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Full Research Article

Prediction of Norduz Sheep Live Weight using Multilayer Perceptron Neural Networks and Least Square Support Vector Machines

A
Aslı Akıllı1,*
S
Suna Akkol2
1Department of Agricultural Economics, Faculty of Agriculture, Kırşehir Ahi Evran University, 40100, Kırşehir, Türkiye.
2Department of Animal Science, Faculty of Agriculture, Van Yüzüncü Yıl University, 65080, Van, Türkiye.

ABSTRACT

Background: Statistical analyses have played a fundamental role in the scientific determination of production traits and environmental factors influencing meat productivity. In recent years, machine learning methods have been increasingly explored due to their potential to enhance the accuracy and efficiency of live weight prediction in sheep.

Methods: In this study, the predictive performance of various machine learning algorithms for estimating body weight in Norduz sheep was comparatively evaluated. multilayer perceptron neural networks (MLPNN) and least squares support vector machines (LS-SVM) were employed, with various network configurations and hyperparameter combinations tested. Biometric measurements-namely age, height at withers (HW), body length (BL), chest width behind paddles (CW), chest depth (CD), chest girth (CG) and thigh circumference (TC)-were utilized as input variables, while body weight (BW) served as the target variable.

Result: The MLPNN model configured using the Bayesian Regularization algorithm and the TanSig activation function yielded the lowest error rates and the highest generalization capability. Within the LS-SVM model, the most accurate predictions were obtained using the radial basis function (RBF) kernel, with optimal hyperparameters set at σ = 5 and γ = 10. Among the biometric traits, Chest Girth was identified as the most influential variable for predicting live weight across both models. Furthermore, Age and Height at Withers were found to be critical determinants in the neural network model, whereas Chest Depth and Chest Width were more prominent in the LS-SVM model.

INTRODUCION

Sheep farming significantly contributes to the food and textile sectors, with the sustainability of products like meat, milk and wool depending on healthy animal populations (Sönmez and Kaymakçı, 1987). Accurate live weight prediction is closely linked to productivity and profitability, playing a vital role in agricultural sustainability. Biometric measurements are essential in animal breeding and research, aiding in breed standard evaluation and growth assessment influenced by environmental and nutritional factors (Sowande and Sobola, 2008; Riva et al., 2004; Shirzeyli et al., 2013). Live weight is a key indicator of health, nutrition and development and biometric traits support selection and genetic improvement programs (Riva et al., 2004). While direct weight measurement is feasible in well-equipped farms, extensive systems often lack such infrastructure, making body measurement-based estimation a practical solution (Olatunji-Akioye and Adeyemo, 2009; Shirzeyli et al., 2013).
       
In recent years, various statistical techniques have been developed to evaluate economically significant biometric traits in sheep, such as live weight, milk yield and wool production (Basak et al., 2024. Recently, machine learning methods have been increasingly investigated due to their potential to improve the accuracy and efficiency of live weight prediction in sheep (Khanikar et al., 2024; Karakuş, 2025). Extensive research in the literature has demonstrated that body measurements serve as practical, accurate and reliable parameters for estimating the live weight of various sheep breeds. Research has been conducted on Thalli sheep by Abbas et al. (2021) and Tırınk (2022); on Harnai sheep by Iqbal et al. (2021); on Norduz sheep by Cakmakçı (2022); on Mengali rams by Celik et al. (2017); on Kajli sheep by Faraz et al. (2023); on Balochi sheep by Norouzian and Vakili Alavijeh (2016) and Huma and Iqbal (2019); on Romane sheep by Tırınk et al. (2023b); and on Suffolk-polish merino sheep by Tırınk et al. (2023a). These studies collectively highlight the applicability of machine learning techniques across a broad range of breeds for live weight estimation.
       
Although machine learning has been applied to predict body weight in several sheep breeds (Abbas et al., 2021; Huma and Iqbal, 2019; Tırınk et al., 2023a), studies on Türkiye’s native breeds remain limited. While algorithms have been used for Thalli, Balochi, Corriedale, Akkaraman and Morkaraman breeds (Tırınk, 2022; Tırınk et al., 2023b), research involving Norduz sheep is scarce (Cakmakçı, 2022). Endemic to the Norduz region in Van’s Gürpýnar district, this breed has adapted to harsh Eastern Anatolian conditions for over 250 years (Yılmaz et al., 2012a; Aydın et al., 2024; Karakuş, 2024). Conservation of this breed is considered essential, as Türkiye is located at the intersection of three global biodiversity hotspots (Gür, 2016) and hosts the richest temperate flora (Sekercioğlu et al., 2011). Although native breeds make up most of the country’s 45 million sheep (Aydın et al., 2024), many are endangered and require protection (Yılmaz et al., 2012b). In Norduz sheep, limited datasets, measurement standardization issues and restricted access to weighing tools hinder the accuracy of machine learning models (Yıldırır et al., 2023; Mia et al., 2025).
               
This study aims to predict the live weight of Norduz sheep using machine learning methods, specifically MLPNN and LS-SVM, based on age and various biometric measurements. 

MATERIALS AND METHODS

Data source
 
The data set comprises the results of study involved 312 Norduz sheep biometric trait record aged 1 to 4 years, reared at the Van Yüzüncü Yıl University Research and Application Management Directorate (Van Yüzüncü Yıl University Rectorate Animal Experiments Local Ethics Committee, decision number: 2018/10). The input variables were defined as Age, HW, BL, CW, CD, CG and TC with BW serving as the output variable.
 
Data preprocessing and model evaluation
 
The dataset was normalized using the D-Min-Max method, as defined in Equation 1 (Akıllı and Atıl, 2020). To prevent overfitting and underfitting, the data were randomly partitioned and k - fold cross -validation was applied to ensure robust performance evaluation. Error metrics were assessed at each training, testing and validation stage. Model performance was evaluated using mean squared error (MSE), mean absolute percentage error (MAPE) and R2Adj. The model yielding the lowest MSE and MAPE, along with the highest R2Adj on the test set, was identified as optimal. Formulations of these metrics are provided in Equations 2-4, where yi denotes the actual value, ŷ1 the predicted value and n the number of observations. All implementations and evaluations were conducted using Matlab (R2024b) and Python (v3.12) on the Google Colab platform. The development and evaluation process are summarized in Fig 1.
 







Fig 1: Flowchart of model development and evaluation processes for NN and LSSVM algorithms.

 
Neural networks
 
This study employed the MLP model, trained by adjusting weights to align outputs with target values using the backpropagation algorithm (Rana et al., 2021; Haldar et al., 2023). The mathematical representation of the output is given in Equation 5. Where xj is the input vector,  (i = 1, 2..., n), wj represents the weight vector, b is the bias term, f is the activation function and y is the output. An activation function limits a neuron’s output to a finite range, enhancing computational stability and nonlinearity (Haykin, 1999). This study employs two sigmoidal activation functions commonly used in multilayer perceptrons, presented in Equation 6 (Ostovar et al., 2025) and Equation 7 (Dubey et al., 2022). The Logistic Sigmoid maps real numbers to [0,1], supporting probability-based interpretations, while the Tanh function compresses inputs to [-1,1], both regulating output amplitude (Haykin, 1999; Dubey et al., 2022).





 
The normalized importance of the predictor variables was assessed using connection weights and the Garson algorithm (Ma et al., 2024).
 
Least square support vector machine
 
A specialized variant of SVM (Ahmad, 2023), known as LS-SVM, was developed by Suykens et al. (2002) to reduce the complexity associated with optimization procedures in quadratic programming problems.
       
In this study, the training set comprises pairs {xi, yi} with model parameters designated as w ∈ R and b ∈ R  Equation 8 defines w; as the weight vector and b represents the bias term. The nonlinear mapping function ϕ is defined as ϕ: R → R. The initial step in creating a kernel-based model involves configuring the Lagrange function, presented in Equation 9, to address the optimization problem. Here, αi represents the Lagrange multipliers.




In the subsequent step, derivatives with respect to the primal and dual variables are computed using the Lagrange formulation and the formulation is then aligned with the Karush-Kuhn-Tucker (KKT) conditions to ensure optimality. The results are derived from the partial derivatives with respect to the parameters w, b, e and a. The kernel matrix is defined as Ωij = ϕ(xi)T ϕ(xj) = K(xi, xj), for (i, j = 1, ..., N). In high-dimensional feature spaces, the mapping function ϕ is not explicitly defined within kernel-based methods. Kernel functions are required to meet Mercer’s conditions (Mercer, 1909). The application of Mercer’s conditions to the  matrix facilitates the derivation of the LS-SVM for regression, as expressed in Equation 8 (Suykens et al., 2002).
               
In this study, radial basis function (RBF) and Polynomial Kernel Function were used. Their mathematical expressions are given in Table 1. The Grid Search method was employed to optimize the RBF model, with σ ranging from 1-100 and γ from 0.46-1. Variable importance was assessed using the permutation importance technique (Dai et al., 2024).

Table 1: Kernel functions.

RESULTS AND DISCUSSION

Descriptive statistics for biometric measurements of Norduz sheep were given in Table 2. The mean Age of the sheep was determined as 2.21 years, with a standard deviation of 1.07 years. Overall results indicated that variables’ distributions closely approximating normality. Heatmap of Pearson Correlation Coefficients Among biometric parameters with body weight was included in Fig 2. The results of the correlation analysis indicated statistically significant associations between most of the examined biometric variables and BW.

Table 2: Descriptive statistics of Norduz Sheeps’ data.



Fig 2: Heatmap of pearson correlation coefficients among biometric traits.


       
Fig 3 and 4 present training and testing error metrics for MLP networks. As seen in Fig 3 and Fig 4, the TanSig function yielded lower MSE and MAPE values with algorithms such as BR, LM and CGB. The BR algorithm maintained low error levels across neuron counts, demonstrating high stability and generalization performance.

Fig 3: Error metrics for MLP network with ‘TanSig’ activation function.



Fig 4: Error metrics for MLP network with ‘Logsig’ activation function.


       
MLP models with varying neuron numbers and TanSig/LogSig activation functions were evaluated in detail, with optimal numerical outcomes reported in Table 3. Most algorithms showed no significant overfitting or underfitting; however, some failed to balance training and test errors, indicating generalization issues. The BR algorithm, configured with 30 hidden neurons and TanSig function, yielded the lowest test errors and the highest , while also achieving the best AIC and BIC scores. In contrast, GD, GDM and GDX algorithms resulted in relatively high errors, with many configurations displaying underfitting. Graphical summaries of Table 3 are provided in Fig 5.

Table 3: Statistical performance criteria for MLP Networks.



Fig 5: Performance metrics by algorithm and activation function for MLP networks.


       
Fig 5 provides graphical representations of performance metrics for configurations that fit the dataset effectively and exhibit strong generalization capabilities within MLP networks. In Fig 5, graphical representations of performance metrics for MLP configurations with strong generalization capability are presented. The BR algorithm with TanSig and LogSig activation functions yielded the lowest MSE and MAPE values and the highest R2Adj. Additionally, the LM, SCG and CGB algorithms also demonstrated low error rates and high R2Adj values.
       
Table 4 presents the statistical performance metrics of the LS-SVM model using the RBF Kernel across various σ and γ combinations. A notable overfitting instance was observed at σ=1 and γ =10, with a large gap between training and test errors. The best performance was achieved at σ=5 and γ =10, yielding low and balanced errors, indicating effective generalization. Conversely, high σ (≥30) and low γ  (≤1) led to increased errors in both sets, suggesting underfitting and insufficient learning capacity.

Table 4: Statistical criteria for LS-SVM with radial basis function.


       
In Fig 6, graphical representations of performance metrics are included for various σ and γ hyperparameter combinations configured with the RBF Kernel function in the LS-SVM technique. As supported by the data presented in Table 4, at low σ (σ = 1) values, as the γ parameter increases, the error rates in the training set decrease rapidly, while the error rates in the test set tend to increase after a certain point. On the other hand, at medium σ values (especially for σ=5 and σ=10), as g increases, both training and test error values decrease significantly and follow a balanced course. As can be seen in Fig 6, at moderate values (notably σ=5 and σ=10), an increment in γ is linked with a pronounced reduction in error rates for both training and testing. Conversely, in conditions with high σ (σ≥50) and low γ (γ≤2.15), a significant rise in error rates for both training and testing is detected, suggesting the emergence of underfitting and a lack of adequate generalization capacity.

Fig 6: Comparative performance metrics of LS-SVM for sigma-gamma combinations.


       
In Table 5, the statistical performance metrics for different polynomial degrees of the LS-SVM model with a Polynomial Kernel Function are presented. It was observed that lower degrees (1 and 2) yielded low training errors, while test errors remained relatively higher but acceptable.

Table 5: Statistical criteria for LS-SVM with polynomial kernel function.


       
According to Tables 3 and 4, the highest prediction performance was achieved by the MLP model configured with the BR algorithm and TanSig activation function. In Fig 7(a), a close alignment between observed and predicted values is illustrated, indicating that the BR-TanSig model captured dataset fluctuations effectively. The Pearson correlation coefficient was calculated as 0.898. Fig 7(b) presents the normalized importance of independent variables. CG, HW and age were identified as the most influential predictors, while BL contributed the least to model performance.

Fig 7: Actual and predicted values of BR algorithm- normalized importance score of MLP (b).


       
In the domain of sheep farming, it has been reported that machine learning algorithms employing k-fold repeated cross-validation have yielded successful outcomes for body weight prediction, as demonstrated in several studies (Shahinfar and Kahn, 2018; Huma and Iqbal, 2019; Cakmakçı, 2022; Chay-Canul et al., 2024; Hamadani and Ganai, 2023; Tırınk et al., 2023a; Tırınk et al., 2023b). Unlike in conducted study by Tırınk (2022), our research has explored neural network methods in a more detailed manner, assessing various configurations comprehensively. Similarly, in the study by Akkol et al. (2017), BR algorithm outperformed other network structures significantly. In Norouzian and Alavijeh (2016)’s study, similar to our results, LM algorithm was employed with a sigmoid activation function, demonstrating substantial effectiveness, according to our results. Unlike our study, a measurement system employing Kinect as a sensor for BW prediction was developed by Chay-Canul et al. (2024). Similar to our study, Iqbal et al. (2021) also employed the RBF Kernel function; however, it introduced two heuristic algorithms, simulated annealing and the simplex method, for adjusting the hyperparameters of the LS-SVM model. Additionally, research by Huma and Iqbal (2019) also included support vector machines, it is seen that the generalization abilities of the models are quite successful. In the study executed by Cakmakçı (2022), contrary to our study, the Boruta algorithm was employed for feature selection. However, align with our results, the most significant variables were found as Chest width, CD and HW. Since the animals in the study had completed their developmental period, it is considered that the significance level of BL differed from the findings of the present study. Another point of divergence is that age was included as an independent variable in our model to assess the effects of different developmental stages. Additionally, the inclusion of the age variable resulted in differences in the correlations among the variables. Contrary to our study results, it was reported that the CART model exhibited lower RMSE and MAPE values compared to the NN mode with different biometric measurements in Celik et al. (2017)’s study. Similar to our study; thoracic perimeter was among the important variables in estimating body weight of sheep. Ali et al. (2015) conducted research with different biometric measurements from our study. Our results are aligned with existing studies in the literature, indicating that chest girth (CG) measurement can be regarded as one of the essential biometric parameters for predicting BW (Sabbioni et al., 2020; Gurgel et al., 2021; Djaout et al., 2022).
       
The potential of machine learning algorithms to support livestock management has been demonstrated. Body weight estimation based on traits such as chest girth and height at withers has been shown to facilitate the assessment of growth, the optimization of feeding strategies and the selection of superior animals without requiring direct weighing, particularly in resource-limited systems. Certain limitations should be acknowledged. The sample size (n = 312) and the use of data from a single location may limit generalizability. Additionally, variations in biometric traits caused by environmental factors such as nutrition and seasonal conditions may reduce prediction accuracy. To enhance reliability, broader validation across diverse datasets is recommended.

CONCLUSION

In this study, the predictive performances of neural networks and LS-SVM models for estimating the live weight of Norduz sheep were compared. Both models demonstrated strong predictive capabilities when optimized, with parameter tuning shown to be critical for success. In the LS-SVM model, biometric variables such as CD and CG had the greatest influence, while age and HW were more prominent in the MLP model. Consistent with the literature, CG emerged as the most influential variable across both models. The study emphasizes the necessity of systematic parameter optimization and adaptive model selection based on dataset characteristics. Findings are intended to support the integration of machine learning into small livestock systems and the development of data-driven prediction and decision support tools. The application of biometric analysis, particularly live weight estimation, is considered to enhance breeder productivity, support genetic selection processes and contribute to sustainable livestock practices. It is anticipated that the results will guide future research involving different breeds and age groups and inform the development of real-time prediction systems. Integrating the proposed model into mobile-based tools may offer practical benefits in livestock management. A user-friendly application enabling rapid weight estimation via basic biometric inputs could improve herd management, especially in rural areas with limited access to veterinary services. Further studies are recommended to assess the feasibility, scalability and practical applicability of such systems in diverse field conditions.

ACKNOWLEDGEMENT

Authors’ contributions
 
Aslı Akıllı (ORCID: 0000-0003-3879-710X) conceptualisation, methodology, analysis, writing, review, editing; Suna Akkol (ORCID: 0000-0001-5123-7516) conceptualisation, methodology, writing, data collection, review, editing. Both authors have read and approved the finalised manuscript.
 
Disclaimers
 
The views and conclusions expressed in this article are solely those of the authors and do not necessarily represent the views of their affiliated institutions. The authors are responsible for the accuracy and completeness of the information provided, but do not accept any liability for any direct or indirect losses resulting from the use of this content.
 
Informed consent
 
No animal experiments were conducted in this study. As such, approval from an animal ethics committee was not applicable.

CONFLICT OF INTEREST

The authors declare that there are no conflicts of interest regarding the publication of this article. No funding or sponsorship influenced the design of the study, data collection, analysis, decision to publish or preparation of the manuscript.

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    Full Research Article

    Prediction of Norduz Sheep Live Weight using Multilayer Perceptron Neural Networks and Least Square Support Vector Machines

    A
    Aslı Akıllı1,*
    S
    Suna Akkol2
    1Department of Agricultural Economics, Faculty of Agriculture, Kırşehir Ahi Evran University, 40100, Kırşehir, Türkiye.
    2Department of Animal Science, Faculty of Agriculture, Van Yüzüncü Yıl University, 65080, Van, Türkiye.

    ABSTRACT

    Background: Statistical analyses have played a fundamental role in the scientific determination of production traits and environmental factors influencing meat productivity. In recent years, machine learning methods have been increasingly explored due to their potential to enhance the accuracy and efficiency of live weight prediction in sheep.

    Methods: In this study, the predictive performance of various machine learning algorithms for estimating body weight in Norduz sheep was comparatively evaluated. multilayer perceptron neural networks (MLPNN) and least squares support vector machines (LS-SVM) were employed, with various network configurations and hyperparameter combinations tested. Biometric measurements-namely age, height at withers (HW), body length (BL), chest width behind paddles (CW), chest depth (CD), chest girth (CG) and thigh circumference (TC)-were utilized as input variables, while body weight (BW) served as the target variable.

    Result: The MLPNN model configured using the Bayesian Regularization algorithm and the TanSig activation function yielded the lowest error rates and the highest generalization capability. Within the LS-SVM model, the most accurate predictions were obtained using the radial basis function (RBF) kernel, with optimal hyperparameters set at σ = 5 and γ = 10. Among the biometric traits, Chest Girth was identified as the most influential variable for predicting live weight across both models. Furthermore, Age and Height at Withers were found to be critical determinants in the neural network model, whereas Chest Depth and Chest Width were more prominent in the LS-SVM model.

    INTRODUCION

    Sheep farming significantly contributes to the food and textile sectors, with the sustainability of products like meat, milk and wool depending on healthy animal populations (Sönmez and Kaymakçı, 1987). Accurate live weight prediction is closely linked to productivity and profitability, playing a vital role in agricultural sustainability. Biometric measurements are essential in animal breeding and research, aiding in breed standard evaluation and growth assessment influenced by environmental and nutritional factors (Sowande and Sobola, 2008; Riva et al., 2004; Shirzeyli et al., 2013). Live weight is a key indicator of health, nutrition and development and biometric traits support selection and genetic improvement programs (Riva et al., 2004). While direct weight measurement is feasible in well-equipped farms, extensive systems often lack such infrastructure, making body measurement-based estimation a practical solution (Olatunji-Akioye and Adeyemo, 2009; Shirzeyli et al., 2013).
           
    In recent years, various statistical techniques have been developed to evaluate economically significant biometric traits in sheep, such as live weight, milk yield and wool production (Basak et al., 2024. Recently, machine learning methods have been increasingly investigated due to their potential to improve the accuracy and efficiency of live weight prediction in sheep (Khanikar et al., 2024; Karakuş, 2025). Extensive research in the literature has demonstrated that body measurements serve as practical, accurate and reliable parameters for estimating the live weight of various sheep breeds. Research has been conducted on Thalli sheep by Abbas et al. (2021) and Tırınk (2022); on Harnai sheep by Iqbal et al. (2021); on Norduz sheep by Cakmakçı (2022); on Mengali rams by Celik et al. (2017); on Kajli sheep by Faraz et al. (2023); on Balochi sheep by Norouzian and Vakili Alavijeh (2016) and Huma and Iqbal (2019); on Romane sheep by Tırınk et al. (2023b); and on Suffolk-polish merino sheep by Tırınk et al. (2023a). These studies collectively highlight the applicability of machine learning techniques across a broad range of breeds for live weight estimation.
           
    Although machine learning has been applied to predict body weight in several sheep breeds (Abbas et al., 2021; Huma and Iqbal, 2019; Tırınk et al., 2023a), studies on Türkiye’s native breeds remain limited. While algorithms have been used for Thalli, Balochi, Corriedale, Akkaraman and Morkaraman breeds (Tırınk, 2022; Tırınk et al., 2023b), research involving Norduz sheep is scarce (Cakmakçı, 2022). Endemic to the Norduz region in Van’s Gürpýnar district, this breed has adapted to harsh Eastern Anatolian conditions for over 250 years (Yılmaz et al., 2012a; Aydın et al., 2024; Karakuş, 2024). Conservation of this breed is considered essential, as Türkiye is located at the intersection of three global biodiversity hotspots (Gür, 2016) and hosts the richest temperate flora (Sekercioğlu et al., 2011). Although native breeds make up most of the country’s 45 million sheep (Aydın et al., 2024), many are endangered and require protection (Yılmaz et al., 2012b). In Norduz sheep, limited datasets, measurement standardization issues and restricted access to weighing tools hinder the accuracy of machine learning models (Yıldırır et al., 2023; Mia et al., 2025).
                   
    This study aims to predict the live weight of Norduz sheep using machine learning methods, specifically MLPNN and LS-SVM, based on age and various biometric measurements. 

    MATERIALS AND METHODS

    Data source
     
    The data set comprises the results of study involved 312 Norduz sheep biometric trait record aged 1 to 4 years, reared at the Van Yüzüncü Yıl University Research and Application Management Directorate (Van Yüzüncü Yıl University Rectorate Animal Experiments Local Ethics Committee, decision number: 2018/10). The input variables were defined as Age, HW, BL, CW, CD, CG and TC with BW serving as the output variable.
     
    Data preprocessing and model evaluation
     
    The dataset was normalized using the D-Min-Max method, as defined in Equation 1 (Akıllı and Atıl, 2020). To prevent overfitting and underfitting, the data were randomly partitioned and k - fold cross -validation was applied to ensure robust performance evaluation. Error metrics were assessed at each training, testing and validation stage. Model performance was evaluated using mean squared error (MSE), mean absolute percentage error (MAPE) and R2Adj. The model yielding the lowest MSE and MAPE, along with the highest R2Adj on the test set, was identified as optimal. Formulations of these metrics are provided in Equations 2-4, where yi denotes the actual value, ŷ1 the predicted value and n the number of observations. All implementations and evaluations were conducted using Matlab (R2024b) and Python (v3.12) on the Google Colab platform. The development and evaluation process are summarized in Fig 1.
     







    Fig 1: Flowchart of model development and evaluation processes for NN and LSSVM algorithms.

     
    Neural networks
     
    This study employed the MLP model, trained by adjusting weights to align outputs with target values using the backpropagation algorithm (Rana et al., 2021; Haldar et al., 2023). The mathematical representation of the output is given in Equation 5. Where xj is the input vector,  (i = 1, 2..., n), wj represents the weight vector, b is the bias term, f is the activation function and y is the output. An activation function limits a neuron’s output to a finite range, enhancing computational stability and nonlinearity (Haykin, 1999). This study employs two sigmoidal activation functions commonly used in multilayer perceptrons, presented in Equation 6 (Ostovar et al., 2025) and Equation 7 (Dubey et al., 2022). The Logistic Sigmoid maps real numbers to [0,1], supporting probability-based interpretations, while the Tanh function compresses inputs to [-1,1], both regulating output amplitude (Haykin, 1999; Dubey et al., 2022).





     
    The normalized importance of the predictor variables was assessed using connection weights and the Garson algorithm (Ma et al., 2024).
     
    Least square support vector machine
     
    A specialized variant of SVM (Ahmad, 2023), known as LS-SVM, was developed by Suykens et al. (2002) to reduce the complexity associated with optimization procedures in quadratic programming problems.
           
    In this study, the training set comprises pairs {xi, yi} with model parameters designated as w ∈ R and b ∈ R  Equation 8 defines w; as the weight vector and b represents the bias term. The nonlinear mapping function ϕ is defined as ϕ: R → R. The initial step in creating a kernel-based model involves configuring the Lagrange function, presented in Equation 9, to address the optimization problem. Here, αi represents the Lagrange multipliers.




    In the subsequent step, derivatives with respect to the primal and dual variables are computed using the Lagrange formulation and the formulation is then aligned with the Karush-Kuhn-Tucker (KKT) conditions to ensure optimality. The results are derived from the partial derivatives with respect to the parameters w, b, e and a. The kernel matrix is defined as Ωij = ϕ(xi)T ϕ(xj) = K(xi, xj), for (i, j = 1, ..., N). In high-dimensional feature spaces, the mapping function ϕ is not explicitly defined within kernel-based methods. Kernel functions are required to meet Mercer’s conditions (Mercer, 1909). The application of Mercer’s conditions to the  matrix facilitates the derivation of the LS-SVM for regression, as expressed in Equation 8 (Suykens et al., 2002).
                   
    In this study, radial basis function (RBF) and Polynomial Kernel Function were used. Their mathematical expressions are given in Table 1. The Grid Search method was employed to optimize the RBF model, with σ ranging from 1-100 and γ from 0.46-1. Variable importance was assessed using the permutation importance technique (Dai et al., 2024).

    Table 1: Kernel functions.

    RESULTS AND DISCUSSION

    Descriptive statistics for biometric measurements of Norduz sheep were given in Table 2. The mean Age of the sheep was determined as 2.21 years, with a standard deviation of 1.07 years. Overall results indicated that variables’ distributions closely approximating normality. Heatmap of Pearson Correlation Coefficients Among biometric parameters with body weight was included in Fig 2. The results of the correlation analysis indicated statistically significant associations between most of the examined biometric variables and BW.

    Table 2: Descriptive statistics of Norduz Sheeps’ data.



    Fig 2: Heatmap of pearson correlation coefficients among biometric traits.


           
    Fig 3 and 4 present training and testing error metrics for MLP networks. As seen in Fig 3 and Fig 4, the TanSig function yielded lower MSE and MAPE values with algorithms such as BR, LM and CGB. The BR algorithm maintained low error levels across neuron counts, demonstrating high stability and generalization performance.

    Fig 3: Error metrics for MLP network with ‘TanSig’ activation function.



    Fig 4: Error metrics for MLP network with ‘Logsig’ activation function.


           
    MLP models with varying neuron numbers and TanSig/LogSig activation functions were evaluated in detail, with optimal numerical outcomes reported in Table 3. Most algorithms showed no significant overfitting or underfitting; however, some failed to balance training and test errors, indicating generalization issues. The BR algorithm, configured with 30 hidden neurons and TanSig function, yielded the lowest test errors and the highest , while also achieving the best AIC and BIC scores. In contrast, GD, GDM and GDX algorithms resulted in relatively high errors, with many configurations displaying underfitting. Graphical summaries of Table 3 are provided in Fig 5.

    Table 3: Statistical performance criteria for MLP Networks.



    Fig 5: Performance metrics by algorithm and activation function for MLP networks.


           
    Fig 5 provides graphical representations of performance metrics for configurations that fit the dataset effectively and exhibit strong generalization capabilities within MLP networks. In Fig 5, graphical representations of performance metrics for MLP configurations with strong generalization capability are presented. The BR algorithm with TanSig and LogSig activation functions yielded the lowest MSE and MAPE values and the highest R2Adj. Additionally, the LM, SCG and CGB algorithms also demonstrated low error rates and high R2Adj values.
           
    Table 4 presents the statistical performance metrics of the LS-SVM model using the RBF Kernel across various σ and γ combinations. A notable overfitting instance was observed at σ=1 and γ =10, with a large gap between training and test errors. The best performance was achieved at σ=5 and γ =10, yielding low and balanced errors, indicating effective generalization. Conversely, high σ (≥30) and low γ  (≤1) led to increased errors in both sets, suggesting underfitting and insufficient learning capacity.

    Table 4: Statistical criteria for LS-SVM with radial basis function.


           
    In Fig 6, graphical representations of performance metrics are included for various σ and γ hyperparameter combinations configured with the RBF Kernel function in the LS-SVM technique. As supported by the data presented in Table 4, at low σ (σ = 1) values, as the γ parameter increases, the error rates in the training set decrease rapidly, while the error rates in the test set tend to increase after a certain point. On the other hand, at medium σ values (especially for σ=5 and σ=10), as g increases, both training and test error values decrease significantly and follow a balanced course. As can be seen in Fig 6, at moderate values (notably σ=5 and σ=10), an increment in γ is linked with a pronounced reduction in error rates for both training and testing. Conversely, in conditions with high σ (σ≥50) and low γ (γ≤2.15), a significant rise in error rates for both training and testing is detected, suggesting the emergence of underfitting and a lack of adequate generalization capacity.

    Fig 6: Comparative performance metrics of LS-SVM for sigma-gamma combinations.


           
    In Table 5, the statistical performance metrics for different polynomial degrees of the LS-SVM model with a Polynomial Kernel Function are presented. It was observed that lower degrees (1 and 2) yielded low training errors, while test errors remained relatively higher but acceptable.

    Table 5: Statistical criteria for LS-SVM with polynomial kernel function.


           
    According to Tables 3 and 4, the highest prediction performance was achieved by the MLP model configured with the BR algorithm and TanSig activation function. In Fig 7(a), a close alignment between observed and predicted values is illustrated, indicating that the BR-TanSig model captured dataset fluctuations effectively. The Pearson correlation coefficient was calculated as 0.898. Fig 7(b) presents the normalized importance of independent variables. CG, HW and age were identified as the most influential predictors, while BL contributed the least to model performance.

    Fig 7: Actual and predicted values of BR algorithm- normalized importance score of MLP (b).


           
    In the domain of sheep farming, it has been reported that machine learning algorithms employing k-fold repeated cross-validation have yielded successful outcomes for body weight prediction, as demonstrated in several studies (Shahinfar and Kahn, 2018; Huma and Iqbal, 2019; Cakmakçı, 2022; Chay-Canul et al., 2024; Hamadani and Ganai, 2023; Tırınk et al., 2023a; Tırınk et al., 2023b). Unlike in conducted study by Tırınk (2022), our research has explored neural network methods in a more detailed manner, assessing various configurations comprehensively. Similarly, in the study by Akkol et al. (2017), BR algorithm outperformed other network structures significantly. In Norouzian and Alavijeh (2016)’s study, similar to our results, LM algorithm was employed with a sigmoid activation function, demonstrating substantial effectiveness, according to our results. Unlike our study, a measurement system employing Kinect as a sensor for BW prediction was developed by Chay-Canul et al. (2024). Similar to our study, Iqbal et al. (2021) also employed the RBF Kernel function; however, it introduced two heuristic algorithms, simulated annealing and the simplex method, for adjusting the hyperparameters of the LS-SVM model. Additionally, research by Huma and Iqbal (2019) also included support vector machines, it is seen that the generalization abilities of the models are quite successful. In the study executed by Cakmakçı (2022), contrary to our study, the Boruta algorithm was employed for feature selection. However, align with our results, the most significant variables were found as Chest width, CD and HW. Since the animals in the study had completed their developmental period, it is considered that the significance level of BL differed from the findings of the present study. Another point of divergence is that age was included as an independent variable in our model to assess the effects of different developmental stages. Additionally, the inclusion of the age variable resulted in differences in the correlations among the variables. Contrary to our study results, it was reported that the CART model exhibited lower RMSE and MAPE values compared to the NN mode with different biometric measurements in Celik et al. (2017)’s study. Similar to our study; thoracic perimeter was among the important variables in estimating body weight of sheep. Ali et al. (2015) conducted research with different biometric measurements from our study. Our results are aligned with existing studies in the literature, indicating that chest girth (CG) measurement can be regarded as one of the essential biometric parameters for predicting BW (Sabbioni et al., 2020; Gurgel et al., 2021; Djaout et al., 2022).
           
    The potential of machine learning algorithms to support livestock management has been demonstrated. Body weight estimation based on traits such as chest girth and height at withers has been shown to facilitate the assessment of growth, the optimization of feeding strategies and the selection of superior animals without requiring direct weighing, particularly in resource-limited systems. Certain limitations should be acknowledged. The sample size (n = 312) and the use of data from a single location may limit generalizability. Additionally, variations in biometric traits caused by environmental factors such as nutrition and seasonal conditions may reduce prediction accuracy. To enhance reliability, broader validation across diverse datasets is recommended.

    CONCLUSION

    In this study, the predictive performances of neural networks and LS-SVM models for estimating the live weight of Norduz sheep were compared. Both models demonstrated strong predictive capabilities when optimized, with parameter tuning shown to be critical for success. In the LS-SVM model, biometric variables such as CD and CG had the greatest influence, while age and HW were more prominent in the MLP model. Consistent with the literature, CG emerged as the most influential variable across both models. The study emphasizes the necessity of systematic parameter optimization and adaptive model selection based on dataset characteristics. Findings are intended to support the integration of machine learning into small livestock systems and the development of data-driven prediction and decision support tools. The application of biometric analysis, particularly live weight estimation, is considered to enhance breeder productivity, support genetic selection processes and contribute to sustainable livestock practices. It is anticipated that the results will guide future research involving different breeds and age groups and inform the development of real-time prediction systems. Integrating the proposed model into mobile-based tools may offer practical benefits in livestock management. A user-friendly application enabling rapid weight estimation via basic biometric inputs could improve herd management, especially in rural areas with limited access to veterinary services. Further studies are recommended to assess the feasibility, scalability and practical applicability of such systems in diverse field conditions.

    ACKNOWLEDGEMENT

    Authors’ contributions
     
    Aslı Akıllı (ORCID: 0000-0003-3879-710X) conceptualisation, methodology, analysis, writing, review, editing; Suna Akkol (ORCID: 0000-0001-5123-7516) conceptualisation, methodology, writing, data collection, review, editing. Both authors have read and approved the finalised manuscript.
     
    Disclaimers
     
    The views and conclusions expressed in this article are solely those of the authors and do not necessarily represent the views of their affiliated institutions. The authors are responsible for the accuracy and completeness of the information provided, but do not accept any liability for any direct or indirect losses resulting from the use of this content.
     
    Informed consent
     
    No animal experiments were conducted in this study. As such, approval from an animal ethics committee was not applicable.

    CONFLICT OF INTEREST

    The authors declare that there are no conflicts of interest regarding the publication of this article. No funding or sponsorship influenced the design of the study, data collection, analysis, decision to publish or preparation of the manuscript.

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