# Research on Generalized Hybrid Probability Convolutional Neural Network
## 2 Research on the Generalization Ability of the CNN Feature Mapper (CFM) to Extract Image Features
As shown in Figure 2, it can be seen that for the determined \(t\) categories from target dataset \(T^{*}\), the value of \(r_{s}^{t}\) was positively correlated with \(s\): as the corresponding \(s\) of the \(\mathbf{CFM_{s}}\) increased, \(r_{s}^{t}\) increased monotonously. That is, for a certain target dataset with \(t\) categories, the larger the value of \(s\) was, the better the generalization ability of the \(\mathbf{CFM_{s}}\) trained by the source dataset \(S^{*}\). For a \(\mathbf{CFM}\) trained on the determined \(s\) source dataset \(S^{*}\), the value of \(r_{s}^{t}\) was negatively correlated with \(T^{*}\) and with the number of \(t\) categories in the target dataset; \(r_{s}^{t}\) decreased monotonously as \(t\) increased. That is, for a \(\mathbf{CFM_{s}}\) that determined the number of categories, a target dataset \(T^{*}\) with a smaller number of \(t\) had a better the generalization ability than a target dataset with larger values of \(t\). When \(r_{s}^{t}\) was a certain value, that is, after the feature was extracted under the \(\mathbf{CFM_{s}}\) for \(t\) different categories, and the magnitude of the classification promotion was the same, the number of \(\mathbf{CFM_{s}}\) for different values of \(t\) corresponding to \(s\) was different. Figure 1: The experimental structure diagram of generalization ability of feature mapper. Analysis of the Generalization Ability of the Feature Mapper to Unknown Target Categories (\(S^{*}\bigcap T^{*}=\emptyset\))  
When \(S^{*}\bigcap T^{*}=\emptyset\), the trained \(\mathbf{CFM_{s}}\) on a multiclass source dataset \(S^{*}\) extracts the features of target dataset \(T^{*}\) and the features are used for training the MLP classifier. In the CIFAR-100 dataset, 90 categories were randomly selected as a candidate source dataset, and the remaining 10 categories were used as a candidate target dataset. The sample sets with number of categories \(s\) (\(s=15,20,25,\cdots,90\)) were selected from the 90 candidate source dataset to be fully trained by VGG-16, and the relatively best classification results and corresponding 14 \(\mathbf{CFM_{s}}\) were obtained and randomly selected from the 10 candidate dataset. The unknown target dataset with a number of categories \(t\) (\(t=2,3,\cdots,8\)) was selected, and the features of the randomly selected unknown target dataset were extracted by the CFM and then trained by the MLP classifier. To make the results more universal, each number of unknown sample subsets was extracted three times, the classification results were counted each time, and the final result was the average of three results. As shown in Figure 3, for the determined \(t\) category target dataset \(T^{*}\), the value of \(r_{s}^{t}\) was positively correlated with \(s\); as the corresponding \(s\) of the \(\mathbf{CFM_{s}}\) increased, \(r_{s}^{t}\) increased monotonously. That is, for a certain \(t\) category target dataset, the larger \(s\) was, the better the generalization ability of the \(\mathbf{CFM_{s}}\) trained by the source dataset \(S^{*}\). For the \(\mathbf{CFM_{s}}\) trained from the determined \(s\) category source dataset \(S^{*}\), the value of \(r_{s}^{t}\) was negatively correlated with the number of \(t\) categories in the target dataset \(T^{*}\); as \(t\) increased, \(r_{s}^{t}\) decreased monotonously. That is, for a \(\mathbf{CFM_{s}}\) that determined the number of categories, the generalization ability of the target dataset \(T^{*}\) with a smaller \(t\) was better. When \(r_{s}^{t}\) was a certain value, that is, after the feature was extracted under the \(\mathbf{CFM_{s}}\) for different \(t\) categories from the target dataset, and the magnitude of the classification promotion was the same, then the number of \(\mathbf{CFM_{s}}\) for \(t\) categories corresponding to \(s\) categories was different.