# Hierarchical Concept Learning by Fuzzy Semantic Cells
## 4 Experiments
### Experimental Results  
Table 2 shows the changes of classification accuracy under different training set scales. We repeat the experiment 100 times to obtain the mean and standard deviation of the classification results, considering the randomness of the dataset segmentation and differences in initializing parameters. In this experiment, we use the second initialization method of \(P\). In particular, we use K-means to initialize one prototype in each class and then combine them together as the prototype initialization. As an initialization for \(\sigma\), we take one-third of the average distances between the samples of each category and the prototypes. From the experimental results, we can see that our method is robust. Even in the case of a small amount of data (only 10%), we can get an acceptable classification result. For the initialization of the prototype, we can limit the initialization method and the number of initial prototypes. In the following two experiments, 30% (3290 samples) of the Pendigits dataset were used as the training set and the rest as the test set (7702 samples). Table 3 shows the difference in classification results for different numbers of prototypes. We initialize one to four prototypes in each category (a total of 10 categories) by K-means, so the number of prototypes ranges from 10 to 40 in the prototype initialization. We also set \(\sigma\) as one-third of the average distance that the samples of each category to the prototypes. We also repeated the experiment 10 times to obtain the mean and standard deviation of the classification results, taking into account the randomness of dataset segmentation and differences in initializing parameters. The experimental results are consistent with the above analysis. The classification effect will improve as the number of prototypes increases. As a result, as the number of prototypes grows, so the computational complexity also increases. At the same time, if there were too many prototypes, most fuzzy semantic cell will become too small and redundant. As a result, we must select the appropriate number of prototypes to strike a balance between computational efficiency and classification effect. In the following experiment, we conducted a controlled trial in four ways as described in Section 4.2 to show the classification accuracy under different initialization methods of prototypes on Pendigits dataset as shown in Table 4. We used ten prototypes (\(\#prototype=\#class\)), and the initialization method of \(\sigma\) is the same as before. The experiment is repeated six times. The experimental results show that the training accuracy decays slightly since more samples are difficult to fit. However, the testing accuracy increases substantially as the model learns more about the training distribution. Despite the objective function being a non-convex problem, the classification effect is nearly stable across the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Ratio as Training Sets** & **Train** & **Test** & **Accuracy on Training Sets** & **Accuracy on Test Sets** \\ \hline
10\% & 52 & 471 & 86.46 \(\pm\) 1.58 & 82.64 \(\pm\) 1.43 \\
20\% & 104 & 419 & 89.91 \(\pm\) 0.85 & 81.42 \(\pm\) 1.19 \\
30\% & 156 & 367 & 89.53 \(\pm\) 1.26 & 79.69 \(\pm\) 1.58 \\
40\% & 208 & 315 & 90.57 \(\pm\) 0.93 & 80.97 \(\pm\) 1.54 \\
50\% & 260 & 263 & 89.10 \(\pm\) 1.25 & 76.81 \(\pm\) 2.03 \\
60\% & 312 & 211 & 87.08 \(\pm\) 1.15 & 79.11 \(\pm\) 3.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The classification accuracy in percentage (mean \(\pm\) standard deviation) under different proportions of the training set on the Forest dataset. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Prototypes** & **Accuracy on Training Sets** & **Accuracy on TEST Sets** \\ \hline
10 & 86.64 \(\pm\) 0.05 & 83.78 \(\pm\) 0.05 \\
20 & 92.52 \(\pm\) 0.11 & 91.46 \(\pm\) 0.07 \\
30 & 94.49 \(\pm\) 0.30 & 92.27 \(\pm\) 0.49 \\
40 & 95.47 \(\pm\) 0.20 & 94.03 \(\pm\) 0.10 \\ \hline \hline \end{tabular}
\end{table}