The publicly available neuroimaging data from the Alzheimer’s disease Neuroimaging Initiative (ADNI) ¹ database (Jack et al., 2010) is adopted. Notably, 127 participants, including sixty-three MCIsand 64 NCs were included in this experiment. The SPM8 toolbox ² is used to pre-process the fMRI data according to a commonly adopted pipeline for fMRI. Finally, the pre-processed BOLD time series signals were partitioned into 116 ROIs, based on the Automated Anatomical Labeling (AAL) atlas.

We adopted the commonly-used BC estimation model to discover the connection patterns, including Pearson’s correlation (PC), sparse representation (SR) and Granger causality mapping (GCM). Let X ∈ R T × N the BOLD signal matrix, where T is the volume length and N is the ROI number. Denote x i ∈ R T the fMRI time series derived from the ith ROI   i = 1 , ⋯ , N . Then, the details of these methods are given as follows.

Pearson’s correlation (PC) is among the most simplicity and intuitiveness scheme for the BC estimation. The edge weights of the PC-based BC W = ( W i j ) ∈ R N × N is in the following: W i j = ( x i − x ¯ i ) T ( x j − x ¯ j ) ( x i − x ¯ i ) T ( x i − x ¯ i ) ( x j − x ¯ j ) T ( x j − x ¯ j ) , (1) where x i − x ¯ i is a centralized counterpart of x i .

Due to the cofounding effect caused by the PC-based method, the partial correlation method involves regressing complex factors from other ROIs that naturally come into being (Huang et al., 2010). Inspired by the sparsity nature of the brain connection, one popular solution is to incorporate an additional l 1 -norm constraint, resulting in a sparse representation (SR)-based BC estimation scheme, as follows. m i n W ∑ i = 1 n ‖ x i − ∑ j ≠ i W i j x j ‖ 2 + λ ∑ j ≠ i | W i j | (2) where λ is the hyper-parameter for controlling the balance of sparsity and partial correlation.

Granger causality mapping (GCM) models the effective connectivity, i.e., causality relations among nodes, which connection is thereby nonsymmetric (Goebel et al., 2003). Specifically, given two-time x [ n ]   and y [ n ], the Granger causality mapping process from x [ n ] to y [ n ] ] is defined as follows: F x , y = ln | ∑ ( ζ t ) | | ∑ ( η t ) |   (3) where ζ t and η t   are the residuals of the restricted and unrestricted regression models, respectively, and Σ indicates the variance.

The simplest way to combine the information for multiple connection patterns is to concatenate all of the data directly. However, this approach is quite inappropriate in cases with high-dimension curves and small samples. To achieve this, this paper provided Multiple Connection Pattern Combination (MCPC), which is given in Figure 1. Specifically, an MK-SVM model is adopted to combine multiple information. Notably, this is the first attempt, which combines the information from different connectomes derived from single-mode data. Here, the primal problem of MK-SVM is given as follows: (Rakotomamonjy et al., 2007) min W 1 2 ∑ m = 1 M β m ‖ w m ‖ 2 + C ∑ i = 1 n ξ i s . t .   y i ( ∑ m = 1 2 β m ( w m ) T φ m ( x i m ) + b ) ≥ 1 − ξ i ξ i ≥ 0 , i = 1 ⋯ , n (4) where n is the number of training samples and M is the number of connection patterns, y i ∈ { 1 , − 1 }   representing the label of the patients or healthy controls from the ith sample. φ m represents the mapping function ,   w m represents t the hyperplane in the Represent Hilbert Kernel Space (RHKS) and β m denotes the combined weight of the mth connection pattern. Then, the dual form of the MK-SVM can be expressed as: max α ∑ i = 1 n α i − 1 2 ∑ i , j α i α j y i y j ∑ m = 1 M β m k m ( x i m , x j m ) s . t . ∑ i = 1 n α i y i = 0 0 ≤ α i ≤ C , i = 1 , ⋯ , n (5) where k m ( x i m , x j m ) = φ m ( x i m ) T φ m ( x j m ) β m is learned based on Alain’s method (Rakotomamonjy et al., 2007). Additionally, we utilized the commonly-used linear kernel as a naive attempt due to its simplicity. The predictive level based on the MK-SVM can be formulated as follows: f ( x 1 , x 2 , … , x M ) = s i g n ( ∑ i = 1 n y i α i ∑ m = 1 M β m k m ( x i m , x m ) + b ) (6)

The PC-based and SR-based BC is estimated by BrainNetClass (Zhou et al., 2020). Note that there exists a hyperparameter λ in SR. To construct the SR-based BC, we selected the hyperparameter λ the SR by leave-one-out cross-validation (LOOCV) at the range of { 2 − 5 , 2 − 4 , … , 2 5 } . Specifically, we empirically set λ = 2 3 , with an accuracy of 81.10%. The accuracies of different hyperparameters by LOOCV are given in Figure 2. For the GCM estimation, the dynamicBC toolbox is selected (Liao et al., 2014).

We visualized the BC adjacency matrices ³ of PC, SR and GCM methods in Figure 3. In Figure 3, the brain connections obtained by different BC estimation methods are completely different in their topology, since these methods model different statistical information or relation across ROIs.

Due to the limited sample size, we adopt the nest LOOCV strategy for evaluating the performance of the MCI classification. Specifically, to determine the optimal parameters (i.e., the optimal value of the hyperparameter C in the SVM), an inner LOOCV is conducted. The hyperparameter C is ranged in { 2 − 5 , 2 − 4 , … , 2 5 }. Moreover, the accuracy, sensitivity, specificity and AUC, are used to evaluate the classification performance of different measurements. The mathematical definitions of these measurements are as follows: A c c u r a c y = T P + T N T P + F P + T N + F N , (7) S e n s i t i v i t y = T P T P + F N , (8) S p e c i f i c i t y = T N T N + F P , (9)

Here, TP (TruePositive) is the number of the positive subjects that are correctly classified in the ASD identification task. Similarly, TN (TrueNegative), FP (FalsePostive) and FN (FalseNegative) are the numbers of their corresponding subjects, respectively.

The classification results based on single connection patterns are given in Table 1, which results are achieved by a single linear kernel SVM classifier. In addition, the results based on combining the partial connection patterns (e.g., PC + SR, PC + GCM and SR + GCM) are also reported. The ROC curve is given in Figure 4.

From these results in Table 1 and Figure 4, we can easily observe that the performance of MCPC achieves much better results than that of the single-kernel SVM. The results indicate the rationality of the proposed MCPC. To investigate the significance of model performance improvement, differences between various AUCs were compared by using a Delong test (Delong et al., 1988), the proposed MCPC methods are significantly superior to results of the single pattern, e.g., PC, SR, GCM under 95% confidence interval with p-value equals to 0.0251, 0.041 and 0.005, respectively. The superior performance illustrated that the proposed MCPC approach can significantly improve the classification performance with only single modal data. In addition, although the MCPC only use single-mode data, it can still significantly improve the accuracy of the MCI diagnosis.

The hub nodes (the top 5% degree of brain nodes) of the MCI and NC groups based on three different BC network estimation methods are obtained. As shown in Tables 2-5, the distribution of hub nodes of the networks estimated by the PC, SR and GCM methods are similar. Most hubs are mainly distributed in the parietal lobes, temporal, and frontal, which correspond to the default mode network (DMN) and frontoparietal task control (FTC) network. Furthermore, the results suggest that hub nodes in the NC group are mainly located in the DMN. In comparison, the distribution of hub nodes in patients with MCI covers a relatively wide range of brain connection distributions, such as the frontoparietal task control network and visual network, in addition to the DMN.

In this study, the nested cross-validation scheme was adopted to evaluate the performance of the proposed MCPC. In particular, the selected connections in each validation loop might vary due to the validation resampling. Thus, we record the consensus connections and regard them as the most discriminative features for differentiating individuals with MCI from NCs (Li et al., 2020b). The consensus connections based on different connection pattern methods are shown in Figure 5. In addition, the degrees of consensus connection for different patterns are given in Tables 6-8. As shown in Tables 6-8, among the three BC estimation methods, the brain connection based on the PC method exhibits the maximum number of consensus connections. It is worth noting that the consensus connections with significant differences between MCI individuals and NCs are associated with multiple brain regions: the frontal lobe, occipital lobe, cingulate gyrus, hippocampus, and thalamus. Moreover, these brain regions corresponding to subnetworks are mainly distributed in the DMN, visual network, and subcortical network.

From the classification results in Table 1, the SR method exhibited the highest accuracy compared to the PC and GCM methods. Although the PC method obtained more consensus connections, GCM considered more graph theory information with directions, SR achieves the best results in the single-pattern methods. These results indicated that the SR approach can effectively overcome the limitations of the PC approach. Moreover, the MCPC achieved a much better performance than the results which only utilize the single connection patterns, indicating that the proposed MCPC approach can significantly improve the diagnosis performance of MCI. Notably, different connection patterns can provide different discriminative information for diagnosis. In addition, the MCPC method outperforms the results which only considers two patterns; this result further confirms the superiority of the proposed method. Overall, as was mentioned in previous studies (Xu et al., 2020a; Xu et al., 2020b), multiple connection patterns can be combined with an MK-SVM to effectively consider the weights of different information types and differentiate MCI patients from NCs.

The hub nodes of the consensus connections obtained from the three different BC estimation methods (PC, SR and GCM) are given in Tables 6-8. It can be significantly found that the most discriminative brain regions and functional connections between the MCI and NC groups were mainly distributed in the temporal, frontal and parietal lobes, which correspond to the DMN, FTC, VN, and AN. Previous studies have verified that these subnetworks correspond to various cognitive functions, such as attention, execution, and spatial positioning (Rolle et al., 2017; Bi et al., 2018). Our results suggest that patients with MCI may have altered subnetworks and corresponding cognitive functions. In particular, the DMN exhibited the most significant discriminative ability, which was consistent with previous studies of brain connections involving MCI and NC groups (Gao et al., 2020). In fact, the DMN has always been regarded as the key role for cognitive function (Anticevic et al., 2012; Liu et al., 2019). In addition, we found abnormalities in the subcortical network involving the thalamus, putamen, and amygdala in MCI. In recent years, several studies have indicated that the individuals in the early stages of AD, including subjective cognitive decline and MCI, exhibit abnormalities in subcutaneous nuclei, e.g., basal forebrain, basal ganglia, and thalamus (Fernández-Cabello et al., 2020; Xu et al., 2021). In a follow-up study, we intend to use a more detailed brain atlas than that used in this study to further explore subcortical nuclei in the early stage of AD.