Machine Learning Algorithmic Models for the Authentication of Albanian Mono-Cultivar Olive Oils

Introduction

kNN (K-Nearest Neighbours)

The kNN algorithm performs the classification task by predicting a new given object based on the Euclidean distance (the distance between the training point and the test observation).

$$d\left(x,y\right)=\sqrt{\sum _{i=1}^n{\left(x_i-y_i\right)}^2}=\sqrt{{\left(x_1-y_1\right)}^2+{\left(x_2-y_2\right)}^2+\dots +{\left(x_n-y_n\right)}^2}$$

(1)

In Equation (1), $n$ represents the counts of dimensions, whereas $x_i$ and $y_i$ denotes the data points.

The equation (1) can also be expressed as follows:

$$d\left(x_i,x_t\right)=\sqrt{\sum _{j=1}^d{\left(x_{ij}-x_{tj}\right)}^2}=‖x_i-x_t‖$$

(2)

where $x_i$ represents the training dataset and $x_t$ indicates the test observation (Zaza et al., 2023).

The Rationale Behind the Algorithm and Its Adjustment to Our Dataset

Suppose we need to create a new data object, such as an olive oil, for which the user can specify attributes like MUFA and PUFA. In this scenario, the purpose of the algorithm is to determine if the olive oil belongs to one of the following categories (origins): Kalinjot, Berat, Fier, or Saranda mono-cultivar OO.

Step 1. Calculate the distance based on the input characteristics (such as for olive oil: MUFA, PUFA, etc.). Since our dataset includes multiple input characteristics, the extended formula (1) will be beneficial, allowing us to work beyond just two dimensions.

Step 2. Determining the rank. In straightforward terms, the first rank corresponds to the smallest distance identified in the initial step.

Step 3. Identify the "nearest neighbor" by selecting a specific value of k. For instance, when k=1, the top-ranked place will be chosen (let’s say Kalinjot). Conversely, with k=4, we examine the top four ranks. If three out of these four ranks correspond to Kalinjot, it indicates that these three data points are closest to Kalinjot in distance. Consequently, this leads to the prediction that the new data object, which pertains to an olive oil production origin of interest to the user, will likely be classified as a Kalinjot olive oil.

An Olive Oil Origin Predictor - Predicting the Origin of the Cultivar

A Brief Description of Our Dataset

The dataset includes 34 samples from the same cultivar, sourced from various regions of Albania. This study aims to predict the cultivar’s origin, termed as a “classification task” or “multi-class classification” in our context. The key question is: how do the input features affect the output variable?

Key features will include specific fatty acids and other substances that allow us to distinguish the oil’s origin, as each region’s unique conditions, including soil and climate, influence its chemical makeup.

Secondly, the machine learning model plays an essential role, enabling the classifier to learn from these values to uncover hidden patterns and forecast the region.

Figure 2. Showcasing a part of the Olive Oil dataset, including the first five data objects. The last column, “Origin,” represents the output variable.

Figure 2. Showcasing a part of the Olive Oil dataset, including the first five data objects. The last column, “Origin,” represents the output variable.

Table 1. A short description of features.

Table 1. A short description of features.

Feature	Explanation of the Feature	Value Type
Saturated Fatty Acids (SFA)	Includes fatty acids like 14:0 (myristic), 16:0 (palmitic), 18:0 (stearic), 20:0 (arachidic), 21:0 (henicosanoic), 22:0 (behenic).	Continuous
Monounsaturated Fatty Acids (MUFA)	Fatty acids with one double bond, such as 16:1(n-9), 16:1(n-7), 18:1(n-9)cis, 18:1(n-9)trans, 18:1(n-7), 20:1(n-9).	Continuous
Polyunsaturated Fatty Acids (PUFA)	Fatty acids with multiple double bonds, including 18:2(n-6)cis, 18:2(n-6)trans, 18:3(n-3), 20:2(n-6), 20:3(n-3).	Continuous
Fatty Acid Ratios	Ratios like (n-6)/(n-3) and 18:1/18:2 reflect the balance between omega-6 and omega-3 fatty acids or specific fatty acids.	Continuous
Special Fatty Acid Types	Uncommon or less abundant fatty acids like 17:0 and 17:1(n-7) indicate additional profile variability.	Continuous

Figure 3. The research methodology used is based on Suleiman et al. (2022).

Figure 3. The research methodology used is based on Suleiman et al. (2022).

Figure 4. Class distribution after SMOTE. The three classes (Vlora, Berat and Fier) have equal division.

Figure 4. Class distribution after SMOTE. The three classes (Vlora, Berat and Fier) have equal division.

Feature Selection and Feature Extraction (PCA) After Splitting the Datasets

In the Olive Oil dataset, feature scaling is important as our chosen ML algorithms must calculate distances between data. If we do not perform feature scaling (i.e., the features are not scaled), then the features with a higher value range will dominate when distances are calculated.

Scikit-learn is a Python module that integrates the newest machine-learning algorithm for supervised and unsupervised problems (Kothawade, 2021). We intend to make our data standardized, which means that it will have a $\mu$=0 and a a $\sigma$=1. The upper and lower values can vary (they don’t need to be in range from 0 to 1).

We use the following formula for standardization so to calculate the standard score of a sample x:

$$z_i={\displaystyle \frac{x_i-\mu }{\sigma }}$$

where ${\mathrm{x}}_{\mathrm{i}}$ is each value, $\mathsf{\mu }$ is the mean of the training samples and $\mathsf{\sigma }$ is the standard deviation of the training samples.

Figure 5. Statistical data (mean and standard deviation) for the 24 features post-standardization are presented. This shows that min-max values might differ from those in normalization, necessitating scaling from 0 to 1.

Figure 5. Statistical data (mean and standard deviation) for the 24 features post-standardization are presented. This shows that min-max values might differ from those in normalization, necessitating scaling from 0 to 1.

Conversely, Principal Component Analysis (PCA) serves as a dimensionality reduction method that lowers the number of input features while preserving as much information from the original dataset as possible. PCA converts the 24 original features into a smaller number of principal components, each representing a significant portion of the dataset’s variance (Da Costa et al., 2021).

For instance, rather than utilizing all 24 features, PCA can condense them into a few components that accurately summarize the same information. This technique reduces computational requirements during model training and enhances resource efficiency while maintaining the dataset’s essential characteristics. By integrating feature scaling with PCA, the dataset is effectively positioned for optimal machine learning analysis.

Feature Importance Using Random Forest

Figure 6 demonstrates the importance of different features for predicting the origin of olive oil cultivars with a Random Forest classification model. The dataset includes samples from the same cultivar, collected from various regions in Albania like Vlora, Berat, and Fier (resulting in three target classes, though more could be added later). This analysis aims to classify the cultivar by its origin, employing chemical characteristics such as the 18:1/18:2 ratio, PUFA, MUFA, SFA, and other fatty acid profiles as input features.

Figure 6. The feature importance of “Random Forest” according to the Olive Oil dataset.

Figure 6. The feature importance of “Random Forest” according to the Olive Oil dataset.

Among these features, the ratio of 18:1/18:2 emerges as one of the most critical in distinguishing between the origins of olive oil samples. MUFA has a very important influence in the origin (our target variable). This indicates that the balance between these fatty acids is highly specific to each region’s environmental and geographical factors. PUFA and SFA also hold substantial importance, reflecting the broader composition of fatty acids that vary with the cultivar’s growing conditions and processing techniques.

On the other hand, features such as f14:0 and certain trans-fatty acids exhibit lower importance scores, implying that they contribute minimally to differentiating between regional origins. While they may play a role in the overall chemical profile, their influence on the classification outcome is limited compared to the more dominant features.

The importance scores are derived from the Gini impurity metric, which assesses the role of each feature in reducing uncertainty during classification. Features with higher importance scores appear more frequently in decision-making nodes within the model, which is pivotal in achieving accurate predictions of the olive oil’s origin. This underscores the significance of leveraging well-selected chemical markers to achieve robust classification outcomes.

In conclusion, the feature importance analysis highlights the key chemical indicators that facilitate the reliable classification of mono-cultivar Albanian OO based on their regional origin.

Evaluation Metrics Analysis

The evaluation metrics provide critical insights into the strengths and weaknesses of each machine learning model in predicting the origin of Albanian mono-cultivar OO. Logistic Regression and SVC demonstrated moderate overall performance, achieving 62.50% accuracy. Despite these models showing balanced precision and recall for specific classes, they struggled with correctly identifying samples from Vlora, evidenced by low precision and recall values for this class. While conceptually simple, the k-Nearest Neighbours (kNN) algorithm underperformed with an accuracy of 50%. However, after hyperparameter tuning these classifiers, kNN performed better (as explained later).

Similarly, the Decision Tree model exhibited overfitting tendencies, resulting in an overall accuracy of 50% and inconsistent predictions across regions. Random Forest, a more robust ensemble method, showed slight improvements for specific classes but failed to generalize effectively, also yielding 50% accuracy. Gradient Boosting provided a more nuanced balance in classifying oils. Yet, its overall accuracy remained constrained by challenges in capturing the underlying data distribution, particularly for samples from Berat and Vlora. These findings underline the limitations of standard classifiers in tackling regionally diverse and imbalanced datasets.

Confusion Matrix Analysis

The confusion matrices revealed key patterns in the misclassification tendencies of the models, shedding light on the regional separability of the olive oil samples. Across most models, samples originating from Fier were consistently classified with higher accuracy, suggesting more distinct feature patterns for this region. Conversely, samples from Berat and Vlora were frequently misclassified, indicating overlapping characteristics between these classes. For example, Logistic Regression and SVC exhibited significant confusion in differentiating Vlora samples, often misclassifying them as belonging to Fier. Gradient Boosting showed marginal improvement in class distribution but struggled with borderline cases between Berat and Fier. Despite its ensemble nature, Random Forest demonstrated similar biases as individual Decision Trees, particularly under classifying Vlora samples.

Since our dataset is relatively small, consisting of only 34 instances, the observed trends reflect both the dataset’s complexity and the limitations of training on such a small sample size. This highlights the importance of adopting advanced pre-processing techniques besides feature scaling, for example, dimensionality reduction or augmentation strategies, to improve class separability and enhance model performance. To achieve greater predictive reliability, future work should explore more sophisticated algorithms and consider collecting a larger, more representative dataset to capture the full variability of the features.

Figure 7. Visualization of confusion matrices created using the ConfusionMatrixDisplay class from the sklearn—metrics library.

Figure 7. Visualization of confusion matrices created using the ConfusionMatrixDisplay class from the sklearn—metrics library.

Hyperparameter Tuning for K-Nearest Neighbors’ Classifier

In our analysis, we systematically tuned the hyperparameters of various models to optimize their performance. Specifically, for Logistic Regression, we adjusted parameters such as the regularization strength; for Support Vector Machines (SVM), we optimized the penalty parameter C; for Decision Trees, we refined criteria like maximum depth and minimum samples per split; and for Random Forests, we explored the number of estimators and maximum features. After conducting a comprehensive evaluation of these models post-tuning, we observed that the k-Nearest Neighbours (kNN) algorithm, with its hyperparameters optimized (e.g., the number of neighbors), performed better than the other models.

The main goal is to find the K-nearest neighbors to a given data point. In this case, the metric used is Euclidean distance, which is the distance between two points in the hyperplane. This metric, along with Manhattan distance are special cases of Minkowski distance²⁴:

$$d\left(x,y\right)={\left(\sum _{i=1}^n{\left(x_i-y_i\right)}^p\right)}^{{\displaystyle \frac{1}{p}}}$$

When the power parameter for the Minkowski metric (p) is set to 2, we get the formula for the Euclidean distance, which we are considering in the code.

According to the documentation of scikit learn²⁵, the value of the other main hyperparameter of kNN (k, number of neighbors) is set to 5 by default. This value does not guarantee the highest accuracy; thus, some experiments with k values up to 28 (also shown in Figure 8) highlight that the optimal value of k is equal to 4, which gives an accuracy of 62,5%.

Another way to find the optimal value of k is to use a graph that describes the error rate for each of our k values in the specified range in Figure 9. From the graph, we have chosen the value of k = 4 because the lowest point (error) represents the best or most optimal value of k (Figure 9).

Value of k	1		2	3	4	5	6	7	8	9	10	11	12	13	14	15
Accuracy		0.5	0.375	0.5	0.625	0.5	0.5	0.5	0.625	0.375	0.375	0.375	0.125	0.125	0.125	0.25

Figure 8. A number of nearest neighbors and their corresponding accuracy.

Figure 8. A number of nearest neighbors and their corresponding accuracy.

Figure 9. Number of nearest neighbors and the corresponding error rate.

Figure 9. Number of nearest neighbors and the corresponding error rate.

GUI of Olive Oil Origin Predictor

The Olive Oil Origin Predictor’s graphical user interface (GUI) is designed to classify the origin of mono-cultivar Albanian olive oil samples based on their chemical composition. It provides input fields for entering various fatty acid concentrations and oil composition parameters.

The user enters the values, and by clicking the "Predict Origin" button, the application employs a pre-trained machine learning model and a scaler to prepare the inputs and determine the origin of the olive oil sample. The predicted region appears below the button in real time. The interface is designed to be straightforward and user-friendly, dynamically updating the prediction while maintaining responsiveness through computations that run in a separate thread.

Figure 10. Implementing the GUI.

Figure 10. Implementing the GUI.

Conclusion

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