cbtr-causality-topological-ranking - SKILL.md Agent Skill

name: cbtr-causality-topological-ranking arxiv_id: 2407.13514v1 utility: 0.88 tags: '[topological data analysis, seizure, effective connectivity, Hodge decomposition, causal inference, EEG, brain hierarchy]' created: 2026-03-31 description: "Causality-Based Topological Ranking (CBTR)"

Causality-Based Topological Ranking (CBTR)

Activation Keywords

CBTR 方法
脑层次拓扑分析
有效连接拓扑
Hodge decomposition brain
因果推断脑网络
癫痫发作脑层次变化

Problem Statement

传统拓扑数据分析（TDA）方法的局限：

Persistent Homology 依赖对称距离度量
无法捕捉有向动力学（有效连接）
难以识别脑区的层次结构
癫痫发作时的层次变化难以量化

Method Overview

El-Yaagoubi et al. (2024) 提出 CBTR 方法：

因果推断（CI）评估有效脑连接
Hodge 分解（HD）进行层次排序
识别脑区间的相互影响
分析癫痫发作期间的层次变化

Tools Used

Component - Analysis component
Causal Inference - Analysis component
Hodge Decomposition - Analysis component
TDA - Analysis component
EEG - Analysis component

Architecture

EEG Time Series Data
        ↓
┌──────────────────────┐
│  Causal Inference    │
│  (Granger/Transfer   │
│   Entropy)           │
└──────────────────────┘
        ↓
  Directed Connectivity Matrix
        ↓
┌──────────────────────┐
│  Hodge Decomposition │
│  - Gradient (hierar) │
│  - Curl (circulation)│
│  - Harmonic          │
└──────────────────────┘
        ↓
  Hierarchical Ranking
        ↓
  Seizure Impact Analysis

Step-by-Step Instructions

CBTR 实现

因果推断评估有效连接

import numpy as np
from statsmodels.tsa.stattools import grangercausalitytests

def compute_granger_causality(eeg_data, maxlag=5):
    """计算 Granger 因果矩阵"""
    n_channels = eeg_data.shape[1]
    causality_matrix = np.zeros((n_channels, n_channels))
    
    for i in range(n_channels):
        for j in range(n_channels):
            if i != j:
                # 测试 j -> i 的因果
                test_result = grangercausalitytests(
                    np.column_stack([eeg_data[:, i], eeg_data[:, j]]),
                    maxlag=maxlag,
                    verbose=False
                )
                # 取最小 p 值
                p_values = [test_result[lag][0]['ssr_ftest'][1] 
                            for lag in range(1, maxlag+1)]
                causality_matrix[i, j] = -np.log(min(p_values) + 1e-10)
    
    return causality_matrix

Hodge 分解

from scipy import sparse
from scipy.sparse.linalg import lsqr

def hodge_decomposition(flow_matrix):
    """
    Hodge 分解：将有向流分解为梯度、旋度和调和分量
    
    flow_matrix: 有向连接矩阵 A[i,j] = flow from j to i
    """
    n = flow_matrix.shape[0]
    
    # 构建图拉普拉斯算子
    # L = D - A (有向版本)
    out_degree = flow_matrix.sum(axis=1)
    in_degree = flow_matrix.sum(axis=0)
    
    # 构建边-节点关联矩阵
    edges = [(i, j) for i in range(n) for j in range(n) 
             if i != j and flow_matrix[i, j] != 0]
    m = len(edges)
    
    # Incidence matrix B: B[e, v] = 1 if v is source, -1 if v is target
    B = sparse.lil_matrix((m, n))
    flow_values = np.zeros(m)
    
    for idx, (i, j) in enumerate(edges):
        B[idx, j] = 1   # source
        B[idx, i] = -1  # target
        flow_values[idx] = flow_matrix[i, j]
    
    B = B.tocsr()
    
    # 求解最小二乘问题: min ||B @ rank - flow||^2
    # 这给出梯度分量（层次排名）
    result = lsqr(B, flow_values)
    gradient_rank = result[0]
    
    # 残差 = 旋度 + 调和分量
    residual = flow_values - B @ gradient_rank
    
    return {
        'gradient': gradient_rank,  # 层次排名
        'residual': residual,        # 非层次分量
        'ranking': np.argsort(gradient_rank)[::-1]  # 从高到低排名
    }

CBTR 完整流程

def cbtr_analysis(eeg_preictal, eeg_ictal):
    """CBTR：癫痫发作前后的层次变化分析"""
    
    # 1. 计算因果矩阵
    causality_pre = compute_granger_causality(eeg_preictal)
    causality_ictal = compute_granger_causality(eeg_ictal)
    
    # 2. Hodge 分解
    hodge_pre = hodge_decomposition(causality_pre)
    hodge_ictal = hodge_decomposition(causality_ictal)
    
    # 3. 层次变化
    ranking_change = hodge_ictal['gradient'] - hodge_pre['gradient']
    
    # 4. 识别变化最大的脑区
    most_influenced = np.argsort(np.abs(ranking_change))[::-1]
    
    return {
        'preictal_ranking': hodge_pre['ranking'],
        'ictal_ranking': hodge_ictal['ranking'],
        'ranking_change': ranking_change,
        'most_influenced_regions': most_influenced[:5],
        'gradient_pre': hodge_pre['gradient'],
        'gradient_ictal': hodge_ictal['gradient']
    }

可视化层次变化

import matplotlib.pyplot as plt

def plot_hierarchical_change(cbtr_result, channel_names):
    """可视化层次变化"""
    fig, axes = plt.subplots(1, 3, figsize=(15, 5))
    
    # 发作前排名
    axes[0].bar(range(len(channel_names)), 
                cbtr_result['gradient_pre'])
    axes[0].set_title('Pre-ictal Hierarchy')
    axes[0].set_xlabel('Channel')
    axes[0].set_ylabel('Gradient Rank')
    
    # 发作时排名
    axes[1].bar(range(len(channel_names)), 
                cbtr_result['gradient_ictal'])
    axes[1].set_title('Ictal Hierarchy')
    
    # 变化量
    axes[2].bar(range(len(channel_names)), 
                cbtr_result['ranking_change'])
    axes[2].set_title('Hierarchical Change')
    axes[2].axhline(y=0, color='r', linestyle='--')
    
    plt.tight_layout()
    return fig

Example Usage

import numpy as np

# 加载 EEG 数据
eeg_preictal = load_eeg_segment('preictal')  # 发作前
eeg_ictal = load_eeg_segment('ictal')        # 发作时

# CBTR 分析
results = cbtr_analysis(eeg_preictal, eeg_ictal)

# 输出结果
print("Top 5 most influenced regions during seizure:")
for i, region in enumerate(results['most_influenced_regions'][:5]):
    print(f"  {i+1}. Channel {region}: Δrank = {results['ranking_change'][region]:.3f}")

# 可视化
plot_hierarchical_change(results, channel_names)

Key Findings

Traditional TDA vs CBTR

Aspect	Traditional TDA	CBTR
Directionality	Symmetric only	Captures directed flow
Hierarchy	Not directly accessible	Explicit ranking
Causal dynamics	Missing	Integrated
Seizure analysis	Limited	Effective

Hodge Decomposition Components

Component	Interpretation
Gradient	Hierarchical influence
Curl	Circular flow
Harmonic	Global structure

Description

Causality-Based Topological Ranking (CBTR)

Key Concepts:

传统拓扑数据分析（TDA）方法的局限：
Persistent Homology 依赖对称距离度量
无法捕捉有向动力学（有效连接）
难以识别脑区的层次结构
癫痫发作时的层次变化难以量化

Instructions for Agents

Follow these steps when applying this skill:

Step 1: 因果推断评估有效连接

Step 2: Hodge 分解

Step 3: CBTR 完整流程

Step 4: 可视化层次变化

Step 5: Understand the Request

Examples

Example 1: Basic Application

User: I need to apply Causality-Based Topological Ranking (CBTR) to my analysis.

Agent: I'll help you apply cbtr-causality-topological-ranking. First, let me understand your specific use case...

Context: 传统拓扑数据分析（TDA）方法的局限：

Persistent Homology 依赖对称距离度量
无法捕捉有向动力学（有效连接）
难以识别脑区的层次

Example 2: Advanced Scenario

User: Complex analysis scenario

Agent: Based on the methodology, I'll guide you through the advanced application...

Example 2: Advanced Application

User: What are the key considerations for cbtr-causality-topological-ranking?

Agent: Let me search for the latest research and best practices...

References

El-Yaagoubi, A.B. et al. (2024). Topological Analysis of Seizure-Induced Changes in Brain Hierarchy Through Effective Connectivity. arXiv:2407.13514.

Related Skills

conex-connect-eeg-extremal
seizure-detection-connectivity
time-varying-brain-connectivity