## 3 Results and Discussion
### Electronic Nose Detection
#### 3.1.5 A Classification Model Based on SVMs  
Support vector machines (SVMs) are effective tools for addressing both classification and regression problems. The fundamental concept behind SVMs is to identify the optimal hyperplane that maximally separates different classes of data points. However, traditional linear SVMs struggle with non-linearly separable datasets. To overcome this limitation, the concept of kernel functions (KFs) was introduced, allowing for the mapping of original data into a higher-dimensional feature space, thereby facilitating linear separability in this extended space. The selection of an appropriate kernel function is a crucial step in the application of SVMs, as different kernel functions are better suited for various types of data distributions. Commonly used kernel functions include the linear kernel, polynomial kernel, and radial basis function (RBF) kernel. The linear kernel is appropriate for linearly separable or nearly linearly separable data, while alternative kernel functions are more effective for non-linear data. In this study, the radial basis kernel function was employed, which is one of the most frequently used non-linear kernel functions, as illustrated in Equation (3). \[K(x,y)=exp\left(-\frac{\|x-y\|^{2}}{(2\cdot\sigma^{2})}\right) \tag{3}\]  
Specifically, \(x\) and \(y\) represent the input samples, and d(\(x,y\)) denote the Euclidean distance between \(x\) and \(y\). Additionally, sigma refers to the standard deviation of the Gaussian distribution, while exp signifies the natural exponential function. It is essential to evaluate the model's performance on the test set, with accuracy being one of the most commonly used metrics, calculated by dividing the total number of correctly predicted samples by the total number of samples. The confusion matrix illustrates the correspondence between actual categories and the predicted categories generated by the model. Figure 6a presents a confusion matrix produced by the SVM algorithm following PCA dimensionality reduction on data processed at 12 \({}^{\circ}\)C. This matrix delineates the relationship between actual and predicted categories. Each row corresponds to actual values, while each column corresponds to predicted values. The matrix is 8 \(\times\) 8, reflecting classifications based on storage time. In the confusion matrix, values along the diagonal indicate the number of correct predictions, whereas off-diagonal values represent incorrect predictions. Ideally, all predictions would lie on the diagonal, signifying that every prediction is accurate. When using support vector machines (SVM) with the radial basis function (RBF) kernel, it is essential to standardize the data, as the RBF kernel is highly sensitive to the scale of the input features. Therefore, preprocessing the data through standardization is a necessary step before training the model. The RBF kernel can create complex decision boundaries, which may lead to high performance on the training set but poor generalization on the test set. Consequently, careful parameter selection and the use of cross-validation are imperative to mitigate the risk of overfitting. Additionally, the computational complexity associated with SVM should not be overlooked. While dimensionality reduction techniques can help reduce the data's dimensionality, employing SVM with an RBF kernel can still result in significant computational demands, particularly when handling large-scale datasets. Thus, selecting appropriate optimization algorithms and computing resources is crucial for the successful application of SVM. The SVM model, constructed using a dataset processed by the Principal Component Analysis (PCA) algorithm at a temperature of 12 \({}^{\circ}\)C, is illustrated in Figure 6a to predict the storage duration of oysters. This model demonstrates a classification accuracy exceeding 80%, indicating robust performance. However, there are several misclassified samples at storage durations of 72, 96 and 144 h, attributed to considerable overlap in sample points, as shown in Figure 4b.