[论文精读]DynBrainGNN: Towards Spatio-Temporal Interpretable Graph Neural Network Based on Dynamic Brain

②They propose a Dynamic Brain Graph Neural Networks (DynBrainGNN), which based on dynamic brain connectom via dynamic variational autoencoders (DVAE) and spatio-temporal attention

③It is the first time that someone put forward such a "build in" dynamic FC?（啥玩意？真真第一次？）

2.3. Proposed Model

2.3.1. Problem Definition

①Graph set: $\left\{\mathcal{G}_{dyn}^{1},\mathcal{G}_{dyn}^{2},...,\mathcal{G}_{dyn}^{N}\right\}$ , where $\mathcal{G}_{dyn}^{i}=\left\{\mathcal{G}^{i}\left(1\right),...,\mathcal{G}^{i}\left(T\right)\right\}$ is the time series with $T$ length of the $i$ -th subject and $N$ is the number of subjects

②Through graphs, they extract and learn features $\left\{h_{\mathcal{G}_{dyn}}^1,h_{\mathcal{G}_{dyn}}^2,...,h_{\mathcal{G}_{dyn}}^N\right\}$

③The real label set: $\{Y_{1},Y_{2},...,Y_{N}\}$

2.3.2. Overall Framework of DynBrainGNN

①The schematic of DynBrainGNN:

which covers graph encoder, spatial attention module, temporal attention module and DVAE four modules;

where decoder recovers $\hat{h}_{G(t)}=\mathcal{X}_{d}\circ\mathcal{X}_{e}\left(h_{G(t)}\right)$ and $\check{h}_{G(t+1)}={\mathcal X}_{d}\circ\theta\circ{\mathcal X}_{e}\left(h_{G(t)}\right)$ ;

然后，作者只是说橙色蓝色那俩框框是“为了保证解码器的可靠”，然后也没多说了

2.3.3. Construction of Dynamic Functional Graph

①Length of time series: $T$

②Length of slicing window: $L$

③Stride: $S$

④By dynamic cutting, they obtain $W=[T-L/S]$ windowed dFC matrices（为啥？如果T=10，L=8，S=1，W不就等于2了吗，但是看上去是不是有1-8，2-9，3-10三个啊，不会要加一吗？）

⑤Each dFC calculated by Pearson correlation

⑥⭐They get the graph $\mathcal{G}\left(t\right)=\left(A\left(t\right),X\left(t\right)\right)$ where $A\left ( t \right )$ is a adjacency matrix that all 1 transformed by the top 20% absolute correlation and $X_{i}\left(t\right)=\left[\rho_{i1},\ldots,\rho_{in}\right]^{\mathrm{T}}$ denotes the node features which constructed by the row or column of FC matrix

2.3.4. Graph Encoder

①Graph encoder: GCN

②Propagation rule of GCN:

$H^l=\sigma\left(D^{-\frac{1}{2}}\hat{A}D^{-\frac{1}{2}}\Theta^{l-1}\right)$

where $\hat{A}=A+I,D=\sum_{j}\hat{A}_{ij}$ , $\Theta^{l-1}$ denotes learnable parameters and $\sigma \left ( \cdot \right )$ denotes Sigmoid

2.3.5. Spatio-Temporal Attention-Based READOUT Module

①They designed two attention based READOUT methods, Spatial Attention READOUT (SAR) and Temporal Attention READOUT (TAR)

②Based on prior $H$ , they define ${\mathcal Z}={\mathcal S}(H), {\mathcal Z}\in\left[0,1\right]^{N},H\in \mathbb{R}^{D\times N}$

③In SAR, $H_{\mathrm{space}}=[x_{i};x_{j}]$ , where $[\cdot ;\cdot ]$ denotes concatenation

④In TAR, $H_{\mathrm{temporal}}$ is constructed by the concatenation of several graph presentations at different times

⑤The specific operation of ${\mathcal S}$ :

${\mathcal Z}=\mathrm{Gumbel}\_\mathrm{Softmax}\left(\mathrm{Sigmoid}\left(\mathrm{MLP}\left(H\right)\right)\right)$

after Sigmoid, ${\mathcal Z}\in[0,1]$ . "Then, attention masks are sampled from Bernoulli distributions, and the gumbelsoftmax reparameterization trick is applied to update ${\mathcal S}$ "

⑥In SAR, $h_{G}=\mathrm{GCN}\left(\mathcal{Z}_{\mathrm{space}}\odot G\right)$

⑦In TAR, $h_{GT}=\mathcal{Z}_{\mathrm{time}}\otimes G$ where $\otimes$ denotes Kronecker product

⑧Schematic of SAR and TAR:

2.3.6. Dynamic Variational Autoencoders (DVAE)

①Temporal transition: $h_{G(t+1)}=\mathrm{LSTM}\left(h_{G(t)}\right)$

②The function of DVAE:

$\begin{aligned} \mathcal{L}_{\mathrm{DVAE}}& =\alpha\left(\sum_{t=1}^{T}\mathbb{E}\left[\left\|h_{G(t)}-\hat{h}_{G(t)}\right\|_{F}\right]+\sum_{t=1}^{T-1}\mathbb{E}\left[\left\|h_{G(t+1)}-\check{h}_{G(t+1)}\right\|_{F}\right]\right) \\ &-\beta\left(\sum_{t=1}^{T}\mathbb{E}\left[D_{\mathrm{KL}}\left[q\left(Z|h_{G(t)}\right)\parallel p\left(Z\right)\right]\right]\right), \end{aligned}$

where $\hat{h}_{G(t)}={\mathcal X}_{d}\circ{\mathcal X}_{e}\left(h_{G(t)}\right),\check{h}_{G(t+1)}={\mathcal X}_{d}\circ\theta\circ{\mathcal X}_{e}\left(h_{G(t)}\right)$ , $q\left(Z|h_{G}\right)$ represents the encoder model（什么东西啊？就是GCN吗？）, $\left\|\cdot\right\|_{F}$ indicates the Frobenius norm, $p\left(Z\right)$ denotes the prior distribution with isotropic Gaussian (assumed), $\alpha$ and $\beta$ are both scaling coefficients of the regularization term

③One more regularization term for compacting:

$\mathcal{L}_{\mathbf{MI}}=\gamma\left(\sum_{t=1}^{T-1}I\left(h_{G(t+1)},h_{GT(t+1)}\right)\right)$

where $I\left ( \cdot \right )$ denotes the matrix-based Renyi’s $\alpha$ -order mutual information and $\gamma$ denotes the scaling coefficient

④Accordingly, combining them all $\mathcal{L}=\mathcal{L}_{\mathrm{CE}}+\mathcal{L}_{\mathrm{DVAE}}+\mathcal{L}_{\mathrm{MI}}$ to get a final loss function, where $\mathcal{L}_{\mathrm{CE}}$ is cross entropy loss

2.4. Experiments

2.4.1. Dataset

①ABIDE I: 289 ASD and 23 HC for no reason

②REST-meta-MDD: 397 MDD and 427 HC

③SRPBS: " This is a multi-disorder MRI dataset"（吓我一跳，总感觉是同时身患玉玉症多动症焦虑症自闭症老年痴呆的被试呢）, selecting 234 SCZ and 92 HC

2.4.2. Baselines

①Settings:

2.4.3. Experimental Settings

①Cross validation: 5 fold

②Decision of hyper-parameter: grid search

2.4.4. Evaluation on Classification Performance

①Comparison table:

2.5. Interpretation Analysis

2.5.1. Disease-Specific Brain Dynamic Network Connections

①The interpretations of dynamically dominant and fluctuant connections（？）are brought by $\mathcal{Z}_{\mathrm{time}}$ and $\mathcal{Z}_{\mathrm{space}}$

②They define dominant subgraph $\mathcal{G}_{\mathrm{dsub}}$ and fluctuant subgraph $\mathcal{G}_{\mathrm{fsub}}$ :

$\mathcal{G}_{\mathrm{dsub}}=\frac{1}{T}\sum\limits_{t=1}^{T}\left(\mathcal{Z}\left(t\right)\right),\mathcal{G}_{\mathrm{fsub}}=\sqrt{\frac{1}{T}\sum\limits_{t=1}^{T}\left(\mathcal{Z}\left(t\right)-\bar{\mathcal{Z}}\right)^{2}}$

where $\mathcal{Z}\left(t\right)=\mathcal{Z}_{\mathrm{space}}\left(t\right)\odot\mathcal{Z}_{\mathrm{time}}\left(t\right)$ and $\overline{\mathcal{Z}}$ is the mean value of $\mathcal{Z}\left(t\right)$

③The top 50 influential edges:

sensorimotor adj. 感觉运动的（等于 sensomotor）

2.5.2. Temporal Properties

①“我们提供的时间属性的解释，以了解大脑的灵活性和适应性在精神疾病。具体而言，我们首先应用k-means聚类算法对有窗时空参与的图表示hGT进行聚类，以评估动态大脑模式(状态)。使用基于轮廓分数的聚类有效性分析来确定最佳聚类数量。然后，我们量化这些状态的时间属性的组差异，包括停留时间(即属于一个状态的连续窗口的持续时间)，分数窗口(即属于一个状态的总窗口的比例)和转换数量(即状态之间的转换数量)。使用带有错误发现率(FDR)校正的双样本t检验(图4)。我们的分析显示，ASD患者在II状态下有更高的分数窗口和平均停留时间，这与最近的一项神经影像学研究一致”（我失去了paraphrase能力）

②Temporal properties:

2.5.3. Conclusion

They want to further try their model in other datasets

3. 知识补充

3.1. Dwell time

搜了一圈没搜到关于医学设备的，提供以下猜测

（1）最可能的，length of time series signals

（2）两个相邻点之间的时间？比如task fMRI两次task之间的时间间隔

（3）嘻嘻，事实证明上面俩都是错的，在2.5.2.作者说它是"the duration of consecutive windows belonging to one state"

4. Reference List

Zheng, K., Ma, B. & Chen, B. (2024) 'DynBrainGNN: Towards Spatio-Temporal Interpretable Graph Neural Network Based on Dynamic Brain Connectome for Psychiatric Diagnosis', Machine Learning in Medical Imaging, 14349.doi: DynBrainGNN: Towards Spatio-Temporal Interpretable Graph Neural Network Based on Dynamic Brain Connectome for Psychiatric Diagnosis | SpringerLink

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