Extracting the Inter-Sub-Network Features

As mentioned in the introduction, after the sub-network division, we must consider both intra-sub-network and inter-sub-network features. The overview of the extraction of inter-sub-network features is vividly illustrated in Figure 5 and the extraction of inter-sub-network features is divided into two steps: (1) Calculating the mean correlation time series for each sub-network (see Figure 5A). (2) Estimating low- and high-order FCNs simultaneously with the MVND based FCN construction method from rs-fMRI mean time series (see Figure 5B). The estimated low- and high-order FCNs are the inter-low-order features and the inter-high-order features, respectively.

The overview of the extraction of inter-sub-network features. (A) Shows the calculation of rs-fMRI mean series. (B) Shows the pipeline of the extraction of the inter-sub-network features.

The inter-sub-network feature extraction method is equivalent to the construction of FCN in the whole brain scale and the FCN construction method is the same as that in the sub-network scale. Both are constructed by MVND based FCN construction method, which can be referred to section “Constructing the FCN Time Series With Sliding-Window Strategy” and section “Extracting the Intra-Sub-Network Features.” Here we describe in detail the generation of mean time series of each sub-network by taking the u-th subnetwork as an example.

The mean correlation time series y_u of the u-th sub-network can be calculated by averaging those rs-fMRI time series assigned to this sub-network. Specifically, each element in y_u is defined as:

Where, m represents the subscript of the element in y_u, and |||u| represents the total number of rs-fMRI time series contained in the u-th sub-network.