[MIA 2025]Brain networks and intelligence: A graph neural network based approach to resting state fM-优快云博客

fluid intelligence (FI)	the ability to reason and solve problems in novel situations
crystallized intelligence (CI)	the ability to use knowledge and experience to solve problems
total intelligence (TI)	a composite measure of overall cognitive ability

②They proposed Brain ROI-aware Graph Isomorphism Networks (BrainRGIN) for cluster-specific learning

2.3. Theory and related work

2.3.1. Graph neural networks

①For graph $G=\left ( V,E \right )$ with node set $V$ and edge set $E$ , to learn a global graph representation to predict $y_G=g\left(h_G\right)$

②Introduced traditional GNNs (not for brains)

2.3.2. Comparison with existing deep learning based architectures for brain network analysis

①Lists relevant GNN research on fMRI

2.4. Proposed architecture

①Overall framework of BrainRGIN:

（图画的太简单了，topk不是他提出的，SERO和GARO也不是他提出的）

2.4.1. Functional connectivity graph creation

①"regions selected based on an atlas lead to an FC matrix, while regions generated by independent component analyzes (ICA) lead to an FNC matrix"

②The adjacency matrix $A_{k}\in R^{N\times N}$ is constructed by Pearson correlation:

$A_{i,j}^k=\left\{ \begin{array} {ll}0, & i=j \\ e_{i,j}, & \mathrm{otherwise} \end{array}\right.$

（1）RGIN convolution

①Message passing in RGIN (combined with RGCN and GIN, the aggregation function of RGCN replaces the function of GIN):

$h_i^{(l)}=\mathrm{MLP}^{(l)}\left(\left(1+\epsilon^{(l)}\right)\cdot W_i^{(l)}\cdot h_i^{(l-1)}+\sum_{j\in N_{(i)}^{(l)}}W_j^{(l)}\cdot e_{i,j}^{(l-1)}\cdot h_j^{(l-1)}\right)$

where $W$ and $\epsilon$ are learnable parameters, and $W_i$ contains the positional information form $r_i$ :

$\mathbf{W}_i^{(l)}=\theta_2^{(l)}\cdot\mathrm{relu}\left(\theta_1^{(l)}\mathbf{r}_i\right)+\mathbf{b}^{(l)}$

where $r$ stores the one-hot positional encoding information

但作者觉得 $r$ 存one hot是稀疏矩阵，其实很占空间，就想优化一下：

$\alpha_k^{(l)}=\theta_1^{(l)}r_i$

其中 $\alpha _i^{(l)}\in R^{K\left(l\right)}$ ，这样直接用可学习参数代替一个矩阵乘上另一个可学习参数。同时把二维的 $\theta_2$ 拆分成集群数个 $K$ 的基矩阵 $\beta_u^{(l)}\in R^{d(l+1)\times d(l)}$ 。这样可以更新为：

$W_i^{(l)}=\sum_{u=1}^{K(l)}\alpha_{iu}^{(l)}\beta_u^{(l)}+b^{(l)}$

②Forward propagation function of RGIN Convolution:

$h_{i}^{(l)}=\mathrm{MLP}^{(l)}\left(\left(1+\epsilon^{(l)}\right)\cdot\sum_{u=1}^{K(l)}\alpha_{iu}^{(l)}\beta_{u}^{(l)}+b^{(l)}\cdot h_{i}^{(l-1)}+\sum_{j\in N_{(i)}^{(l)}}h_{j}^{(l-1)}\cdot\sum_{u=1}^{K(l)}\alpha_{ju}^{(l)}\beta_{u}^{(l)}+b^{(l)}\cdot e_{i,j}^{(l-1)}\right)$

（2）Pooling layers

①Top k selection:

$s^{(l)}=\frac{H^{(l)}w^{(l)}}{\left\|w^{(l)}\right\|_2}$

$\tilde{s}^{(l)}=\frac{\left(s^{(l)}-\mu\left(s^{(l)}\right)\right)}{\sigma\left(s^{(l)}\right)}$

$i=\mathrm{topk} \begin{pmatrix} \tilde{s}^{(l)},k \end{pmatrix}$

$H^{\left(l+1\right)}=\left(H^{\left(l\right)}\mathrm{\odot ~sigmoid}{\left(\tilde{s}^{\left(l\right)}\right)}\right)_{i:}$

$E^{(l+1)}=E_{i,i}^{(l)}$

（3）Readout

①都不是你自己的了干嘛非要又把GARO和SERO详细介绍一遍？？没看过的人建议转移去STAGIN原文

（4）Loss functions

①SmoothL1Loss: compared with MSE, SmoothL1Loss is robuster and less sensitive:

$L_{\mathrm{smoothL}1}\left(x,y\right)= \begin{array} {cc}0.5\cdot\left(x-y\right)^2, & \mathrm{if}|x-y|<1 \\ \left|x-y\right|-0.5, & \mathrm{otherwise} \end{array}$

②Unit loss for learnable constraining vector:

$L_{\mathrm{unit}}(v)=\left\|\omega\right\|_{2}-1$

③Top k loss:

$L_{\mathrm{TPK}}^{(l)}=-\frac{1}{M}\sum_{m=1}^{M}\frac{1}{N^{(l)}}\sum_{i=1}^{k}\log\left(\hat{s}_{m,i}\right)+\sum_{i=1}^{N^{(l)}-k}\log\left(1-\hat{s}_{m,i+k}\right)$