## 4 Performance Analysis  
### Results and Discussion  
The effectiveness of the suggested algorithm is tested in this section. A Pentium (R) dual-core E5400 processor clocked at 2.70 GHz and operating with 2 Gb of memory was used for all tests in the MATLAB 7.10.0 (2010a) environment. The activation function used  
Figure 4: An optimized FNNRW learning algorithm flowchart. The graphic depicts each phase of the FNNRW optimization process, and the chosen approach corresponds to that step specifically. The flow chart may be used to more clearly illustrate the improved FNNRW algorithm’s execution process, condition judgment at its start, and condition at its conclusion.  
by the algorithm is the sigmoid function \(g(x)=\frac{1}{1+\epsilon^{-2}}\). Because it is for large-scale data processing, the dataset used in this paper is the MNIST dataset. The Mixed National Institute of Standards and Technology database, also known as the MNIST dataset, is a sizable collection of handwritten digits that the National Institute of Standards and Technology has collected and organized. It includes a training set of 60,000 examples and a test set of 10,000 examples. In comparison to other types of datasets, MNIST, a publicly accessible handwritten digital dataset, has small image pixels, relatively low computing power, the ability to build a neural network with fewer layers, is amenable to computer arithmetic, and the dataset has sufficient quantity, high discrimination, and low noise. Consequently, it was selected as the experiment's dataset. The samples are initially separated into m equal subgroups and all samples are normalized in order to test the algorithm's efficacy. During the experiment, the parameters \(r=0.1\) and \(s=3\) were selected in the process of calculating the input weights and biases. Additionally, take the regularization parameter \(\sigma=0.05\), learning rate \(\mu=10^{-3}\), the threshold \(\epsilon=10^{-3}\). The following charts intuitively show the performance of the optimized algorithm.  
When the number of subsets \(m\) is 10 or 20, respectively, Tables 1 and 2 compare the accuracy of the FNNRWs learning algorithm and the improved FNNRWs learning method. As shown in Tables 1 and 2, the accuracy of the optimized FNNRWs learning algorithm is greater than the accuracy of the FNNRWs learning algorithm as sample size or the number of hidden layer nodes increases. Figures 5 and 6 compare the training accuracy and test accuracy while displaying the accuracy of the optimized FNNRWs learning algorithm and the accuracy of the FNNRWs learning algorithm as the number of training rises, respectively. In the figure, the advantages of the optimized FNNRWs learning algorithm in terms of accuracy can be seen very intuitively. Figures 7 and 8 show the performance advantages of the optimized FNNRWs learning algorithm from the aspect of relative error by calculating the relative error.  
Figure 5: Comparison of the learning algorithms used by the FNNRW for training accuracy. The accuracy of the improved FNNRW method is superior to the FNNRW algorithm in the training dataset in terms of different training durations.  
Figure 6: Test accuracy comparison of learning algorithms for the FNNRW. The accuracy of the improved FNNRWs method is superior to the FNNRW algorithm in the test dataset in terms of various training durations.  
Figure 7: Algorithm for learning the FNNRW’s relative error. While the error of the optimized FNNRW learning algorithm is typically lower than 0.05, the relative error of the FNNRW learning algorithm drops with the number of training repetitions but stays around 0.1.