[论文精读]Spatio-Temporal Graph Convolution for Resting-State fMRI Analysis

论文网址：Spatio-Temporal Graph Convolution for Resting-State fMRI Analysis | SpringerLink

论文代码：GitHub - sgadgil6/cnslab_fmri: CNS (Computational Neuroscience) Lab project for age/sex classification of fMRI scans

英文是纯手打的！论文原文的summarizing and paraphrasing。可能会出现难以避免的拼写错误和语法错误，若有发现欢迎评论指正！文章偏向于笔记，谨慎食用

1. 省流版

1.1. 心得

1.2. 论文总结图

2. 论文逐段精读

2.1. Abstract

2.2. Introduction

2.3. ST-GCN for rs-fMRI Analysis

2.4. Experiments

2.5. Results and Analysis

2.6. Conclusion

3. Reference List

1. 省流版

1.1. 心得

（1）提出问题和解决问题的写法是好的

（2）那个正对称的“边重要性”矩阵 $\mathbf{M}$ 看上去好好用的样子

1.2. 论文总结图

2. 论文逐段精读

2.1. Abstract

①Exsting works ignore functional dependency between ROIs or dynamic information

②They construct a novel spatio-temporal graph convolutional network (ST-GCN) on short sub-sequences of the BOLD time series

2.2. Introduction

①⭐Adopting partial correlation on edge feature might ignore the time information. Additionally, RNN considers the temporal features rather than ROI dependence

②⭐If applying physical space and temporal information together, related ROIs with long European distances are easily overlooked

distal adj. [解剖] 末梢的，末端的

2.3. ST-GCN for rs-fMRI Analysis

（1）Representing Functional Networks as Spatio-Temporal Graphs

①Time series extraction framework:

②Constructing an undirected ST graph $\mathcal{G}:=(\mathcal{V},\mathcal{E})$ , where $\mathcal{E}$ denotes the edge set between pairwise nodes on specific time points $\mathcal{V}=\{v_{t,i}|t =1,...,T;i=1,...,N\}$ , $T$ denotes time point and $N$ is the number of ROI

③⭐In temporal graph, there are edges between the same ROI in adjacent time points.

④⭐And in spatial graph, edges connect nodes at the same time points. The value of edges are $d\left ( v_{tj},v_{ti} \right )$ , which constructs affinity matrix $\mathbf{A}$ （但是没说是什么距离吧？相关程度？相关性计算方式也有好多）

（2）Spatio-Temporal Graph Convolution (ST-GC)

①Node feature: the average BOLD signal of ROI $i$ at time $t$

②The ST neighbourhood of $v_{ti}$ :

$B(v_{ti}):=\{v_{qj}|d(v_{tj},v_{ti})\leq K,|q-t|\leq\lfloor\Gamma/2\rfloor\}$

where $K$ and $\Gamma$ represents the spatial/temporal kernel size of the neighborhood

③The ST-GC operation on $v_{ti}$ :

$f_{out}(v_{ti}):=\frac1{Z_{ti}}\sum_{v_{qj}\in B(v_{ti})}f_{in}(v_{qj})\cdot\mathbf{w}(v_{qj})$

where $Z_{ti}$ denotes normalization factor, $f_{in}(v_{qj})$ denotes input feature of $v_{ti}$ and $\mathbf{w}\left ( \cdot \right )$ denotes convolutional kernel

④For input features of the $N$ ROIs at the $t$ -th frame $\mathbf{f}_{t}\in\mathbb{R}^{N\times C}$ with $C$ channel（这个C channel是截取的时间序列吗还是什么？还是说是很多个时间点的，每个ROI就一个特征，有C个）, the output $\mathbf{f}_{t}^{\prime}\in\mathbb{R}^{N\times M}$ with $M$ channel of spatial graph convolution can be:

$\mathbf{f}_{t}^{\prime}:=\Lambda^{-\frac{1}{2}}(\mathbf{A}+\mathbf{I})\Lambda^{-\frac{1}{2}}\mathbf{f}_{t}\mathbf{W}_{SG}$

where $\Lambda$ denotes degree matrix (containing self loop), $\mathbf{W}_{SG}\in \mathbb{R}^{C\times M}$ denotes spatial graph convolutional kernel

⑤The final output in ST-GC can be:

$\mathbf{f}_{i}^{\prime}\circledast \mathbf{W}_{TG}\in \mathbb{R}^{\Gamma \times T}$

where $\circledast$ denotes 1D convolution, $\mathbf{f}_{i}^{\prime}\in \mathbb{R}^{M\times T}$ nodetes the node feature

⑥ $\mathbf{W}_{SG}$ and $\mathbf{W}_{TG}$ are both for approximate ST concolutional kernel on Fourier domain

（3）Classifying BOLD Time Series by ST-GCN

①Layer of ST-GCN: 3

②Input of ST-GCN: $\mathbf{f}\in\mathbb{R}^{N\times T}$ (time series)

③Output channel: 64→class number by FC with sigmoid

④Temporal kernel size: $\Gamma =11$

⑤Stride: 1

⑥Dropout rate: 0.5

⑦⭐To verify the importance of edges, they add “edge importance” matrix $\mathrm{M}\in\mathbb{R}^{N\times N}$ to replace $\mathbf{A}+\mathbf{I}$ by $(\mathbf{A}+\mathbf{I})*\mathbf{M}$ (element-wise multiplication). Moreover, $\mathbf{M}$ is shared in all the layers. The diagonal elements of $\mathbf{M}$ denotes the importance of each ROI and the others are the importance of functional connectivity（最早是Yan提出的，但是负值和不对称的矩阵会破坏它的意义。因此作者在这里强制M为各层共享以及正对称的）

（4）Training ST-GCN

①FC matrix fluctuates with time

②Learnig rate: 0.001

③Weight decay: 0.001

2.4. Experiments

①Tasks: classifying sex and age

②NCANDA: 773 samples with 376 males and 397 females. Number of ROI is 34.

③HCP: 1096 samples. Excluding 5 whose frames less than 1200, there are 498 females and 593 males. Number of ROI is 22

④Time segments: $T{}'=16$ to full sequence

⑤Number of sub-sequence: $S=64$

⑥Running times: 20, to get an average edge importance matrix

⑦Comparison baselines: MLP and LSTM

2.5. Results and Analysis

（1）NCANDA:

①Comparison charts:

which presents there is no significant difference between alcoholic and non alcoholic participants

②Visualization of ROI (left) and edge (＞0.3) (right) importance:

（2）HCP:

①Accuracy comparison chart:

②The impact of voting:

③Visualization of ROI (left) and edge (＞0.3) (right) importance on sex prediction:

2.6. Conclusion

The future works can be defining the size of sliding window automatically and recgonizing biomakers.

3. Reference List

Gadgil, S. et al. (2020) 'Spatio-Temporal Graph Convolution for Resting-State fMRI Analysis', MICCAI, pp. 528-538. doi: Spatio-Temporal Graph Convolution for Resting-State fMRI Analysis | SpringerLink

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