Evolvable Graph Diffusion Ot

---
name: evolvable-graph-diffusion-ot
description: 可进化图扩散最优传输脑连接组建模方法（EDT-PA）。结合结构-功能连接对齐和高阶依赖建模，用于脑疾病分类。触发词：脑连接组、最优传输、optimal transport、结构-功能对齐、高阶依赖、brain connectome、EDT-PA。
user-invocable: true
---

# Evolvable Graph Diffusion Optimal Transport for Brain Connectome

## 核心方法论

EDT-PA (Evolvable Graph Diffusion Optimal Transport with Pattern-Specific Alignment) 是一种创新的脑连接组建模框架：

1. **高阶结构依赖** - 使用可进化建模块动态捕获脑区高阶关系
2. **模式特定对齐** - 使用最优传输对齐结构连接（SC）和功能连接（FC）
3. **KAN 节点聚合** - Kolmogorov-Arnold 网络实现灵活的非线性交互建模
4. **疾病分类** - 识别疾病特异性连接模式

### 核心创新

- 打破"SC 是 FC 固定支架"的假设
- 几何感知的结构-功能对齐
- 捕获脑区高阶依赖关系

## Python 代码示例

### 1. 最优传输对齐模块

```python
import torch
import torch.nn as nn
import numpy as np

class OptimalTransportAlignment(nn.Module):
    """
    最优传输对齐模块 - 将结构连接和功能连接在几何感知的方式下对齐
    """
    
    def __init__(self, n_regions, regularization=0.1):
        super().__init__()
        self.n_regions = n_regions
        self.regularization = regularization
        
        # 可学习的传输成本矩阵
        self.cost_matrix = nn.Parameter(
            torch.eye(n_regions) + torch.randn(n_regions, n_regions) * 0.01
        )
    
    def compute_transport_plan(self, source_dist, target_dist, cost=None):
        """使用 Sinkhorn 算法计算最优传输计划"""
        if cost is None:
            cost = self.cost_matrix.detach().numpy()
        
        K = np.exp(-cost / self.regularization)
        u = np.ones(self.n_regions) / self.n_regions
        v = np.ones(self.n_regions) / self.n_regions
        
        for _ in range(100):
            u = source_dist / (K @ v + 1e-10)
            v = target_dist / (K.T @ u + 1e-10)
        
        transport_plan = np.diag(u) @ K @ np.diag(v)
        return torch.from_numpy(transport_plan).float()
    
    def align_sc_fc(self, sc_matrix, fc_matrix):
        """对齐结构连接和功能连接"""
        sc_dist = sc_matrix.sum(dim=1)
        sc_dist = sc_dist / sc_dist.sum()
        fc_dist = fc_matrix.sum(dim=1)
        fc_dist = fc_dist / fc_dist.sum()
        
        transport_plan = self.compute_transport_plan(sc_dist.numpy(), fc_dist.numpy())
        aligned_matrix = transport_plan @ fc_matrix @ transport_plan.T
        transport_cost = torch.sum(transport_plan * self.cost_matrix)
        
        return aligned_matrix, transport_cost
```

### 2. 可进化图扩散模块

```python
class EvolvableDiffusionBlock(nn.Module):
    """可进化图扩散模块 - 动态捕获脑区高阶依赖"""
    
    def __init__(self, n_features, n_heads=4, evolution_steps=3):
        super().__init__()
        self.n_features = n_features
        self.evolution_steps = evolution_steps
        
        self.attention = nn.MultiheadAttention(embed_dim=n_features, num_heads=n_heads, batch_first=True)
        self.evolution_weights = nn.ParameterList([
            nn.Parameter(torch.randn(n_features, n_features) * 0.01)
            for _ in range(evolution_steps)
        ])
        self.layer_norm = nn.LayerNorm(n_features)
        
    def forward(self, x, adjacency):
        h = x
        for weight in self.evolution_weights:
            diffused = torch.bmm(adjacency, h)
            transformed = torch.matmul(diffused, weight)
            attn_out, _ = self.attention(h, h, h)
            h = self.layer_norm(h + transformed + attn_out)
        return h
```

### 3. KAN 节点聚合模块

```python
class KANLayer(nn.Module):
    """Kolmogorov-Arnold Network 层 - 使用样条函数实现灵活的非线性变换"""
    
    def __init__(self, in_features, out_features, grid_size=10):
        super().__init__()
        self.grid_size = grid_size
        
        grid = torch.linspace(-1, 1, grid_size + 1)
        self.register_buffer('grid', grid)
        
        self.spline_weight = nn.Parameter(torch.randn(out_features, in_features, grid_size + 3) * 0.1)
        self.base_weight = nn.Parameter(torch.randn(out_features, in_features) * 0.1)
    
    def b_splines(self, x):
        """计算 B-样条基函数"""
        x = x.unsqueeze(-1)
        grid = self.grid.unsqueeze(0).expand(x.shape[1], -1).unsqueeze(0)
        distances = torch.abs(x - grid)
        basis = torch.exp(-distances * 5)
        return basis
    
    def forward(self, x):
        base_out = torch.matmul(x, self.base_weight.T)
        basis = self.b_splines(x)
        spline_out = torch.einsum('bif,oif->bo', basis, self.spline_weight)
        return base_out + spline_out


class KANNodeAggregation(nn.Module):
    """使用 KAN 进行节点聚合"""
    
    def __init__(self, n_features, hidden_dim=64, n_classes=2):
        super().__init__()
        self.kan1 = KANLayer(n_features, hidden_dim)
        self.kan2 = KANLayer(hidden_dim, hidden_dim)
        self.kan3 = KANLayer(hidden_dim, n_classes)
        self.activation = nn.GELU()
    
    def forward(self, node_features):
        x = node_features.mean(dim=1)
        x = self.activation(self.kan1(x))
        x = self.activation(self.kan2(x))
        x = self.kan3(x)
        return x
```

### 4. 完整 EDT-PA 模型

```python
class EDT_PA(nn.Module):
    """Evolvable Graph Diffusion Optimal Transport with Pattern-Specific Alignment"""
    
    def __init__(self, n_regions, n_features, hidden_dim=64, n_classes=2):
        super().__init__()
        self.n_regions = n_regions
        
        self.sc_encoder = nn.Linear(n_regions, n_features)
        self.fc_encoder = nn.Linear(n_regions, n_features)
        self.ot_alignment = OptimalTransportAlignment(n_regions)
        self.diffusion_block = EvolvableDiffusionBlock(n_features)
        self.kan_aggregation = KANNodeAggregation(n_features * 2, hidden_dim, n_classes)
    
    def forward(self, sc_matrix, fc_matrix):
        batch_size = sc_matrix.shape[0]
        
        # 1. 对齐 SC 和 FC
        aligned_fc = []
        transport_costs = []
        for i in range(batch_size):
            aligned, cost = self.ot_alignment.align_sc_fc(sc_matrix[i], fc_matrix[i])
            aligned_fc.append(aligned)
            transport_costs.append(cost)
        aligned_fc = torch.stack(aligned_fc)
        transport_cost = torch.stack(transport_costs).mean()
        
        # 2. 特征编码
        sc_features = self.sc_encoder(sc_matrix)
        fc_features = self.fc_encoder(aligned_fc)
        
        # 3. 融合特征
        combined_features = torch.cat([sc_features, fc_features], dim=-1)
        
        # 4. 图扩散
        adjacency = 0.5 * (sc_matrix + aligned_fc)
        adjacency = adjacency / (adjacency.sum(dim=-1, keepdim=True) + 1e-10)
        evolved_features = self.diffusion_block(combined_features, adjacency)
        
        # 5. KAN 聚合分类
        logits = self.kan_aggregation(evolved_features)
        
        return logits, transport_cost
```

## 应用场景

1. **脑疾病分类** - MDD（抑郁症）、AD（阿尔茨海默病）诊断
2. **结构-功能关系研究** - 理解 SC-FC 对应关系
3. **生物标志物发现** - 识别疾病特异性脑网络模式
4. **多模态融合** - 整合 DTI、fMRI 等多源数据

## 关键参数

- **正则化系数**: 最优传输熵正则化（0.05-0.2）
- **进化步数**: 扩散迭代次数（2-5）
- **样条阶数**: KAN 的样条阶数（3-5）

## Activation Keywords
- 脑连接组
- 最优传输
- optimal transport
- 结构-功能对齐
- 高阶依赖
- brain connectome
- EDT-PA
- KAN网络
- Sinkhorn算法
- 疾病分类

## Tools Used
- pytorch
- numpy
- scipy

## Instructions for Agents
1. 理解最优传输对齐：使用Sinkhorn算法对齐SC和FC
2. 掌握可进化图扩散：动态捕获脑区高阶依赖
3. 实现KAN节点聚合：使用B-样条函数进行非线性变换
4. 计算传输成本：量化SC-FC对齐的代价
5. 注意正则化系数对传输计划的影响

## Examples
```python
# 使用示例
from evolvable_graph_diffusion_ot import EDT_PA, OptimalTransportAlignment

# 1. 创建模型
model = EDT_PA(
    n_regions=100,
    n_features=64,
    hidden_dim=128,
    n_classes=2
)

# 2. 前向传播
logits, transport_cost = model(sc_matrix, fc_matrix)
print(f"传输成本: {transport_cost.item():.4f}")

# 3. 最优传输对齐
ot_align = OptimalTransportAlignment(n_regions=100, regularization=0.1)
aligned_fc, cost = ot_align.align_sc_fc(sc_matrix, fc_matrix)
```

## 参考文献

- Paper: arXiv:2509.16238