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Directed graph neural networks with partial directed coherence for seizure prediction and epileptogenic network characterization.

Code ↔ Paper

13 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 13 matches
  1. [1] § STAR★Methods › Method details › DiGCN architecture › Personalised PageRank and stationary distribution ↔ models/digcn.py, lines 6–148 · score 0.96 · approximate stationary distribution, unique left eigenvector, Perron vector, construction guarantees, teleport probability, channel node
  2. [2] § STAR★Methods › Method details › DiGCN architecture › Personalised PageRank and stationary distribution ↔ models/digcn.py, lines 6–148 · score 0.91 · auxiliary teleport node, channel nodes transitions, stationary distribution, teleport probability, transition matrix, augmented
  3. [3] § STAR★Methods › Method details › GNNExplainer and HITS analysis › Hub–authority analysis on the explanation subgraph ↔ explainer/gnn_explainer.py, lines 162–200 · score 0.90 · Hyperlink Induced Topic, L2 normalised, authority score, hub score, explanation adjacency matrix, iteratively
  4. [4] § STAR★Methods › Method details › DiGCN architecture › Multi-scale inception block and network architecture ↔ models/digcn.py, lines 287–325 · score 0.84 · Inception block, node embedding, linear classifier, concatenation, node features, stacked
  5. [5] § STAR★Methods › Method details › GNNExplainer and HITS analysis › Edge mask optimisation ↔ explainer/gnn_explainer.py, lines 38–123 · score 0.78 · sigmoid mask, edge mask, node feature matrix, original weighted, PDC weights, adjacency matrix
  6. [6] § STAR★Methods › Method details › DiGCN architecture › Model training configuration ↔ experiments/run_experiment.py, lines 117–221 · score 0.78 · cross entropy loss, weight decay, DiGCN, Adam, batch, dropout
  7. [7] § STAR★Methods › Method details › DiGCN architecture › Model training configuration ↔ training/train.py, lines 146–229 · score 0.76 · cross entropy loss, weight decay, Adam, batch, training, dropout
  8. [8] § STAR★Methods › Method details › GNNExplainer and HITS analysis › Edge importance extraction ↔ explainer/gnn_explainer.py, lines 125–160 · score 0.70 · zero entries, explanation adjacency matrix, original PDC graph, threshold, mask, scores
  9. [9] § STAR★Methods › Method details › DiGCN architecture ↔ models/digcn.py, lines 196–247 · score 0.68 · multi scale Inception, weighted matrix, fuses, Digraph, block, Convolutional
  10. [10] § STAR★Methods › Method details › GNNExplainer and HITS analysis › Objective function ↔ explainer/gnn_explainer.py, lines 38–123 · score 0.68 · gradient descent, entropy regularisation, Adam, loss, mask, edge
  11. [11] § STAR★Methods › Method details › DiGCN architecture › Graph representation and transition matrix ↔ models/digcn.py, lines 151–193 · score 0.62 · row normalised, transition matrix, weighted PDC, identity
  12. [12] § Results › Component and configuration ablation analyses ↔ models/digcn.py, lines 196–247 · score 0.60 · Inception block, symmetric normalized, digraph, module, convolution, proximity
  13. [13] § STAR★Methods › Method details › GNNExplainer and HITS analysis ↔ explainer/run_explainer.py, lines 90–135 · score 0.51 · GNNExplainer, DiGCN, architecture, HITS, window, electrode

Paper

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The authors' code

Python · 325 lines · 11 KB · no license · 6 matches

  1. import torch
  2. import torch.nn as nn
  3. import torch.nn.functional as F
  6. class DiGraphConv(nn.Module):
  7. """
  8. First-order directed graph convolution layer based on Personalized PageRank.
  10. Accepts raw weighted PDC adjacency matrices directly.
  11. Internally builds a row-stochastic transition matrix from the weighted adj,
  12. then symmetrizes forward and backward propagation operators scaled by the
  13. stationary distribution (paper Section 3.2).
  15. Input adj: raw PDC weight matrix [n_nodes, n_nodes], values in [0, 1].
  16. No binarization or external normalization required.
  17. """
  19. def __init__(self, in_features, out_features, alpha=0.15):
  20. super(DiGraphConv, self).__init__()
  21. self.in_features = in_features
  22. self.out_features = out_features
  23. self.alpha = alpha # PageRank teleport probability
  24. self.weight = nn.Parameter(torch.FloatTensor(in_features, out_features))
  25. nn.init.xavier_uniform_(self.weight)
  27. def _build_transition_matrix(self, adj):
  28. """
  29. Build row-stochastic transition matrix P from raw weighted PDC adj.
  30. Self-loops are added to ensure irreducibility.
  31. """
  32. n = adj.size(0)
  33. device = adj.device
  34. adj_sl = adj + torch.eye(n, device=device) # add self-loops
  35. deg = adj_sl.sum(dim=1)
  36. deg_inv = torch.where(deg > 0, 1.0 / deg, torch.zeros_like(deg))
  37. P = torch.diag(deg_inv) @ adj_sl # row-stochastic
  38. return P
  40. def _build_augmented_transition_matrix(self, P):
  41. """
  42. Construct the (n+1) x (n+1) augmented transition matrix P_ppr
  43. per paper Eq. 6, introducing auxiliary teleport node xi.
  45. Each of the n channel nodes transitions to xi with probability alpha,
  46. and xi returns uniformly to all channel nodes with probability 1/n.
  48. P_ppr = | (1-alpha)*P alpha*1_{n x 1} |
  49. | (1/n)*1_{1 x n} 0 |
  51. This construction guarantees P_ppr is irreducible and aperiodic,
  52. ensuring a unique left Perron eigenvector (stationary distribution).
  54. Args:
  55. P: row-stochastic transition matrix [n, n]
  57. Returns:
  58. P_ppr: augmented transition matrix [n+1, n+1]
  59. """
  60. n = P.size(0)
  61. device = P.device
  63. # top-left block: (1 - alpha) * P [n, n]
  64. top_left = (1.0 - self.alpha) * P
  66. # top-right block: alpha * ones column [n, 1]
  67. top_right = torch.full((n, 1), self.alpha, device=device)
  69. # bottom-left block: (1/n) * ones row [1, n]
  70. bottom_left = torch.full((1, n), 1.0 / n, device=device)
  72. # bottom-right block: 0 (teleport node has no self-loop)
  73. bottom_right = torch.zeros(1, 1, device=device)
  75. # assemble P_ppr [n+1, n+1]
  76. top_row = torch.cat([top_left, top_right], dim=1) # [n, n+1]
  77. bottom_row = torch.cat([bottom_left, bottom_right], dim=1) # [1, n+1]
  78. P_ppr = torch.cat([top_row, bottom_row], dim=0) # [n+1, n+1]
  80. return P_ppr
  82. def _pagerank_power_iteration(self, P, max_iter=500, tol=1e-9):
  83. """
  84. Compute the Personalized PageRank stationary distribution via power
  85. iteration on the explicit (n+1) x (n+1) augmented matrix P_ppr
  86. (paper Eq. 6).
  88. Iteration: pi^(t+1) = pi^(t) @ P_ppr
  90. The first n components of the converged left eigenvector (Perron vector)
  91. are extracted and L1-normalised to yield pi_appr (paper Eq. 6).
  93. Args:
  94. P: row-stochastic transition matrix [n, n]
  95. max_iter: maximum iterations
  96. tol: L1 convergence tolerance
  98. Returns:
  99. pi: stationary distribution over the n channel nodes [n], sums to 1
  100. """
  101. n = P.size(0)
  102. device = P.device
  104. # construct (n+1) x (n+1) augmented transition matrix (paper Eq. 6)
  105. P_ppr = self._build_augmented_transition_matrix(P)
  107. # initialize uniform distribution over all n+1 nodes (including xi)
  108. pi = torch.full((n + 1,), 1.0 / (n + 1), device=device)
  110. for _ in range(max_iter):
  111. pi_new = pi @ P_ppr
  113. if torch.abs(pi_new - pi).sum() < tol:
  114. pi = pi_new
  115. break
  117. pi = pi_new
  119. # extract first n components (channel nodes only, excluding xi)
  120. pi_channel = pi[:n]
  122. # L1-normalisation per paper: "first n components of this eigenvector,
  123. # after l1-normalisation, yield the approximate stationary distribution"
  124. pi_channel = pi_channel / (pi_channel.sum() + 1e-10)
  126. return pi_channel
  128. def forward(self, x, adj):
  129. """
  130. Args:
  131. x: node feature matrix [n_nodes, in_features]
  132. adj: raw weighted PDC adjacency matrix [n_nodes, n_nodes]
  134. Returns:
  135. support: transformed node features [n_nodes, out_features]
  136. """
  137. P = self._build_transition_matrix(adj)
  138. pi = self._pagerank_power_iteration(P)
  140. pi_sqrt = torch.sqrt(pi + 1e-10)
  141. pi_inv_sqrt = 1.0 / pi_sqrt
  143. # symmetrized forward + backward propagation (paper Eq. 5-6)
  144. propagate_forward = torch.diag(pi_sqrt) @ P @ torch.diag(pi_inv_sqrt)
  145. propagate_backward = torch.diag(pi_inv_sqrt) @ P.t() @ torch.diag(pi_sqrt)
  147. support = 0.5 * (propagate_forward + propagate_backward) @ x @ self.weight
  148. return support
  151. class KthOrderProximity(nn.Module):
  152. """
  153. Compute k-th order proximity matrices from raw weighted PDC adj.
  155. k=0: identity
  156. k=1: row-normalized transition matrix P
  157. k>=2: intersection of meeting-path and diffusion-path matrices (paper Eq. 8)
  159. Input adj: raw PDC weight matrix, no preprocessing needed.
  160. """
  162. def __init__(self, k_max):
  163. super(KthOrderProximity, self).__init__()
  164. self.k_max = k_max
  166. def forward(self, adj):
  167. device = adj.device
  168. n = adj.size(0)
  170. # build row-stochastic P from raw weighted adj
  171. adj_sl = adj + torch.eye(n, device=device)
  172. deg = adj_sl.sum(dim=1)
  173. deg_inv = torch.where(deg > 0, 1.0 / deg, torch.zeros_like(deg))
  174. P = torch.diag(deg_inv) @ adj_sl
  176. proximity = {0: torch.eye(n, device=device), 1: P}
  178. for k in range(2, self.k_max + 1):
  179. P_km1 = torch.linalg.matrix_power(P, k - 1)
  180. PT_km1 = torch.linalg.matrix_power(P.t(), k - 1)
  182. meeting = P_km1 @ PT_km1 # paths that meet at node i from j
  183. diffusion = PT_km1 @ P_km1 # diffusion paths
  185. # intersection: only retain positions where both paths are active
  186. intersection = torch.where(
  187. (meeting > 0) & (diffusion > 0),
  188. (meeting + diffusion) / 2.0,
  189. torch.zeros_like(meeting)
  190. )
  191. proximity[k] = intersection
  193. return proximity
  196. class InceptionBlock(nn.Module):
  197. """
  198. Multi-scale Inception block aggregating 0th, 1st, and k-th order proximities.
  200. Fuses zero-order (skip), first-order (DiGraphConv), and higher-order
  201. (k=2..k_max) proximity signals via summation (paper Eq. 9).
  203. Input adj: raw PDC weight matrix, passed through to DiGraphConv and
  204. KthOrderProximity without any external normalization.
  205. """
  207. def __init__(self, in_features, out_features, k_max, alpha=0.15):
  208. super(InceptionBlock, self).__init__()
  209. self.k_max = k_max
  211. # k=0: skip connection (identity path)
  212. self.skip_connection = nn.Linear(in_features, out_features)
  214. # k=1: first-order directed convolution
  215. self.digraph_conv = DiGraphConv(in_features, out_features, alpha=alpha)
  217. # k=2..k_max: higher-order proximity projections
  218. self.kth_convs = nn.ModuleList(
  219. [nn.Linear(in_features, out_features) for _ in range(2, k_max + 1)]
  220. )
  222. self.proximity_builder = KthOrderProximity(k_max)
  224. def forward(self, x, adj):
  225. Z_0 = self.skip_connection(x) # zero-order
  226. Z_1 = self.digraph_conv(x, adj) # first-order
  228. proximity = self.proximity_builder(adj)
  229. Z_list = [Z_0, Z_1]
  231. for k in range(2, self.k_max + 1):
  232. P_k = proximity[k]
  234. # symmetric normalization of k-th proximity matrix
  235. deg_k = P_k.sum(dim=1)
  236. deg_k_inv_sqrt = torch.where(
  237. deg_k > 0,
  238. 1.0 / torch.sqrt(deg_k + 1e-10),
  239. torch.zeros_like(deg_k)
  240. )
  241. P_k_norm = torch.diag(deg_k_inv_sqrt) @ P_k @ torch.diag(deg_k_inv_sqrt)
  243. theta_k = self.kth_convs[k - 2]
  244. Z_k = P_k_norm @ x @ theta_k.weight.t() + theta_k.bias
  245. Z_list.append(Z_k)
  247. return sum(Z_list)
  250. class DiGCN(nn.Module):
  251. """
  252. Stacked DiGCN with n_layers Inception blocks.
  254. Accepts raw weighted PDC adjacency matrices. All normalization and
  255. transition matrix construction happens internally per forward pass.
  256. """
  258. def __init__(self, n_feat, n_hid, n_out, n_layers=3, k_max=2, alpha=0.15, dropout=0.5):
  259. super(DiGCN, self).__init__()
  260. self.n_layers = n_layers
  261. self.dropout = dropout
  263. dims = [n_feat] + [n_hid] * (n_layers - 1) + [n_out]
  264. self.inception_blocks = nn.ModuleList([
  265. InceptionBlock(dims[i], dims[i + 1], k_max, alpha)
  266. for i in range(n_layers)
  267. ])
  269. def forward(self, x, adj):
  270. """
  271. Args:
  272. x: node feature matrix [n_nodes, n_feat]
  273. adj: raw weighted PDC adjacency matrix [n_nodes, n_nodes]
  274. values in [0, 1], no binarization applied
  276. Returns:
  277. node embeddings [n_nodes, n_out]
  278. """
  279. for i, block in enumerate(self.inception_blocks):
  280. x = block(x, adj)
  281. if i < self.n_layers - 1:
  282. x = F.relu(x)
  283. x = F.dropout(x, self.dropout, training=self.training)
  284. return x
  287. class DiGCNClassifier(nn.Module):
  288. """
  289. Graph-level classifier built on DiGCN backbone.
  291. Pools node embeddings via mean + max concatenation, then applies a
  292. linear classification head.
  294. Args:
  295. n_feat: input node feature dimension (10 for EEG PDC dataset)
  296. n_hid: hidden embedding dimension
  297. n_class: number of output classes (2: interictal / preictal)
  298. n_layers: number of stacked Inception blocks
  299. k_max: maximum proximity order (paper: k=1,2)
  300. alpha: PageRank teleport probability (paper: α=0.15)
  301. dropout: dropout rate applied between blocks
  302. """
  304. def __init__(self, n_feat, n_hid, n_class, n_layers=3, k_max=2, alpha=0.15, dropout=0.5):
  305. super(DiGCNClassifier, self).__init__()
  306. self.digcn = DiGCN(n_feat, n_hid, n_hid, n_layers, k_max, alpha, dropout)
  307. self.classifier = nn.Linear(n_hid * 2, n_class)
  309. def forward(self, x, adj):
  310. """
  311. Args:
  312. x: node feature matrix [n_nodes, n_feat]
  313. adj: raw weighted PDC adjacency matrix [n_nodes, n_nodes]
  315. Returns:
  316. logits [n_class]
  317. """
  318. node_emb = self.digcn(x, adj)
  320. # graph-level pooling: mean + max concatenation
  321. mean_pool = torch.mean(node_emb, dim=0)
  322. max_pool, _ = torch.max(node_emb, dim=0)
  323. graph_emb = torch.cat([mean_pool, max_pool], dim=0)
  325. return self.classifier(graph_emb)

digcn.py at commit f9af255, no license · at the source

Overview

Authors: Chenshuo Zhao1,2, Hui Huang3, Chao Fang1, Hong Zhang1, Suyue Zheng1
  1. Department of Neurosurgery, The First Affiliated Hospital of Nanchang University, Nanchang, China
  2. Huankui College, Nanchang University, Nanchang, China
  3. Department of Neurosurgery, The Second Affiliated Hospital of Nanchang University, Nanchang, China
Institutions: Nanchang University (China); First Affiliated Hospital of Nanchang University (China); Second Affiliated Hospital of Nanchang University (China)
Journal: iScience, volume 29, issue 8, article 117068
Dates: received 25 February 2026; accepted 20 July 2026; published online 10 August 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1016/j.isci.2026.117068 · PMID 42621081 · PMCID PMC13486768 · OpenAlex W7202149450
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: epilepsy (population), systems (subfield)
Methods: Spectral & time-frequency, Preprocessing, Connectivity, Statistics, Smoothing, state filtering, decompositions, Machine learning
Keywords: seizure prediction, partial directed coherence, directed graph neural networks, epileptogenic network characterization, explainable artificial intelligence
Topic: Functional Brain Connectivity Studies (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: Natural Science Foundation of Jiangxi Province (20242BAB25470); Jiangxi Provincial Health Commission Science and Technology (202210372, 202406820104, 202308360151); China Scholarship Council as exchange scholars
Citations: not cited yet (Europe PMC); 82 references in the paper
Research resources: EEGLAB RRID:SCR_007292, BrainNet Viewer RRID:SCR_009446

Abstract

While electroencephalography (EEG) analyses using undirected connectivity are well-established for seizure prediction and epileptogenic zone (EZ) network characterization, the complementary value of directed connectivity in graph neural networks (GNNs) remains unclear. We integrated partial directed coherence (PDC) graphs into a Digraph Inception Convolutional Network (DiGCN) to preserve directional edge information for seizure prediction, achieving accuracies of 96.11 ± 0.76%, 96.32 ± 0.70%, and 97.69 ± 0.67% on CHB-MIT, Siena, and the institutional cohort, respectively. In the institutional cohort, preictal modularity and small-world index were both significantly elevated (p < 0.001), reflecting increased modular segregation and topological reorganization. PDC in-degree was significantly elevated at EZ-concordant electrodes across five epilepsy subtypes (p < 0.05), whereas out-degree changes were not statistically significant. GNNExplainer identified compact, prediction-relevant subgraphs preserving these directed connectivity patterns. PDC-DiGCN provides an interpretable sensor-level framework for seizure prediction and EZ-concordant network characterization, though requiring larger prospective validation.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above, with 13 matches between paragraphs and lines of code.

chenshuozhao/PDC-DiGCN-Seizure-Prediction

License: none: the authors keep all their rights
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: f9af2554c7bc02db9f6457f2ab40ac61c591fb42, 25 February 2026
Languages: Python (14)
Size: 14 files, 14 scripts
Software Heritage: not archived
Found in: “Data and code availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: PyTorch (10 files), NumPy (8 files), h5py (4 files), scikit-learn (4 files)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
14 files
At the source: github.com/chenshuozhao/PDC-DiGCN-Seizure-Prediction

The paper's code and data availability statement is in the Data section.

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  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
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Data

Datasets cited

Data and code availability

• This paper analyzes existing, publicly available datasets. The CHB-MIT Scalp EEG Database is available at PhysioNet (https://physionet.org/content/chbmit/1.0.0/), and the Siena Scalp EEG Database is available at PhysioNet (https://physionet.org/content/siena-scalp-eeg/1.0.0/). • The institutional cohort EEG data reported in this paper cannot be publicly deposited because of patient privacy, institutional data-sharing policies, and ethics restrictions. De-identified data are available from the lead contact upon reasonable request, subject to institutional approval and applicable data-sharing regulations. • The original code implementing the PDC-DiGCN framework is publicly available at GitHub (https://github.com/chenshuozhao/PDC-DiGCN-Seizure-Prediction). • Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

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Versions

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Recorded: type, language, journal, volume, issue, pages, dates, 5 authors, 5 keywords, 3 funders, 80 references, 2 RRIDs.

Cite

This paper

Zhao, C., Huang, H., Fang, C., Zhang, H., & Zheng, S. (2026). Directed graph neural networks with partial directed coherence for seizure prediction and epileptogenic network characterization. iScience, 29(8), 117068. https://doi.org/10.1016/j.isci.2026.117068

BibTeX

@article{zhao2026directed,
author = {Zhao, Chenshuo and Huang, Hui and Fang, Chao and Zhang, Hong and Zheng, Suyue},
title = {{Directed graph neural networks with partial directed coherence for seizure prediction and epileptogenic network characterization}},
journal = {iScience},
year = {2026},
month = aug,
volume = {29},
number = {8},
pages = {117068},
publisher = {Elsevier},
issn = {2589-0042},
doi = {10.1016/j.isci.2026.117068},
url = {https://doi.org/10.1016/j.isci.2026.117068},
pmid = {42621081},
pmcid = {PMC13486768}
}

RIS

TY - JOUR
AU - Zhao, Chenshuo
AU - Huang, Hui
AU - Fang, Chao
AU - Zhang, Hong
AU - Zheng, Suyue
TI - Directed graph neural networks with partial directed coherence for seizure prediction and epileptogenic network characterization
T2 - iScience
J2 - iScience
PY - 2026
DA - 2026/08/10
VL - 29
IS - 8
SP - 117068
SN - 2589-0042
PB - Elsevier
DO - 10.1016/j.isci.2026.117068
UR - https://doi.org/10.1016/j.isci.2026.117068
LA - en
ER -

CSL-JSON

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[5] doi:10.3390/e28060599
Large-Scale Synchronization Dynamics During Epileptic Seizures: A Patient-Independent EEG Network Analysis.
Journal: Entropy (Basel, Switzerland)
In common: DOI 10.13026/c2k01r, physionet.org/content/chbmit, epilepsy, 1 reference
[6] doi:10.3390/s26175623
MF-TopoNet: A Multi-Frequency Topological Neural Network for Epileptic Seizure Prediction.
Journal: Sensors (Basel, Switzerland)
In common: physionet.org/content/siena-scalp-eeg, physionet.org/content/chbmit, epilepsy
[7] doi:10.1016/j.mex.2026.103929 [code]
MCLF: Montage consistent CNN-Liquid fusion for long-term scalp EEG seizure detection.
Journal: MethodsX
In common: PyTorch, scikit-learn, NumPy, physionet.org/content/chbmit, epilepsy
[8] doi:10.1186/s40708-026-00300-6 [code]
Anatomical-connectivity-guided functional connectivity reveals task-relevant pathways during proactive task-switching via recurrent graph neural networks.
Journal: Brain informatics
In common: NumPy, 4 references
[9] doi:10.1088/1741-2552/ae5fd7 [code]
Metric validation for detection of delayed and directed coupling.
Journal: Journal of neural engineering
In common: h5py, scikit-learn, NumPy, 3 references
[10] doi:10.1038/s41598-026-47627-y [code]
QuantumNeuroXAI: a quantum-inspired deep learning framework with explainability for brain signal analysis and neurological disorder detection.
Journal: Scientific reports
In common: PyTorch, scikit-learn, NumPy, physionet.org/content/chbmit

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