## 3 Results and Discussion
### Training and Validation of the VGG16 Network and the CF-VGG11 Network  
The training set and validation set used for VGG16 contains 333 samples and the test set contains 83 samples, at a ratio of 6:2:2 (Table 3). In the actual training process, we expanded the images by gamut distortion and mirror flipping. Although the transformed images can not represent the 3D fluorescence characteristics, it can improve the training efficiency of the model and prevent the poor training effect due to the lack of data. The VGG16 classification network was evaluated by using the cross-entropy loss function and training accuracy. We trained the network with 100 epochs and set the initial learning rate of the first 50 epochs to 1.0 \(\times\) 10\({}^{-3}\) and the last 50 epochs to 1.0 \(\times\) 10\({}^{-4}\). We use the stepLR method to automatically update the learning rate. The optimizer adopts the Adam optimizer, with the step parameter set to one and the gamma parameter set to 0.94. In addition, the input size of the network is 224 \(\times\) 224, the output is 4 classes, the batch_size of the first 50 epochs is set to 8, and the batch_size of the last 50 epochs is set to 16. During the training process, the training loss and validation loss decrease gradually, and the training loss value tends to be stable after 80 epochs. The training loss and validation loss curve is shown in Figure 9. After 5 repeat experiments, as the training logs, we take the best epoch of all as the training result. The loss value is: 2.39 \(\times\) 10\({}^{-2}\) (training loss) and 1.03 \(\times\) 10\({}^{-3}\) (validation loss). Then, we tested the accuracy of the model using the test set samples and the top-5 accuracy is 100%. In the dataset, the test set has a small amount and few types, so the appearance of the test accuracy is good. This is a normal training result since the network can always distinguish the 3D-EEM types well. At the same time, we used the PCA + SVM method (Figure 10) to reduce the dimension and classify 3D-EEMs with an accuracy of 99.69%. However, the PCA + SVM approach has the same requirements as the PARAFAC analysis method, which requires a large amount of data as inputs, so the convolutional neural network has greater advantages (Table 4). The training results show that there are significant differences between different classes of 3D-EEMs and using the convolutional neural network can easily identify the type of 3D-EEMs and the number of their components.  
The CF-VGG11 network structure contains six VGG11 network model structures (Figure 5), where each submodel gets a corresponding one component map of each of four datasets based on 3D-EEMs. We used the VGG11 model to fit a component map, which is a vector of size 60 \(\times\) 60 (it is not an output class), we could not judge the results by the method of traditional target detection and object recognition algorithms, so we used cosine similarity [38] to replace the accuracy of the model fitting results. We divided the data in a ratio of 3:1:1 (250 samples for training and 83 samples for validation and 83 samples for test) and input each 3D-EEM datum into each sub-model while the fitting component map of each model is given by the PARAFAC analysis results. The results of model training are shown in Figure 11.  
Figure 10: In the PCA experiment, the cumulative of the first three PCs is 87.77%, and the cumulative of the first four PCs is 91.73%. The classification accuracy of SVM is 99.69. The reason for the error is that there are some similar characteristics between PC1 and PC2 of F and PU.  
Figure 9: Loss curve and training accuracy curve of VGG16.In (**a**), when epoch \(>\) 80,the training loss and validation loss are both stable. In (**b**), the training accuracy reaches 99.6% at epoch 97 (the accuracy also reaches 99.6% at epoch 80 and epoch 81).