## 3 Results  
### Convolution-GRU Classification  
The training and classification of the classifier in this study are completed on a laptop computer, including an Intel (R) Core (TM) i7-9750H@ 2.60 GHz, 6 CPU cores and an NVIDIA GeForce GTX 1660 Ti 6.0 GB GPU, and 8.0 GB memory, the classification model used are all written in Python 3.8 environment using Pytorch 1.4.0 and Sklearn 0.22.2 under Windows 10. In order to compare with the classification performance of convolution-GRU classifier, we also trained four traditional classifiers (SVM (C = 0.01), k-nearest neighbor (KNN)(n_neighbors = 2), linear discriminant analysis (LDA) (solver = '1 sqr'), LGR) and CNN and GRU networks. It should be noted that we have used independent component data to train these classifiers, but FNC data have no time series features, so only four traditional classifiers and CNN networks have been trained. Considering that the size of the data is small, 90% of the data set is used as the training set and 10% is used as the test set to allow the classifier to learn more information, and the model is tested using 10-fold cross validation. During the training of the convolution-GRU network, the batch size is set to 64, and we used the Adam optimizer to reduce the cross-entropy loss of the model. The initial value of the learning rate is set to 0.01, and the learning rate is adjusted using the ReduceLROnPlateau method, that is, when the decrease in three consecutive training losses is not less than a certain threshold, the learning rate is reduced to half, and the threshold is set to 0.001. Figure 5 and Table 1 show the classification performance of seven classification methods using independent component time series as training data in this study. Classification using the convolution-GRU network resulted in a classification accuracy of \(72.2\pm 2.9\%\), while using traditional classifiers (LDA, KNN, LGR, SVM) to classify time series of independent components yielded poor results. SVM gives the best performance in the traditional classifiers which achieved \(63.2\pm 4.4\%\). It indicates that the convolution-GRU network used in this study has achieved a large improvement in classification accuracy. In terms of the precision and recall of the two classes, the convolution-GRU model has achieved the best classification effect of the majority class, and the precision of the minority class has also reached \(26.7\pm 6\%\). While the precision of the majority class of the traditional classifier is comparable to that of the deep learning model, the recall of the majority class is lower, and the best performing SVM reaches only \(70.9\pm 5.0\%\). This indicates that the convolution-GRU model has fully learned the features of the majority class. For minority class, traditional classifiers often have a higher recall rate, but the precision rate is the same or lower than some simple deep learning models,while the minority class precision rate of the convolution-GRU model reached \(26.7\pm 6.1\%\), which shows that this model can reduce the probability that samples from majority class are misclassified, thereby improving the credibility of the classification results. For deep learning models, when CNN, GRU, or convolution-single GRU models are used for classification, the performance of the majority class is similar to the convolution-GRU model, but the performance of the minority class is poor. Considering that LP, LR, SP, and SR have different levels in each classifier, this article uses weighted F1 values to integrate these types of index to form a comprehensive index to evaluate the classifier used in this study. In the case of imbalanced sample sizes, the weighted F1 score can objectively evaluate the performance of the classifier compared to other scores. In fact, many studies have used this indicator [35; 36]. The calculation method of the weighted F1 value is as follows:  
\[\textit{weighted\_F1}=\frac{2}{\frac{1}{LP}+\frac{1}{LR}}\cdot\frac{n_{l}}{n_{ l}+n_{s}}+\frac{2}{\frac{1}{SP}+\frac{1}{SR}}\cdot\frac{n_{s}}{n_{l}+n_{s}} \tag{11}\]