The data used in this paper were from the public dataset MPHC (https://figshare.com/articles/EEG_Data_New/%204244171) [16], which recruited 34 patients with MDD (17 men and 17 women, mean age = 40.3 $\pm$ 12.9 years). Patients with MDD meet the Diagnostic and Statistical Manual of Mental Disorders, fourth edition, diagnostic criteria for depression, which are internationally accepted [22]. Study participants signed a consent form and were informed about the experimental design. Additionally, 30 age-matched healthy controls (21 men and 9 women, mean age = 38.3 $\pm$ 15.6 years) were recruited as a control group. The control group was confirmed to be healthy after the examination. The EEG data with 5 min each of EC and EO resting states included 30 control subjects and 34 patients with depression. Both patients with MDD and controls sat in a semirecumbent position. Each dataset has 19 electrode EEG signals with a sampling frequency of 256 Hz.

In this paper, the placement of brain electrodes on the scalp followed the International 10–20 system [23]. EEG data were gathered using an EEG cap with 19 electrode channels.

The preprocessing of the EEG data in this study was conducted using EEGLAB (EEGLAB2022.1, Swartz Center for Computational Neuroscience, San Diego, CA, USA). The electrodes are positioned using the electrode system after each set of EC and EO data has been imported. Then, the data were filtered and a finite-length unit impulse response (finite impulse response) filter was used to perform high-pass filtering at 0.1 Hz. Low-pass filtering at 45 Hz was introduced to reduce the interference caused by the power frequency. After carefully examining the waveform, the bad channel was manually removed, and its average value was substituted with the channels close to it. Independent component analysis (ICA) can effectively extract and remove artifacts produced by eye and head movements [24]. The collected raw EEG data shown various artifacts and valid EEG signals. These data are not dependent on one another and typically follow a non-Gaussian distribution [25], making it possible to divide them into independent components using ICA. This study uses EEGLAB’s ICA tool, which uses a “runica” algorithm with default settings, calculates independent components based on the actual number of channels, and removes artifact components by observing brain topography and time domain chromatograms, and power spectra.

After data preprocessing, some subjects lacked EC or EO data, and data with a short data lengths were removed. Data of EO and EC for 4 min each were collected from 25 healthy controls and 24 patients with MDD. We segmented all the data with a length of 10 s and finally obtained 576 and 576 segments with EC and EO for patients with depression, respectively, whereas the control group had 600 and 600 segments with EC and EO, respectively.

The frequency domain feature selected in this paper is PSD [26], with a sampling frequency of 256 Hz and a hanging window. First, the full-band PSD value of each electrode was calculated. Lempel and Ziv [27] proposed the LZC feature, and Kaspar [28] later designed it as a simple and user-friendly program. Before calculating the complexity, the EEG signal X(x(1), x(2), …, x(n)) must be transformed into a binary sequence Y(s(1), s(2), …, s(n)), where n is the total number of sampling points of the signal, 1 $\le$ r $\mathrm{\le }$ n. The specific operations are as follows:

(1)

In this study, the threshold m was set to be the median value of the EEG because the median value performs better than the average value when there are abnormal values in the signal [29]. Then, we traverse all characters of sequence Y to obtain the complexity c(n) of sequence Y.

Lempel and Ziv [27] have shown that the upper bound on c(n) is b(n). a is the number of coarse-grained segments.

(2)$$\underset{n\to \mathrm{\infty }}{lim}c(n)=b(n)=\frac{n}{{\log }_{a}n}$$

In this paper, the EEG signal sequence is binarized, so a = 2. To avoid changes caused by the length of the sequence segment, it is necessary to perform a normalization operation on c(n); the operation is as follows:

(3)$$C(n)=\frac{c(n)}{b(n)}$$

In principle, LZC represents the rate at which new patterns appear in the EEG signals. The normalized LZC is higher, indicating that the number of new patterns in EEG is large and that the brain activity is more complex. Because brain regions discharge irregularly, the EEG sequence tends to be more random.

Support vector machine (SVM) is a classic model for binary classification. This paper selects SVM as the classifier to classify the extracted features from the preprocessed data with EC and EO with a “linear” kernel and the BoxConstraint of 1.

In the cross-subject experiment, healthy individuals and patients with depression were divided into five groups. One random group was selected from all groups, and the feature matrix of the selected groups was used as the test set, whereas the feature matrix of the remaining groups was used as the training set. That is, samples from the same person cannot be used simultaneously as training and test data. The results were averaged after 100 times fivefold cross-validations.

In the binary classification, according to the predicted situation of the sample and the actual label, it can be divided into true positive (TP), false positive (FP), true negative (TN), and false negative (FN). Then, the confusion matrix of the binary classification, shown in Table 1. Patients with MDD were positive, and controls were negative. TP is the patients with MDD and predicted as MDD. FP is the control group and predicted as patients with MDD. TN is the control group and predicted as control. FN is the patients with MDD and predicted as control.

This matrix can obtain its sensitivity, specificity, accuracy, and other indicators. We need to examine a model from various indicators to assess its quality. Therefore, in addition to comparing the model’s accuracy, it is often necessary to comprehensively consider the model along with indicators such as sensitivity and specificity. The specific calculation formula is as follows:

(4)$$\mathit{\text{sensitivity}}=\frac{TP}{TP+FN}$$

(5)$$\mathit{\text{specificity}}=\frac{TN}{FP+TN}$$

(6)$$\mathit{\text{accuracy}}=\frac{TP+TN}{TP+TN+FP+FN}$$

According to the International 10–20 system, the brain regions are divided, as shown in Table 2.

According to the 10–20 system, electrodes can be divided into frontal, temporal, central, and occipital brain regions, which can be better analyzed by the brain region. First, we construct feature matrices for specific brain regions. The splicing of a feature matrix of the brain regions results in a feature matrix of a combination of multiple brain regions. For example, B1 and B2 are the corresponding feature matrices of two brain regions (The columns of the matrix represent the proposed features of a piece of data), then the feature matrix after the combination of brain regions is (B1; B2).

After the LZC and PSD features are extracted, the average value is obtained for analysis. The topographic maps of the control group and the patients with MDD in EC state are shown in (a) and (b) in Fig. 1, respectively, whereas the topographic maps of the control group and the patients with MDD in EO state are shown in (c) and (d) in Fig. 1, respectively.

From Fig. 1, we can see that the mean LZC value of the patients with MDD is higher than that of the control group, indicating that the irregular discharge of brain regions and the complexity of brain activity in patients with MDD are higher than those in the control group. Additionally, it can be seen that the mean LZC value of the control group and patients with MDD in EO state is higher than that in EC state, indicating that the brain activity in the EO state is more complex than that in the EC state.

From Fig. 2, we can see that the mean PSD of patients with MDD is lower than that of the control group, indicating that the activation degree of the brain of patients with MDD is lower than that of the control group, which corresponds to the findings of the study by Lechinger et al. [30]. And, as can be seen, the mean PSD of the control group and patients with MDD in the EO state is higher than that in the EC state, indicating that the EO state has higher brain activity than the EC state.

Tables 3,4 demonstrate the detection performance of EC and EO states, respectively. According to Tables 3,4, using the nonlinear feature LZC and the frequency domain feature PSD together has a better detection effect than using only the LZC or PSD feature in both the EC and EO states. Furthermore, the highest detection accuracy rate of multiple features can reach 91.0%, which is much higher than that of one feature. This result shows that these two features have complementary roles in identifying MDD and that subsequent studies use multi feature fusion for experiments. In this paper, t-test is used to test the differences between patients with MDD and control group in various feature matrices. As we can see from Tables 3,4, we calculated the p-value of LZC, PSD and LZC + PSD between two groups in the EC and EO states respectively, all features show significant differences with p 0.05.

According to the division of brain regions in Table 2, the fusion features extracted from the channels of each brain region are used as feature sets, a two-dimensional matrix of features of each brain region is constructed, and SVM is used for classification. For example, in EC and EO states, the classification results of each single brain area are shown in Tables 5,6. In Tables 5,6 and Figs. 3,4, F, T, C, and O stand for the frontal, temporal, central, parietal and occipital lobes, respectively, and ALL stands for the entire brain region.

Tables 5,6 shows that in the EC state, the best effect was in the temporal lobe region, with a sensitivity of 80.3%, specificity of 78.6%, and accuracy of 79.4%. In the EO state, the best effect was also in the temporal lobe region, with sensitivity of 84.7%, specificity of 90.0%, and accuracy of 87.4%. This confirms the temporal significance for MDD recognition and is consistent with how the data providers of this study interpreted the pathology. We used t-tests on the feature matrices of single brain region between patients with MDD and control group and found that the O brain region shows significance with p 0.05 in EC state, while the others p 0.01.

We tried merging two or three brain regions or the feature matrix of the three brain regions channels and used SVM for classification. For example, in EC and EO states, the combined detection effects of each multi brain regions are shown in Figs. 3,4.

From Figs. 3,4, it was found that the combination of frontal, temporal, and central lobe regions performed the best in both EC and EO states, with sensitivity, specificity, and accuracy rates of 82.2%, 81.1%, and 81.7% in the EC state and 93.9%, 90.8%, and 92.4% in the EO state, respectively. Additionally, we discovered that the frontal, temporal, and central lobe regions combination increased accuracy by 5% over the best single brain region. The best multi brain regions combination compared with the full brain, the accuracy is 1.4% higher, the specificity is 1.6%, and the sensitivity is 1.1%. We used t-tests on the feature matrices of various brain region combinations between patients with MDD and control group and found that the frontal, temporal, and central region combinations show significant differences with p 0.01 in EC and EO state.

The confusion matrix of optimal combination is shown in Fig. 5. From the confusion matrix, we can observe that the proposed model in this paper owns well sensitivity for detecting MDD patients.