

2.4. Machine Learning

In the first step, a dataset was prepared based on the obtained numerical data from various unit processes. The dataset contained 6 attributes informing about the physical and rheological properties of pectin, i.e., concentration, pH, color parameters (L*, a*, b*) and value of average viscosity of the pectin. The set contained a total of 482 learning cases with the 70:30 ratio included in the article. This means that 337 cases belong to the training set and the rest to the testing set (145 cases). The attribute for the decision variable was the value responsible for the average viscosity of pectin as a function of concentration and pH range. The process of supervised learning with the decision variable attempts to predict the acquired data in the learning set.
The dataset was divided into a learning set and a test set in a ratio of 70:30. The train and test (TandT) method was used. The splitting of the set was conducted using the train_test_split method from the Scikit-learn library. In the train_test_split method, when the hyperparameters are set, it becomes possible to split the dataset by setting the percentage of the dataset for the learning cases as well as the test cases, respectively.
In the next stage of machine learning, data normalization was performed using the StandardScaler method. This is a well-known method in machine learning. In the Python environment, it allows for scaling the data for both learning and test data, respectively. Data normalization can also improve the learning performance of the extracted models.
According to the issue, 7 predictive models were selected: linear regression (LR), Decision Tree (DT), Random Forest (RF), Support Vector Machine (SVR), Bayesian, ElsaticNet, Huber regression (HR). The learning process also established hyperparameters for the proposed models. In the selection of the models, it focused attention on those models that are quite popular and perform strongly in various decision-making problems. The structure of the hyperparameters for each regression model is provided in Table 1.
The LR model is popular in regression analysis because of its simple, logical interpretation of the data and ease of implementation. The idea behind this model is to fit the data in a set and at the same time look for relationships between the dependent variable (viscosity value) and the other attributes (responsible for the physical properties of pectin). The DT model in the regression works by dividing the learning cases into regions and fitting the model to the decision variable responsible for the level of pectin viscosity. The DT model uses the max_depth hyperparameter at level 9. This hyperparameter optimizes the DT model to control it against overfitting. The RF method involves ensemble learning by building multiple decision trees. RF appears to be equally effective because of its control against over-fitting the model. The RF model learning process used a hyperparameter of n_estimators with a value of 120. The support vector machine in the regression is designed to predict learning cases on physical properties in the learning set. The learning process in SVR with the hyperparameter kernel = ‘rbf’ is mainly based on determining the optimal hyperplane with respect to the distance of the values of the learning cases (maximizing the data margin) compacted in the learning set. Bayesian regression, unlike linear regression based on point estimates of data, allows for estimating the entire probability distribution of learning cases in the set. The ElasticNet model combines the two well-known Lasso and Ridge regression methods in Python. The ElasticNet model uses a hyperparameter for the maximum number of iterations (max_iter), which is set at 1000 iterations. In the Bayesian model, the hyperparameter n_iter = 300 was used, which indicates that the model is taught for 300 iterations. This model was also used to prevent over-fitting the model. The last HR model is a robust regression method minimizing the sum of absolute errors. The HR model used the max_iter hyperparameter at 50 iterations. The HR model provides a balance between robustness and efficiency in regression analysis.

2.5. Statistical Analysis

In this study, the Python language version 3.10 was used for the design and learning process of machine learning algorithms. Currently, Python significantly determines high usability through its friendly syntax, dynamic typification, the ability to quickly name objects and the ability to create modules—collections of functions [25,26,27]. Elementary modules offer advanced operation on, among other things, arrays as well as statistical data through NumPy ver. 1.25.2 and Scikit-learn ver. 1.2.2.
In Python, a Pearson correlation was also performed to determine the relationship between the variables in the set. The significance level (p-value) for Pearson’s correlation was set at 0.05.
Other statistical analyses for each individual parameter characterizing the systems studied were carried out using Statistica 14.1 (TIBCO, Palo Alto, CA, USA) and OriginPro, Version 2024 (OriginLab Corporation, Northampton, MA, USA). An analysis of variance (ANOVA) was conducted to compare means between pairs of L*a*b* color space model groups and viscosity values for different pH values and concentrations. Tukey’s test was applied with a level of importance of p = 0.05.

3. Results and Discussion

3.1. Viscosity Results

Dynamical viscosity is one of the basic physical parameters of homogeneous fluid systems, characterizing intermolecular interactions within the fluid. While analyzing the obtained viscosity values of pectin solutions in aqueous buffers as an individual, separate parameter, it can be observed that the viscosity within a single pH value increases with increasing pectin concentration. In addition, the values obtained for any fixed concentration are lower, the higher the pH of the environment is—Figure 1. It is possible to determine the basic parameters of the relationship describing viscosity substitutions as a function of concentration on the basis of the results obtained. These changes can be described by an exponential function of the type η = A × eB×c, where c represents the concentration, while A and B are constants. This type of relationship is characteristic of hydrocolloids, among others [24,28,29]. Table 2 shows the calculated A and B parameters for the studied structures along with the correlation coefficients of the functions (R2).
The obtained results of viscosity measurements for different pH and concentrations are presented in Table 3 and Figure 2. When analyzing the statistical diversity of density cases, it should be noted that within a given environment (buffer pH), viscosity values are statistically different (p = 0.05) almost for the entire concentration range studied only for low pH (acidic environments)—Figure 2a. The statistically significant differences disappear for low concentrations as the pH increases, and solutions with concentrations higher than 3% and 4% for pH 4–6 and 7–8, respectively, can be considered significantly different cases. Analyzing the statistical differences within a given concentration against pH, it can also be seen that for low concentrations, the samples for all pHs are not statistically different. The higher the pectin concentration, the more noticeable the statistical differences between environments (Figure 2b).

3.2. L*a*b* Color Results

In the result of measuring L*a*b* colors, statistical changes between different ranges of pectin concentration and pH values were determined. In the literature, the team of Gamm et al. also focused on studying the difference between probability distributions of L*a*b* color measurements but proposed a metric called Threshold for Color Difference Discrimination (TCDD) in units of ΔE. They applied Hotelling’s T2 test to the color measurement of color coatings focused, among other things, on evaluating the precision of outlier detection within color reproduction [30]. Badaró’s team and others focused their research on the hyperspectral imaging technique, which is classified based on orange peels according to their pectin content. They focused on principal components analysis (PCA) and linear discriminant analysis (LDA) techniques to separate the group of suppliers of different pectins into three classes of primary, intermediate and external pectin content. The team’s research results from the hypothesis that NIR-HSI may have a quantitative impact on the pectin content in orange peels. The literature has concluded that this technique has potential as an alternative to colorimetric methods, for the quantification of pectin in orange peels and for categorizing orange peel into a group with a pectin concentration driver [31]. The team of Zhu et al. 2016, as part of their analysis of peach fruit, conducted research on determining color differences with pectin distribution as well as fruit maturity. They used hyperspectral imaging, providing a promising alternative and enabling the visualization of pectin distribution at the pixel level [32]. In this research, the Tukey test was chosen to analyze the differences in L*a*b color for pectin between their concentration ranges and pH values. In Table 4, the results of the values determining the lightness (L*) of pectin are shown. It was observed for the results in Table 4 that at a low pH = 3 and pH = 4, there are groups (a or b) that are not statistically significantly different from each other. However, the higher the pH value is, it can be observed that there are several groups (a–f) whose average values are statistically significantly different from each other. That is, changing the concentration from 1% to 8% of pectin viscosity at a fixed value of pH = 5 showed statistical differences in color brightness among themselves. In comparison, at pH = 6, differences in color lightness were similarly shown depending on the change in pectin viscosity concentration.
Table 4 shows the results for the other L*a*b* color parameters a and b. In Table 4, it is observed that the a* component showed for pectin the existence of group a in the viscosity concentration range of 4–8% at pH = 7 and pH = 8. This means that at high pH values, it does not show statistically significant differences between each other. In comparison, a decrease in the pH value at the a* component of the L*a*b* color space model affects the existence of different groups (a–e). This translates into the establishment of differences in viscosity changes relative to the a* component lowering the pH value of pectin.
In Table 4, presenting the results of the L*a*b* colors for the b* component, statistical differences in pectin viscosity are shown as a function of concentration and pH value similarly to the a* component. Considering the values of pH = 7 and pH = 8, no statistically significant differences in pectin viscosity were observed between different concentrations with respect to the b* component. This means that the lower the pH value, the more effectively the existence of groups (a–f) was demonstrated according to the range of pectin concentrations. The results for the color space model L*a*b* unambiguously showed the existence of groups for pectin at pH = 5 and pH = 6. However, it seems crucial to establish the similarity for groups (a and b) at pH = 3 and pH = 4, which are responsible for recognizing the viscosity of pectin with the lightness component (L). Statistical analysis made it possible to identify with a* and b* components the viscosity of pectin at pH = 7 and pH = 8.

3.3. Results of Machine Learning

The study evaluated the capabilities of predictive models. It compared the capabilities of selected machine learning algorithms characterized by different structures (Table 1). In the prediction, the determination index R2 was determined, i.e., a measure of the model’s fit to the data in the set. The higher the R2 index achieved, the more the model fitted the data, i.e., explained the dependence of the viscosity variable (decision variable) on the physical properties of pectin (i.e., selected attributes in the learning set). When considering the fit criterion at a good level, i.e., above 0.7, it can be observed that four out of seven models met this criterion. The best fit with R2 = 0.999 and R2 = 0.998 was achieved on the test set for the DT and RF models, respectively. For comparison, the loss function for the regression models was also determined using mean square error (MSE), mean absolute error (MAE) and root mean square error (RMSE). The error results are shown on the test set in Table 5. The lower the RMSE value, the smaller the difference between the predicted and actual values. It was observed that the most successful regression model’s DT and RF achieved RMSE values of 0.108 and 0.294, respectively (Table 5). This means that an effective fit and the smallest error on the test set were achieved with the Decision Tree architecture. Other models with a good determination index did not achieve an adequate value for the loss function on the test set. This means that the prediction of pectin viscosity is most effectively explained by the algorithm using the Decision Tree or Random Forest architecture. Increasingly, the literature finds more effective learning in classification or model prediction issues using Random Forest or Decision Tree than the traditional use of single neural network models [33,34,35]. The reason is that DTs can quickly perform the learning process and at the same time more efficiently determine the prediction. For RF, the aim is to avoid over-fitting the data on the learning set, achieving high learning efficiency [36,37,38]. While the set appears to be interpretable, a higher efficiency in estimating viscosity for pectin, however, was provided by the DT model.
Pearson’s correlation is also shown in Table 5. The results for individual models explain that the strongest linear relationship between variables (physical properties of pectin) was achieved for the DT, RF and SVR models with r = 0.999, r = 0.999 and r = 0.914, respectively. However, in Table 5, it can be observed that variables for all models are moderately, strongly and even very strongly correlated. This means that there is a strong linear relationship between the variables especially in the models DT and RF. Figure 3 also compares the correlations of actual data to predicted data for all regression models. The best fit can also be observed with the DF and RF models. This is due to the fact that the models fit perfectly to the line of perfect fit (Figure 3). Considering the loss function in the example of RMSE, it can be assessed that the larger the value of RMSE on the test set, the more the model deviates from the value of the perfect fit.
In the literature, you can see many articles on the issue of regression. This is due to the popularity as well as the effectiveness of this method when resolving relationships between data. In a study led by Roop and Asha, it was shown that the regression model using principal component analysis (PCA-LRM) achieved better performance than other approaches in the regression aspect [39]. Yang also showed that MLRM models achieved a decision accuracy significantly higher than traditional regression models [40]. This research work focused on using a machine learning technique to predict pectin viscosity using DF and RF. This is due to the use of these algorithms in other aspects of research in, among others, the identification of fruit powders [12]. As a result, it turned out that the selected machine learning algorithms also achieved better performance compared to the traditional models (i.e., linear regression) [39,40].
In view of the destination of pectin products and the conditions for their effective use, you will find works that analyze the physical, chemical or sensory properties of pectin solutions or suspensions as a separate system (component) [41,42,43]. Nevertheless, research is still being conducted to analyze the properties of pectins. This is due to the fact that they are difficult to solubilize in water, and their use is usually based on the interaction of pectin with other components of the product or intermediate product (in particular, sugars), resulting in the formation of a gel structure. It should be noted that the thickening or gelling properties of pectins are revealed only as a result of their interactions with sugars and that the effectiveness of the overhang and the stability of the structure depend largely on pH. Therefore, in most applications, in order to obtain a gel, it is advisable to add citric acid or other food acids to initiate the gelation process and effectively hold water in the structure [44,45,46]. Producing pectin solutions in aqueous buffers without any additive did not lead to a gel structure, even for extremely low pH values. Nevertheless, the produced pectin solutions were characterized by satisfactory stability (assessed visually—no degradation of the solutions or mold formation was observed during 1 week of storage (under home refrigeration)) and, above all, statistically significant differences in viscosity of the produced systems. Nevertheless, looking at the various applications and behaviors of pectin post-mediately, they can contribute to the understanding of their stability in various aspects, including the fact that high methoxyl pectin (PPOP) showed greater dilution at higher shear rates [47]; pectin-rich acid extract from onion flesh showed stable emulsions with good stability before creaming [48]; and pectin is used as gelling, thickening and stabilizing agents in the food industry [49]. Thus, it was concluded that although the obtained solutions can only serve as a substrate for further industrial use, they are excellent model systems of the variation in physical parameters (especially viscosity) for the analysis and evaluation of the usefulness of machine learning algorithms [50,51].

4. Conclusions

Physical and rheological analyses showed that pectin solutions in aqueous buffers without any additives did not lead to the formation of a gel structure, even at extremely low pH (pH = 3). It was also shown that pectin has a high shelf life over a long period of storage, including at home.
In the case of L*a*b* color analysis, the possibility of determining homogeneous groups between pH changes was demonstrated. In the case of the L* component, homogeneity was statistically significantly demonstrated at low pH (pH = 3 and pH = 4). For the components a* and b*, pectin solutions were shown to maintain homogeneity at high pH (pH= 7 and pH = 8).
The proposed machine learning algorithms successfully estimated pectin viscosity based on concentration, pH and L*a*b*. In fact, it is confirmed that the best performance for estimating pectin viscosity changes was obtained using Random Forest and Decision Tree. The lowest MSE errors of 0.087 and 0.012 were achieved for RF and DT, respectively.
In the future, predicting changes in pectin viscosity online could increase production efficiency while improving the quality of the final product obtained. Applying the modeling of physical parameters through concentration, pH and L*a*b*, it becomes possible to influence pectin viscosity. The application of machine learning leads to the optimization of the current pectin quality control process, which will translate into, among other things, waste control. Machine learning can lead to the development of new food product formulations (i.e., food gelation) by controlling the optimal conditions of selected physical parameters.

Author Contributions

Conceptualization, K.W., P.S., Ł.M. and K.P.; methodology, K.W., P.S., Ł.M. and K.P.; software, K.P., Ł.M. and P.S.; validation, K.P. and P.S.; formal analysis, K.W., P.S., Ł.M. and K.P.; investigation, K.W., P.S., Ł.M., R.R. and K.P.; resources, K.W., P.S., Ł.M. and K.P.; writing—original draft preparation, K.W., P.S., Ł.M. and K.P.; writing—review and editing, K.W., P.S., Ł.M., H.M.B., R.R. and K.P.; visualization, P.S. and K.P.; supervision, K.P. and H.M.B.; project administration, K.W. and H.M.B. All authors have read and agreed to the published version of the manuscript.

Funding

This research was partially funded by the Polish Ministry of Education and Science, grant number: 506.784.03.00/UPP.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

All data are available from the corresponding author upon request.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. The variation in dynamic viscosity values as a function of pectin concentration for different pH.
Figure 1. The variation in dynamic viscosity values as a function of pectin concentration for different pH.
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Figure 2. The analysis of statistically significantly different viscosity cases: (a)—grouping against pH; (b)—grouping against concentration. a–g: the differences between mean values not sharing same letter were statistically significant (p < 0.05).
Figure 2. The analysis of statistically significantly different viscosity cases: (a)—grouping against pH; (b)—grouping against concentration. a–g: the differences between mean values not sharing same letter were statistically significant (p < 0.05).
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Figure 3. A graph of actual values to predicted values for regression models.
Figure 3. A graph of actual values to predicted values for regression models.
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Table 1. The structure of hyperparameters for regression models.
Table 1. The structure of hyperparameters for regression models.
Machine Learning Algorithm TypeNameHyperparameters
LinearRegressionLRdefault
DecisionTreeRegressorDTmax_depth = 9
RandomForestRegressorRFn_estimators = 120
SVRSVRkernel = ’rbf’
BayesianRidgeBayesianRidgen_iter = 300
Elastic NetElastic Netmax_iter = 1000
HuberRegressorHRmax_iter = 50
Table 2. Viscosity function fitting parameters for the exponential model of the test samples.
Table 2. Viscosity function fitting parameters for the exponential model of the test samples.
pHA ± ΔAB ± ΔBR2
30.155 ± 0.0160.648 ± 0.0130.999
40.194 ± 0.0310.578 ± 0.0200.999
50.303 ± 0.0700.444 ± 0.0330.968
60.231 ± 0.0620.461 ± 0.0380.972
70.117 ± 0.0200.554 ± 0.0240.989
80.116 ± 0.0260.542 ± 0.0330.977
Table 3. Results of pectin viscosity measurements.
Table 3. Results of pectin viscosity measurements.
CpH
[%]345678
10.596 ± 0.159 Ga0.699 ± 0.147 Fa0.831 ± 0.090 Ea0.887 ± 0.194 Ea0.812 ± 0.132 Ea0.665 ± 0.104 Ea
20.763 ± 0.840 Ga0.858 ± 0.183 Fa0.915 ± 0.049 Ea1.025 ± 0.498 Ea0.626 ± 0.188 Ea0.585 ± 0.109 Ea
31.512 ± 0.436 Fa1.220 ± 0.197 Fab1.153 ± 0.080 Eab1.004 ± 0.191 Eab0.635 ± 0.129 Eb0.641 ± 0.037 Eb
42.694 ± 0.399 Ea2.095 ± 0.284 Ea2.682 ± 0.296 Da1.442 ± 0.201 Db0.733 ± 0.208 Ec0.746 ± 0.138 Ec
54.044 ± 0.127 Da3.401 ± 0.189 Db2.292 ± 0.218 Dc1.961 ± 0.106 EDcd1.862 ± 0.075 Dcd1.498 ± 0.071 Dd
67.676 ± 0.149 Ca5.301 ± 0.530 Cb3.656 ± 0.125 Cc3.337 ± 0.079 Ccd3.250 ± 0.092 Ccd2.934 ± 0.207 Cd
713.928 ± 0.159 Ba9.866 ± 0.766 Bb6.047 ± 0.252 Bc6.164 ± 0.063 Bc5.537 ± 0.161 Bcd5.351 ± 0.104 Bd
827.758 ± 0.132 Aa19.894 ± 0.105 Ab11.291 ± 0.191 Ac8.681 ± 0.127 Ae9.945 ± 0.177 Ad8.409 ± 0.317 Ae
a–e: the differences between mean values not sharing same letter in row were statistically significant (p < 0.05). A–G: the differences between mean values not sharing same letter in columns were statistically significant (p < 0.05).
Table 4. Results of L*a*b* color measurement for L* considering pectin concentration and different pH values.
Table 4. Results of L*a*b* color measurement for L* considering pectin concentration and different pH values.
ParameterpH\Concentration1%2%3%4%5%6%7%8%
331.63 ± 0.05 c26.68 ± 0.01 b28.12 ± 0.01 b28.70 ± 0.02 d32.04 ± 0.14 b27.76 ± 0.03 a27.45 ± 0.06 a26.17 ± 0.01 b
433.11 ± 0.03 d26.58 ± 0.01 a27.83 ± 0.18 ab26.11 ± 0.01 a27.93 ± 0.68 a27.18 ± 0.25 a31.56 ± 0.01 d28.21 ± 0.13 a
L*533.41 ± 0.02 e35.67 ± 0.03 f34.70 ± 0.02 d33.51 ± 0.02 e32.48 ± 0.02 b33.44 ± 0.45 b36.17 ± 0.01 f30.15 ± 0.01 d
634.13 ± 0.01 f34.09 ± 0.02 e34.14 ± 0.02 c34.54 ± 0.02 f34.65 ± 0.03 c36.42 ± 0.01 c34.68 ± 0.03 e34.17 ± 0.07 e
728.53 ± 0.01 b28.27 ± 0.01 d27.62 ± 0.01 a28.02 ± 0.01 c27.71 ± 0.01 a27.72 ± 0.06 a27.95 ± 0.01 c27.63 ± 0.08 c
827.67 ± 0.01 a26.88 ± 0.01 c27.61 ± 0.01 a27.62 ± 0.01 b27.57 ± 0.01 a27.94 ± 0.01 a27.83 ± 0.01 b28.18 ± 0.01 a
33.15 ± 0.02 a 1.88 ± 0.01 e2.54 ± 0.01 a2.06 ± 0.02 e1.48 ± 0.06 d1.97 ± 0.01 e1.82 ± 0.02 b1.03 ± 0.01 d
43.22 ± 0.02 a 0.75 ± 0.02 d2.49 ± 0.02 a0.90 ± 0.02 d1.74 ± 0.08 e0.38 ± 0.19 d1.37 ± 0.04 b1.63 ± 0.02 b
a*52.82 ± 0.04 d 2.38 ± 0.03 a0.77 ± 0.03 d0.75 ± 0.06 c0.73 ± 0.04 c−0.85 ± 0.07 c−2.33 ± 0.07 c1.73 ± 0.07 b
62.95 ± 0.03 e 2.36 ± 0.05 a1.11 ± 0.09 e0.54 ± 0.04 b−1.29 ± 0.08 b−4.91 ± 0.06 b−0.98 ± 0.32 d−0.71 ± 0.23 c
70.05 ± 0.02 b 0.12 ± 0.02 b0.23 ± 0.01 c−0.04 ± 0.01 a−0.07 ± 0.02 a −0.18 ± 0.02 a−0.19 ± 0.02 a−0.25 ± 0.02 a
8 0.05 ± 0.01 c 0.12 ± 0.01 c0.23 ± 0.01 b−0.04 ± 0.02 a−0.07 ± 0.01 a −0.18 ± 0.02 a−0.19 ± 0.01 a−0.25 ± 0.01 a
3 1.41 ± 0.01 c0.91 ± 0.01 a0.77 ± 0.01 c0.50 ± 0.02 d0.94 ± 0.03 b0.40 ± 0.01 d0.26 ± 0.02 c0.54 ± 0.02 d
4 1.49 ± 0.01 e1.72 ± 0.01 b 1.19 ± 0.01 c0.92 ± 0.02 c0.76 ± 0.04 c0.86 ± 0.01 b1.15 ± 0.01 b0.63 ± 0.02 c
5 1.63 ± 0.02 d1.44 ± 0.02 c1.15 ± 0.02 d1.18 ± 0.02 e0.87 ± 0.02 d0.98 ± 0.01 e0.87 ± 0.01 d0.86 ± 0.01 e
b*6 1.63 ± 0.01 f1.44 ± 0.02 d1.15 ± 0.01 d1.18 ± 0.01 f0.87 ± 0.02 b0.98 ± 0.01 f0.87 ± 0.01 b0.86 ± 0.01 f
7 1.07 ± 0.01 a0.88 ± 0.02 a0.48 ± 0.01 b0.28 ± 0.02 b0.08 ± 0.01 a0.15 ± 0.01 c0.02 ± 0.01 a0.18 ± 0.01 b
8 1.18 ± 0.01 b0.93 ± 0.01 a0.37 ± 0.01 a0.10 ± 0.01 a0.10 ± 0.02 a−0.02 ± 0.01 a0.04 ± 0.01 a0.02 ± 0.01 a
a–f: the differences between mean values with the same letter in columns were statistically insignificant (p < 0.05).
Table 5. Loss and quality metrics for regression models on a test set.
Table 5. Loss and quality metrics for regression models on a test set.
Machine Learning Algorithm TypeMSERMSEMAECoefficient of Determination (R2)Pearson Correlation (r)
LinearRegression8.0692.8411.6560.7710.893
DecisionTreeRegressor0.0120.1080.0130.9990.999
RandomForestRegressor0.0870.2940.0910.9980.999
SVR10.5223.2441.0350.7020.914
BayesianRidge8.1222.8501.6480.7700.892
Elastic Net20.4324.5202.3190.4200.782
HuberRegressor11.8853.4471.5360.6630.875
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Siejak, P.; Przybył, K.; Masewicz, Ł.; Walkowiak, K.; Rezler, R.; Baranowska, H.M. The Prediction of Pectin Viscosity Using Machine Learning Based on Physical Characteristics—Case Study: Aglupectin HS-MR. Sustainability 2024, 16, 5877. https://doi.org/10.3390/su16145877

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Siejak P, Przybył K, Masewicz Ł, Walkowiak K, Rezler R, Baranowska HM. The Prediction of Pectin Viscosity Using Machine Learning Based on Physical Characteristics—Case Study: Aglupectin HS-MR. Sustainability. 2024; 16(14):5877. https://doi.org/10.3390/su16145877

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Siejak, Przemysław, Krzysztof Przybył, Łukasz Masewicz, Katarzyna Walkowiak, Ryszard Rezler, and Hanna Maria Baranowska. 2024. "The Prediction of Pectin Viscosity Using Machine Learning Based on Physical Characteristics—Case Study: Aglupectin HS-MR" Sustainability 16, no. 14: 5877. https://doi.org/10.3390/su16145877

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