Electroencephalogram identification in this study is a binary classification problem to recognize one EEG segment whether it belongs to Depression (label: 1) or Healthy (label: 0). A multivariate series (one matrix) X^{m × n} (20 × 1024 in this study) is reshaped into a 3D tensor T^{m × a × b} (20 × 32 × 32 in this study) for the input of the FCCNN.

Figure 1 illustrates the architecture of FCCNN. The main design strategy of the classifier is to use as few network layers as possible without reducing the classification performance. The classifier firstly applied an attention block on the input EEG segment (reshaped to 20 × 32 × 32). It is then followed by one dropout layer, two convolutional layers, one flatten layer, and three fully connected layers. The hyper-parameters of the FCCNN are fine-tuned by our previous grouping Bayesian optimization algorithm (Ke et al., 2020b) and also illustrated in Figure 1. The hyper-parameter of convolutional layer is denoted as “filters @ [receptive map size].” The activation function of all fully connected (FC) layers is “sigmoid,” and that of the convolutional layer is “ReLU.” The final “sigmoid” of FCCNN outputs the classification label of a specific segment. The main design principles are as follows:

We use the momentum SGD algorithm with a learning rate of 0.01 to optimize the FCCNN via backpropagation algorithm (Krizhevsky et al., 2012). This study sets a small momentum attenuation factor (decay = 1e-4, momentum = 0.9, nesterov = True) to reduce the residual error (Krizhevsky et al., 2012). The initialization strategy follows the setting in reference (He et al., 2015) and sets the batch normalization of 80 and epochs of 83. The model reports the performance on the test set (or new EEG segment) after training.

This subsection mainly discusses the activation maximization (see section 2.2.1) of the input layer. The feature visualization (Zeiler and Fergus, 2014) of neurons will provide a global view of the network. The network rarely uses neurons in isolation, while understanding stays at the subjective level. To verify the rationality of the model and enhance the objectivity of the interpretation, the information entropy of the input based on AP clustering (see section 2.2.3) is then measured.

This set of experiments evaluated the classification performance in terms of a learning curve, receiver operating characteristic curve (ROC) curve, and performance indexes regarding sensitivity, specificity, and accuracy.

Figure 2 was the learning curve of the classifier on training the MPHC data set. Here, “accuracy” and “loss” denoted the accuracy and error in the training stage, respectively; “val_accuracy” and “val_loss” indicated the accuracy and error in the validation stage, respectively. It could verify the generalization ability of the classifier. In the training stage, the accuracy of the classifier on the training set and validation set was consistent, and no obvious gap between the curves existed. At the same time, the excellent classification performance on the test set denoted that the classifier had a desirable generalization ability in the current case study, and the overfitting or underfitting did not occur (Ke et al., 2020a).

ROC curve is introduced into the field of machine learning to evaluate the results of classification and detection. When the positive and negative samples are not balanced, the ROC curve (AUC value) will be a more stable indicator to reflect the quality of the model than the Precision-Recall curve. Figure 3 illustrated the ROC curve on identifying depression state on the MPHC data set. The high AUC (value = 1) indicated that the proposed classifier could distinguish the depression state effectively.

The table represented that the classifier proposed in this study was the best in all performance indicators. Meanwhile, the attention block could improve the performance and stability with lower SD, and high sensitivity and specificity also illustrated that the classifier could effectively screen out patients with depression and health controls together.

Moreover, we performed a t-test for most of the approaches on the performance indexes regarding sensitivity, specificity, and accuracy to evaluate discrimination via p-values. Figures 4–6 illustrated the p-values on performance indexes regarding accuracy, sensitivity, and specificity, respectively. From the figures, we concluded that (1) greater statistical significance of most approaches were observed for the three performance indexes (cool color), (2) all the p-values on specificity illustrated statistical significance, (3) smaller statistical significance between Lenet and other approaches on accuracy and sensitivity were observed (hot color), and (4) the p-values on the diagonal of the matrix did not make sense.

This set of experiments was to explain the FCCNN on identifying MDD. The classifier always tended to classify according to the features with significant differences (less complexity) in the classification problem. In the field of information, entropy was a measure of the uncertainty on random variables. To our best knowledge, the greater the information entropy, the greater the amount of information contained in the variable, and the greater the uncertainty of that. In summary, the classification was that of reducing uncertainty (complexity) of the problem aiming to obtain lower entropy.

Moreover, the activation maximization of the input layer of the classifier was visualized to understand the mechanism of the classifier in processing EEG data because the input of FCCNN reflected the channel level characteristics of EEG data. The activation maximization of the first layer is 20 (the same as channel number) activation matrices with respect to the size of the input layer (20 × 32 × 32), each of which represents the maximum activation feature of each channel. Then, the AP clustering partition algorithm calculated the information entropy of each activation matrix and projected it to the scalp topographic map at the channel level. Besides, we also visualized the average entropy corresponding to brain regions partitioned by Table 1.

Figure 7 illustrated the 3D scalp topographies map visualizations from the activation maximization of FCCNN with channel level (Figure 7A) and brain region level (Figure 7B). From Figure 7A, the entropies of channels (Cz, P6, Fp2, F3, F4, O1, O2, F8) were lower than those of other channels, which indicated that the classifier mainly distinguishes depression and health according to extracting and classifying the features hidden in these channels correctly. Figure 7B also illustrated a 3D scalp topographic map corresponding to the brain region level. The lower mean entropy values in the left and right temporal, frontal lobe concluded that significant differences existed in these brain regions. This result reproduced the study of the data provider (Mumtaz et al., 2017), which meant that our model made correct classification by analyzing the key features among the depression state.

Two experiments analyzed the attention block. The average power [0, 200 Hz] of each channel was first obtained by Fourier transform to evaluate the statistical difference in frequency between MG (segments: 9,789) and HG (segments: 8,653). Notice that the attention used in the training stage was the average power of frequency on each channel. Figure 8 illustrated the average frequency-power representations of the different class labels (Healthy & MDD) of a typical channel (Fz), and similar results were obtained in other channels. From the figure, we arrive at the following conclusions: (1) the frequency distribution was concentrated in low-frequency bands, (2) the power peak of the HG was at 3.015 and 22.11 Hz, while that of the MG was at 7.035 Hz, and (3) the power value of MG was generally higher than that of HG.

Figure 9 illustrated the mean entropy values with and without the attention module. They evaluated whether the classifier focused on those “important” channels of interest, especially the channels located in the brain regions of the left and right temporal, frontal lobe (Mumtaz et al., 2017). From Figure 9, we concluded the following insights. First, the information entropy of almost all channels decreased except for Pz, which meant the attention module could (1) greatly reduce the complexity of the classifier, (2) improve the classification performance. The root cause might be that the classifier paid attention to and acted on the features of more channels. Second, the information entropy of channels including F8, Cz, P6, O1, and O2 was very small whether the classifier contained an attention module or not, which meant the classifier with or without attention module were both effective.

Experiments were performed on the same Desktop (equipped with AMD R7 3700X CPU@3.59GHz, NVidia RTX 3080 10G GPU, and 16GB RAM on 64bit Windows 7). The classifier proposed in this study was based on a sub CNN and sub dense neural network. The time complexity of the sub CNN was proportional to the number of layers (L) and the corresponding number of neurons (N). Thus, the time complexity was calculated as follows:

where n_L and n_L−1 were, respectively, the number of filters (also known as “width”) in the L-th and (L-1)-th layers, with the overall network depth d; moreover, s_L and m_L represented the spatial sizes of the filter and the corresponding feature map, respectively.

For the sub dense network, let L denote the number of layers and U denoted the number of neurons in each layer, the time complexity is O(UL). In summary, the overall complexity of the proposed approach is O(S(N, L)) + O(UL).

Figure 10 illustrated the information entropies according to traditional and our strategy in terms of the data partition. The main difference between the two strategies was the assumptions of data distribution. First, the traditional one divided the neural data into partitions with the equivalent range because of obeying uniform distribution (in Figure 10B, the data was divided into six partitions equally). In this case, the result would be close to the grand truth with enough sample points. However, this would produce a big residual with the insufficient data, which led to the inaccuracy of uncertainty measurement between the model and neural data. Second, our strategy assumed that the neural data obeyed general adaptive distribution. That is, it learned the distribution of the data itself in terms of a data-driven approach and made a reasonable partition (in Figure 10A, the three partitions with different data distribution had obtained). In this case, the algorithm calculated the information entropy accurately and measured the uncertainty correctly.

The classification performance was not related to the number of layers of its model in this study. For example, Resnet-16 and Capsulenet, which had more layers, did not achieve the expected performance indicators but needed a longer training time. The root cause was that the complex classifier might bring the over-fitting problem, which led to the degradation of classification performance. It was a considerable challenge to make the classifier better fit the non-linearity of different data. Furthermore, understanding the non-linear fitting mechanism would be one of the key issues in understanding the neural network black box, which would be one of the key research directions in the future.

This subsection compared different optimization methods in the classifier, including momentum SGD in this study, RMSprop, Adagrad, Adadelta, Adam, Adamax, and Nadam. Figure 11 illustrated that momentum SGD achieved the best performance, while the three-optimizer including Adagrad, Adam, and Nadam performed poorly in this study. Adagrad optimizer was to modify the learning rate for each parameter according to the previously calculated parameter gradient in each time step. However, the learning rate was always decreasing and decaying, and the learning ability of the model decreased rapidly. In this case, it was very likely that the classification performance became poor without crossing the local minimum value. As an extension of the Adagrad, Adadelta solves the attenuation problem of learning rate and improved performance. Momentum-based methods such as the momentum SGD utilized in this study and the RMSprop optimization method could skip the local optimum. Aiming at training the neural network with complex structure quickly, the optimization methods regarding Adam, Adamax, and Nadam failed to train the light-weighted neural network, such as the classifier in this study. The most likely root reason might be that the oscillation would occur when closing to the optimization goal, which resulted in the performance failing to meet the requirements.

It was believed that the extended model should be proposed in the future to enable multiple classifications to identify the subtypes of depression state. Moreover, it played a vitally important role in understanding the dynamic evolution mechanism of multi-dimensional EEG data via interpreting the complexity of the classifier evolution over time. A suitable way in the future to extend the ability of neural networks for processing ongoing EEG data would be the Long Short-Term Memory neural network and temporal CNN (Chen et al., 2020).

The use of a single dataset means that the results should not be generalized to a wider population. In future work, multiple datasets will be created and used for validation of the method.