# Hierarchical Concept Learning by Fuzzy Semantic Cells
## 4 Experiments
### Experimental Results
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Ratio as Training Set** & **0.1** & **0.3** & **0.5** & **0.7** \\ \hline
**Prototypes Initialization** & **Train Acc/Test Acc** & **Train Acc/Test Acc** & **Train Acc/Test Acc** & **Train Acc/Test Acc** \\ \hline K-means in categories & 84.75\({}^{\pm 7.11}\)/ 75.60\({}^{\pm 6.87}\) & 79.08\({}^{\pm 6.13}\)/ 75.04\({}^{\pm 6.71}\) & 79.52\({}^{\pm 5.51}\)/ 77.17\({}^{\pm 5.83}\) & 78.12\({}^{\pm 5.24}\)/ 76.39\({}^{\pm 5.12}\) \\ K-means the training set & 67.95\({}^{\pm 4.51}\)/ 60.26\({}^{\pm 4.78}\) & 65.00\({}^{\pm 5.34}\)/ 61.97\({}^{\pm 5.85}\) & 65.29\({}^{\pm 5.14}\)/ 63.54\({}^{\pm 5.28}\) & 67.55\({}^{+4.03}\)/ 66.14\({}^{\pm 4.31}\) \\ Randomly selection & 72.87\({}^{\pm 6.06}\)/ 70.39\({}^{\pm 6.03}\) & 69.39\({}^{\pm 7.36}\)/ 68.06\({}^{\pm 7.45}\) & 70.60\({}^{\pm 4.80}\)/ 70.12\({}^{\pm 4.56}\) & 70.45\({}^{\pm 6.16}\)/ 70.55\({}^{\pm 5.81}\) \\ Average in categories & 83.25\({}^{\pm 0.94}\)/ 82.37\({}^{\pm 0.64}\) & 83.05\({}^{\pm 0.65}\)/ 83.10\({}^{\pm 0.44}\) & 82.97\({}^{\pm 0.32}\)/ 83.07\({}^{\pm 0.60}\) & 82.92\({}^{\pm 0.31}\)/ 82.71\({}^{\pm 0.66}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The classification accuracy (%) under different prototype initialization methods on Pendigits dataset. The ratio of training samples varies from 0.1 to 0.7. All results are the summary of repeated six runs on different training sets. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **0.1** & **0.3** & **0.5** & **0.7** \\ \hline Adam [17] & 82.37 \(\pm\) 0.64 & 83.10 \(\pm\) 0.44 & 83.07 \(\pm\) 0.60 & 82.71 \(\pm\) 0.66 \\ SGD & 78.72 \(\pm\) 1.07 & 79.71 \(\pm\) 0.61 & 79.54 \(\pm\) 0.39 & 79.36 \(\pm\) 0.73 \\ RMSprop [50] & 82.32 \(\pm\) 0.71 & 82.27 \(\pm\) 0.50 & 82.56 \(\pm\) 0.27 & 82.25 \(\pm\) 0.41 \\ L-BFGS & 44.89 \(\pm\) 37.8 & 80.68 \(\pm\) 0.01 & 80.45 \(\pm\) 0.01 & 81.17 \(\pm\) 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The classification accuracy in percentage (mean \(\pm\) standard deviation) when using different optimization methods. All results are the summary of repeated six runs. From the results in Table 6, we can conclude that seven algorithms have similar performance on the synthetic datasets. When the sample size used for the training is relatively large, the neural network algorithm has the best consequences, such as in handwritten datasets Pendigits and MNIST. However, when the number of training samples are small, the neural network algorithm stability rapidly declines. Not only does the classification effect deteriorate, but it also fluctuates dramatically (high standard deviation) in the Forest and MIT face datasets. In contrast, regardless of the amount of data, the algorithm proposed in this paper produces a stable output. Moreover, we also found that the KNN algorithm also has outstanding performance on different datasets. However, a better performance of KNN is reached when the parameter of neighborhood is manually chosen.Accordingly, in our algorithm, the same parameter initialization method is utilized for all datasets, and a general classification algorithm is obtained without further human intervention. In this experiment, we use K-means (K = 3) in each category as the prototype initialization and take one-third of average distances that the samples of each class to the prototypes as corresponding \(\sigma\) initialization. The Naive Bayes algorithm is more sensitive to datasets and has diverse experimental results for different datasets. For example, it has a better performance on Forest datasets but lags behind other methods on MIT face datasets. This shows that the NaiveBayes algorithm does not have a strong generalization ability. The performance of the SVM algorithm on each dataset is neither remarkable nor bad. As for the DecisionTree algorithm and AdaBoost algorithm, the performance lags behind other algorithms when only 10% of the data is used as a training set.