[IEEE TMI 2024]A Multi-Graph Cross-Attention-Based Region-Aware Feature Fusion Network Using Multi-

① $\boldsymbol{X}^{\boldsymbol{z}}\in\mathbb{R}^{N_z\times T}\left(z=1,2,\cdots,Z\right)$ denotes time series of the templet $z$ , where $N_z$ is the number of ROIs and $T$ denotes time point

② $x_n^{z,m}(t)=[x_n^{z,m}(1),x_n^{z,m}(2),\cdots,x_n^{z,m}(T)]^{\prime}$ denotes the time series of the $m$ -th subject, $n$ -th ROI and $'$ denotes transpose operation（这里的定义好混乱...）

③ $x_n^{z,m}$ is the combination of current and previous time series of other ROIs:

$x_n^{z,m}(t)=\sum_{q=0}^QX_n^{z,m}(t-q)\theta_n^{z,m}(q)+e_n^{z,m}(t)$

where $Q$ is the order of the time delay and it is set to 1 for fair comparison

④And

$X_{n}^{z,m}(t-q)=[\mathbf{x}_{1}^{z,m}(t-q),\cdots,\mathbf{x}_{n-1}^{z,m}(t-q),\mathbf{x}_{n+1}^{z,m}(t-q),\cdots,\mathbf{x}_{N_{z}}^{z,m}(t-q)]\in\mathbb{R}^{T\times(N_{z}-1)}$

$\theta_{n}^{z,m}(q)=[\theta_{1,n}^{z,m}(q),\cdots,\theta_{n-1,n}^{z,m}(q),\theta_{n+1,n}^{z,m}(q),\cdots,\theta_{N_{z},n}^{z,m}(q)]^{\prime}\in\mathbb{R}^{(N_{z}-1)\times1}$

and $e_n^{z,m}(t)$ is a residual term

④Then the equation can be:

$x_n^{z,m}(t)=X_n^{z,m}\theta_n^{z,m}+e_n^{z,m}(t)$

where $\boldsymbol{X}_{n}^{z,m}=[\boldsymbol{X}_{n}^{z,m}(t),\boldsymbol{X}_{n}^{z,m}(t-1),\cdots,\boldsymbol{X}_{n}^{z,m}(t-Q)]\in\mathbb{R}^{T\times((N_{z}-1)\times(Q+1))}$ , $\theta_{n}^{z,m}=[\theta_{n}^{z,m}(0)^{\prime},\theta_{n}^{z,m}(1)^{\prime},\cdots,\theta_{n}^{z,m}(Q)^{\prime}]^{\prime}\in\mathbb{R}^{((N_{z}-1)\times(Q+1))\times1}$ （公式这么长，我感觉就是全连接的图神经网络？但是没有自循环，相当于一个节点把上个时间步（或者上个+上上个时间步）所有其他节点特征全部拿过来了）

⑤Removing spurious connections:

$\boldsymbol{\Theta}_n^z=argmin\sum_{m=1}^M||\boldsymbol{x}_n^{z,m}(t)-\boldsymbol{X}_n^{z,m}\boldsymbol{\theta}_n^{z,m}||_2^2+\lambda||\boldsymbol{\Theta}_n^z||_{2,1}$

where $\boldsymbol{\Theta}_n^z=[\boldsymbol{\theta}_n^{z,1},\boldsymbol{\theta}_n^{z,2},\cdots,\boldsymbol{\theta}_n^{z,M}]\in\mathbb{R}^{((N_z-1)\times(Q+1))\times M}$ is coefficient matrix set

⑥For time series matrix $X^z\in\mathbb{R}^{N_z\times T}$ and its corresponding static adjacency matrix $A_{sf}^z\in\mathbb{R}^{N_z\times N_z}$ , the GCN can be:

$H_{sf}^{z}=\sigma(D_{sf}^{-1}A_{sf}\sigma(X^{z}W_{s1}^{z})W_{s2}^{z})$

where $D_{sf}^{z}$ denotes degree matrix, $\boldsymbol{W}_{s1}^z\in\mathbb{R}^{T\times P},\boldsymbol{W}_{s2}^z\in\mathbb{R}^{P\times B}$ denotes weight matrix, $\sigma$ is ELU（啊，魔改了的GCN吗）

⑦Sliding windows to get $h$ dynamic series with length of $\frac{T}{h}$ . 然后对每个滑窗进行时间卷积Blabla看图吧那一块很明确了。最后的输出是：

$H_{df}^z=concat(H_{df}^{z,1},H_{df}^{z,2},\cdots,H_{df}^{z,h}),\boldsymbol{H}_{df}^z\in\mathbb{R}^{N_z\times B}$

（2）DVCA

①Schematic of dual-view cross-attention (DVCA):

②Positional encoding:

$\tilde{\boldsymbol{H}}_{sf}^{z}=LN(\boldsymbol{H}_{sf}^z+\boldsymbol{E}_{sf-pos}^z)\\\tilde{\boldsymbol{H}}_{df}^{z}=LN(\boldsymbol{H}_{df}^z+\boldsymbol{E}_{df-pos}^z)$

where $E_{sf-pos}^z,E_{df-pos}^z\in\mathbb{R}^{N_z\times B}$ denotes absolute positional embedding of static and dynamic sequence

③后面的自己看图，已经很明确了

2.3.3. Region-Aware Feature Fusion Network

①Schematic of RAFFNet:

对于不同脑模板提取到的特征，把每个八个脑区的ROI都分出来拼在一起，可能形状不一样

②The schematic of region-aware controller:

③The region aware attention is calculated by:
$\boldsymbol{F}_g^{head}=\left(softmax\left(\frac{QK^{\prime}}{\sqrt{d_k}}\right)+A_R\right)\boldsymbol{V}$