# A Self-Supervised Tree-Structured Framework for Fine-Grained Classification
## 4 Experiment
### Conducted Experiments and Results
#### 4.3.2 Experiment 2  
To assess the impact of different distance calculation methods in clustering algorithms on the accuracy and training time of tree classifiers on the bird dataset, Experiment 2 evaluates the training time and classification accuracy of clustering algorithms using three different distance calculation methods: Euclidean distance [31], Manhattan distance [31], and correlation distance [31]. While keeping other variables constant, the experiment employs a machine-learning matcher using SVM with a linear kernel function and a CNN model using ResNet. Additionally, the number of child clusters is fixed at three. In Table 5, the impact of utilizing k-means++ with varying distance calculation methods is presented. Initially, to illustrate the impact of the proposed classifier model, Figure 10 illustrates partial figures of the training and validation losses of the images using different distance calculation methods.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number of** **Child Clusters**} & **Traditional ResNet Classifier Accuracy** & **Proposed Classifier Accuracy** & **Traditional ResNet Classifier Training Time** & **Proposed Classifier Classifier Training Time** \\ \hline
2 & & 69.80\% & & 1395.08 s \\
3 & 68.63\% & 70.15\% & & 993.25 s \\
4 & 69.94\% & 69.94\% & & 927.64 s \\
5 & & 68.50\% & & 873.20 s \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance of proposed method with different child clusters.  
Figure 10: Training and validation loss of proposed classifiers using different distance calculation.  
Figure 9: Training and validation loss of proposed classifiers with different child clusters.  
The classification accuracy attained by the traditional ResNet model on the bird dataset is 68.63%, as indicated in Table 5. Furthermore, Table 5 demonstrates that the proposed method enhances the accuracy of classification trees with different distance calculation methods, namely, Euclidean distance, Manhattan distance, and correlation distance, by 1.52%, 1.71 %, and 1.33%, respectively. The results indicate that k-means++ with Manhattan distance can produce better classification results, while correlation distance exhibits the worst accuracy. Generally, k-means++ with different distance calculation methods has improved classification accuracy, which validates the effectiveness of the proposed method. However, the lacking performance of correlation distance might be related to its purpose of calculating the distance, which measures the linear relationship between two variables. On the other hand, Euclidean distance and Manhattan distance are similar since they both measure distance between variables in multi-dimensional space. Hence, during the construction of the initial classification tree, k-means++ with correlation distance places more emphasis on the linear relationship between two variables, which leads to the suboptimal performance of the generated cluster. In terms of training time, the proposed classifier model shows a reduction in training time of 32.91%, 26.33%, and 42.62%, respectively, compared to the conventional Resnet architecture using different distance calculation methods, namely, Euclidean distance, Manhattan distance, and correlation distance. Based on the experimental results, it is concluded that while k-means++ using correlation distance does not result in a significant improvement in accuracy, it requires the least amount of training time. On the other hand, k-means++ with Manhattan distance has the highest accuracy, but it needs the longest training time. The authors suggest that researchers may consider selecting the appropriate k-means++ with different distance calculation methods based on a combination of accuracy and training time.