# FnmOS-ELM: A Flexible Neural Network Mixed Online Sequential Elm
## 4 Experimental Design and Result Analysis
### OS-ELM Mixed with CNN  
We now compare the performance of ResNet-110 [49], ELU [50], RCNN [51], VGG16 [52], ELM-LRF, CNN-ELM, and fnnmOS-ELM on the CIFAR-10 dataset. In ELM-LRF, we set the size of receptive field to \(4\times 4\), and the highest accuracy that can be achieved is lower than 85.3, and the result is unstable. The VGG16 used for feature extraction is shown in Figure 5a, and after making some minor changes to the VGG16 network, the highest accuracy achieved on the CIFAR-10 dataset is 93.01 (\(\pm 0.3\), epoch = 40). CNN-ELM uses the feature maps of VGG16 as feature extractor and ELM as classifier. Its highest accuracy is less than 90.73, and the result is also unstable. With \(i~{}=~{}55\), we access the fnnmOS-ELM (see Figure 5b) and set the hidden nodes of the network as 600. The training batch size and epochs are set to 1000 and 20, respectively. The maximum test accuracy of 0.9397, which exceeds that of the other methods or models (Table 4), has also entered the top 7 on Kaggle. Using the OS-ELM instead of full connection layers, not only improves the accuracy compared to the VGG16 network, but also reduces the parameters of new training data from 15M to 6K. The training time elapsed to achieve the highest accuracy is only approximately 1.55 s (CPU), which is much shorter than that of the most other methods (except ELM-LRF) that were tested on the same dataset. To verify the optimization effect of the fnnmOS-ELM on CNNs, the former is used as the optimiser of VGG16 classification, as in Figure 5c. Although we used only nine hidden nodes, the maximum accuracy is raised from 0.9301 to 0.9380, exceeding that of other algorithms tested on the same dataset.  
Figure 4: Performance of different methods and network structures. (**a**) Comparison of accuracy. (**b**) Network structure of the recurrent neural network (RNN) model. (**c**) With \(i\) = 4, the fnnmOS-ELM model uses the first four layers of the RNN as the feature extraction layers.  
On more complex CIFAR-100 dataset, we compare the performances of ELU, RCNN, NIN-APL [53], VGG16, ELM-LRF, and CNN-ELM with fnnmOS-ELM (using the VGG16 as a pre-training network). The structure of the fnnmOS-ELM network is the same as in Figure 5. After training 80 epochs, the highest accuracy of the VGG16 is 69.73 (\(\pm\)0.59). It is lower than that of ELU and higher than that of RCNN and NIN-APL with much larger training parameters (Table 4). With \(i~{}=~{}55\), using OS-ELM as the classifier, we set the batch size to 1000 and epoch to 20, consisting of 850 hidden nodes, the accuracy of the test data is 0.7064, which is second only to ELU's highest accuracy. When \(i~{}=~{}65\), we set hidden the nodes to 70, the batch size to 1000, and the epoch to 20, in order to optimize the classification accuracy of the VGG16. These settings improve the maximum accuracy from 69.73 to 70.67 (entering the top 3 on Kaggle). The accuracy of the fnnmOS-ELM on the test data exceeds that of the RNN, RCNN, and NIN-APL, at the same time, the highest accuracy of ELM-LRF (the receptive field size \(=6\times 6\)) and CNN-ELM reached 60.31 and 67.77, respectively, which is not as good as our method. Although the accuracy of fnnmOS-ELM is lower than the highest accuracy of the ELU, it has much smaller trainable parameters than other models and the training time is less than 10 s (CPU).  
Figure 5: The network structure of VGG16 and fnnmOS-ELM. (**a**) Modified VGG16 network structure used as the pre-training model, divided into two parts: feature ex- traction and classifier. The fnnmOS-ELM network structure on the CIFAR-10 dataset with (**b**) \(i=55\) and (**c**) \(i=65\).