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SPIDER: spatially integrated denoising via embedding regularization with single cell supervision.

Code ↔ Paper

7 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 7 matches
  1. [1] § 2 Methods › 2.2 Overview of the SPIDER framework ↔ SPIDER-main.zip/SPIDER/model.py, lines 62–86 · score 0.77 · zero inflation probability, Zero Inflated Negative, dispersion, Binomial, ZINB, loss
  2. [2] § 3 Experiments and results › 3.2 SPIDER generates denoised ST expression for accurate clustering ↔ SPIDER-main.zip/train.py, lines 10–55 · score 0.72 · Homogeneity Score, Adjusted Rand, Normalized Mutual, PCA, mclust, ARI
  3. [3] § 3 Experiments and results › 3.2 SPIDER generates denoised ST expression for accurate clustering ↔ SPIDER-main.zip/tutorial.ipynb, lines 38–42 · score 0.68 · Homogeneity Score, Adjusted Rand, Normalized Mutual, mclust, ARI, HS
  4. [4] § 2 Methods › 2.4 Modeling and training › 2.4.2 Training › 2.4.3 Gene expression reconstruction ↔ SPIDER-main.zip/SPIDER/model.py, lines 62–86 · score 0.60 · zero inflation probability, dispersion, ZINB, predict, model, loss
  5. [5] § 2 Methods › 2.2 Overview of the SPIDER framework ↔ SPIDER-main.zip/SPIDER/trainer.py, lines 39–170 · score 0.60 · cross entropy loss, predict, ratios, MMD, trained, graphs
  6. [6] § 2 Methods › 2.4 Modeling and training › 2.4.2 Training › 2.4.6 Overall objective function ↔ SPIDER-main.zip/SPIDER/trainer.py, lines 39–170 · score 0.59 · gradient clipping, Adam, weighting, optimized, loss, Model
  7. [7] § 2 Methods › 2.2 Overview of the SPIDER framework ↔ SPIDER-main.zip/SPIDER/utils.py, lines 167–220 · score 0.53 · nearest neighbors, spatial graph, distance, spot

Paper

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The authors' code

Python · 300 lines · 12 KB · CC-BY-4.0 · 2 matches

  1. import numpy as np, random
  2. from tqdm import tqdm
  3. import torch
  4. import torch.nn.functional as F
  5. import torch.nn as nn
  6. import random
  7. from typing import Union, Tuple, Optional
  8. from torch_geometric.typing import (OptPairTensor, Adj, Size, NoneType,
  9. OptTensor)
  11. from torch import Tensor
  12. from torch.nn import Parameter
  13. from torch_sparse import SparseTensor, set_diag
  14. from torch_geometric.nn.dense.linear import Linear
  15. from torch_geometric.nn.conv import MessagePassing
  16. from torch_geometric.utils import remove_self_loops, add_self_loops, softmax
  19. def mean_act(x):
  20. return torch.clamp(torch.exp(x), 1e-5, 1e6)
  21. def disp_act(x):
  22. return torch.clamp(F.softplus(x), 1e-4, 1e4)
  23. def pi_act(x):
  24. return torch.sigmoid(x)
  26. class RBF(nn.Module):
  28. def __init__(self, n_kernels=5, mul_factor=2.0, bandwidth=None, device='cuda:0'):
  29. super().__init__()
  30. self.device = device
  31. self.bandwidth_multipliers = mul_factor ** (torch.arange(n_kernels, device=self.device) - n_kernels // 2)
  32. self.bandwidth = bandwidth
  34. def get_bandwidth(self, L2_distances):
  35. if self.bandwidth is None:
  36. n_samples = L2_distances.shape[0]
  37. return L2_distances.sum() / (n_samples ** 2 - n_samples)
  38. return self.bandwidth
  40. def forward(self, X):
  41. X = X.to(self.device)
  42. L2_distances = torch.cdist(X, X) ** 2
  43. bw = self.get_bandwidth(L2_distances)
  44. bw = torch.tensor(bw, device=self.device) if not isinstance(bw, torch.Tensor) else bw.to(self.device)
  45. K = torch.exp(-L2_distances[None, ...] / (bw * self.bandwidth_multipliers)[:, None, None])
  46. return K.sum(dim=0)
  47. class MMDLoss(nn.Module):
  48. def __init__(self, kernel=None, device='cuda:0'):
  49. super().__init__()
  50. self.device = device
  51. self.kernel = kernel if kernel is not None else RBF(device=self.device)
  52. def forward(self, X, Y):
  53. X = X.to(self.device)
  54. Y = Y.to(self.device)
  55. K = self.kernel(torch.vstack([X, Y]))
  56. X_size = X.shape[0]
  57. XX = K[:X_size, :X_size].mean()
  58. XY = K[:X_size, X_size:].mean()
  59. YY = K[X_size:, X_size:].mean()
  60. return XX - 2 * XY + YY
  62. def ZINB_loss(y_true, mean, disp, pi, device):
  63. """
  64. Computes the Zero-Inflated Negative Binomial (ZINB) loss.
  66. Args:
  67. y_true (torch.Tensor): Ground truth tensor.
  68. mean (torch.Tensor): Predicted mean tensor.
  69. disp (torch.Tensor): Predicted dispersion tensor.
  70. pi (torch.Tensor): Predicted zero-inflation probability tensor.
  71. device (torch.device): Device to perform the computation on.
  73. Returns:
  74. torch.Tensor: Computed ZINB loss.
  75. """
  76. eps = 1e-10
  77. r = torch.minimum(disp, torch.tensor(1e6, device=device))
  78. t1 = torch.lgamma(r + eps) + torch.lgamma(y_true + 1.0) - torch.lgamma(y_true + r + eps)
  79. t2 = (r + y_true) * torch.log(1.0 + (mean / (r + eps))) + (y_true * (torch.log(r + eps) - torch.log(mean + eps)))
  81. NB = t1 + t2 - torch.log(1 - pi + eps)
  83. z1 = torch.pow(r / (mean + r + eps), r)
  84. zero_inf = -torch.log(pi + (1 - pi) * z1 + eps)
  86. return torch.mean(torch.where(y_true < 1e-8, zero_inf, NB))
  88. class GATConv(MessagePassing):
  89. r"""The graph attentional operator from the `"Graph Attention Networks"
  90. <https://arxiv.org/abs/1710.10903>`_ paper
  93. Args:
  94. in_channels (int or tuple): Size of each input sample, or :obj:`-1` to
  95. derive the size from the first input(s) to the forward method.
  96. A tuple corresponds to the sizes of source and target
  97. dimensionalities.
  98. out_channels (int): Size of each output sample.
  99. heads (int, optional): Number of multi-head-attentions.
  100. (default: :obj:`1`)
  101. concat (bool, optional): If set to :obj:`False`, the multi-head
  102. attentions are averaged instead of concatenated.
  103. (default: :obj:`True`)
  104. negative_slope (float, optional): LeakyReLU angle of the negative
  105. slope. (default: :obj:`0.2`)
  106. dropout (float, optional): Dropout probability of the normalized
  107. attention coefficients which exposes each node to a stochastically
  108. sampled neighborhood during training. (default: :obj:`0`)
  109. add_self_loops (bool, optional): If set to :obj:`False`, will not add
  110. self-loops to the input graph. (default: :obj:`True`)
  111. bias (bool, optional): If set to :obj:`False`, the layer will not learn
  112. an additive bias. (default: :obj:`True`)
  113. **kwargs (optional): Additional arguments of
  114. :class:`torch_geometric.nn.conv.MessagePassing`.
  115. """
  116. _alpha: OptTensor
  118. def __init__(self, in_channels: Union[int, Tuple[int, int]],
  119. out_channels: int, heads: int = 1, concat: bool = True,
  120. negative_slope: float = 0.2, dropout: float = 0.0,
  121. add_self_loops: bool = True, bias: bool = True, **kwargs):
  122. kwargs.setdefault('aggr', 'add')
  123. super(GATConv, self).__init__(node_dim=0, **kwargs)
  125. self.in_channels = in_channels
  126. self.out_channels = out_channels
  127. self.heads = heads
  128. self.concat = concat
  129. self.negative_slope = negative_slope
  130. self.dropout = dropout
  131. self.add_self_loops = add_self_loops
  134. self.lin_src = nn.Parameter(torch.zeros(size=(in_channels, out_channels)))
  135. nn.init.xavier_normal_(self.lin_src.data, gain=1.414)
  136. self.lin_dst = self.lin_src
  138. self.att_src = Parameter(torch.Tensor(1, heads, out_channels))
  139. self.att_dst = Parameter(torch.Tensor(1, heads, out_channels))
  140. nn.init.xavier_normal_(self.att_src.data, gain=1.414)
  141. nn.init.xavier_normal_(self.att_dst.data, gain=1.414)
  144. self._alpha = None
  145. self.attentions = None
  147. def forward(self, x: Union[Tensor, OptPairTensor], edge_index: Adj,
  148. size: Size = None, return_attention_weights=None, attention=True, tied_attention = None):
  149. r"""
  150. Args:
  151. return_attention_weights (bool, optional): If set to :obj:`True`,
  152. will additionally return the tuple
  153. :obj:`(edge_index, attention_weights)`, holding the computed
  154. attention weights for each edge. (default: :obj:`None`)
  155. """
  156. H, C = self.heads, self.out_channels
  158. if isinstance(x, Tensor):
  159. assert x.dim() == 2, "Static graphs not supported in 'GATConv'"
  160. x_src = x_dst = torch.mm(x, self.lin_src).view(-1, H, C)
  161. else:
  162. x_src, x_dst = x
  163. assert x_src.dim() == 2, "Static graphs not supported in 'GATConv'"
  164. x_src = self.lin_src(x_src).view(-1, H, C)
  165. if x_dst is not None:
  166. x_dst = self.lin_dst(x_dst).view(-1, H, C)
  168. x = (x_src, x_dst)
  170. if not attention:
  171. return x[0].mean(dim=1)
  173. if tied_attention == None:
  174. alpha_src = (x_src * self.att_src).sum(dim=-1)
  175. alpha_dst = None if x_dst is None else (x_dst * self.att_dst).sum(-1)
  176. alpha = (alpha_src, alpha_dst)
  177. self.attentions = alpha
  178. else:
  179. alpha = tied_attention
  182. if self.add_self_loops:
  183. if isinstance(edge_index, Tensor):
  184. num_nodes = x_src.size(0)
  185. if x_dst is not None:
  186. num_nodes = min(num_nodes, x_dst.size(0))
  187. num_nodes = min(size) if size is not None else num_nodes
  188. edge_index, _ = remove_self_loops(edge_index)
  189. edge_index, _ = add_self_loops(edge_index, num_nodes=num_nodes)
  190. elif isinstance(edge_index, SparseTensor):
  191. edge_index = set_diag(edge_index)
  193. out = self.propagate(edge_index, x=x, alpha=alpha, size=size)
  195. alpha = self._alpha
  196. assert alpha is not None
  197. self._alpha = None
  199. if self.concat:
  200. out = out.view(-1, self.heads * self.out_channels)
  201. else:
  202. out = out.mean(dim=1)
  204. if isinstance(return_attention_weights, bool):
  205. if isinstance(edge_index, Tensor):
  206. return out, (edge_index, alpha)
  207. elif isinstance(edge_index, SparseTensor):
  208. return out, edge_index.set_value(alpha, layout='coo')
  209. else:
  210. return out
  212. def message(self, x_j: Tensor, alpha_j: Tensor, alpha_i: OptTensor,
  213. index: Tensor, ptr: OptTensor,
  214. size_i: Optional[int]) -> Tensor:
  215. alpha = alpha_j if alpha_i is None else alpha_j + alpha_i
  217. alpha = torch.sigmoid(alpha)
  218. alpha = softmax(alpha, index, ptr, size_i)
  219. self._alpha = alpha
  220. alpha = F.dropout(alpha, p=self.dropout, training=self.training)
  221. return x_j * alpha.unsqueeze(-1)
  223. def __repr__(self):
  224. return '{}({}, {}, heads={})'.format(self.__class__.__name__,
  225. self.in_channels,
  226. self.out_channels, self.heads)
  230. class SPIDER(nn.Module):
  231. """
  232. SPIDER: SPIDER: Spatially Integrated Denoising via Embedding Regularization with Single-Cell Supervision
  234. Args:
  235. hidden_dims (list): List of dimensions for input, hidden, and output layers.
  236. """
  237. def __init__(self, hidden_dims,num_classes,alpha=1.5):
  238. super(SPIDER, self).__init__()
  239. [in_dim, num_hidden, out_dim] = hidden_dims
  240. self.conv1 = GATConv(in_dim, num_hidden, heads=1, concat=False,
  241. dropout=0, add_self_loops=False, bias=False)
  242. self.conv2 = GATConv(num_hidden, out_dim, heads=1, concat=False,
  243. dropout=0, add_self_loops=False, bias=False)
  244. self.conv3 = GATConv(out_dim*2, num_hidden, heads=1, concat=False,
  245. dropout=0, add_self_loops=False, bias=False)
  246. self.disp = GATConv(num_hidden, in_dim, heads=1, concat=False,
  247. dropout=0, add_self_loops=False, bias=False)
  248. self.mean = GATConv(num_hidden, in_dim, heads=1, concat=False,
  249. dropout=0, add_self_loops=False, bias=False)
  250. self.pi = GATConv(num_hidden, in_dim, heads=1, concat=False,
  251. dropout=0, add_self_loops=False, bias=False)
  252. self.alpha = alpha
  254. self.conv_gene_psd1 = GATConv(in_dim, num_hidden, heads=1, concat=False,
  255. dropout=0, add_self_loops=False, bias=False)
  256. self.conv_gene_psd2 = GATConv(num_hidden, out_dim, heads=1, concat=False,
  257. dropout=0, add_self_loops=False, bias=False)
  259. self.conv_gene_std1 = GATConv(in_dim, num_hidden, heads=1, concat=False,
  260. dropout=0, add_self_loops=False, bias=False)
  261. self.conv_gene_std2 = GATConv(num_hidden, out_dim, heads=1, concat=False,
  262. dropout=0, add_self_loops=False, bias=False)
  264. self.conv_gene3 = GATConv(out_dim, num_hidden, heads=1, concat=False,
  265. dropout=0, add_self_loops=False, bias=False)
  266. self.disp_gene = GATConv(num_hidden, in_dim, heads=1, concat=False,
  267. dropout=0, add_self_loops=False, bias=False)
  268. self.mean_gene = GATConv(num_hidden, in_dim, heads=1, concat=False,
  269. dropout=0, add_self_loops=False, bias=False)
  270. self.pi_gene = GATConv(num_hidden, in_dim, heads=1, concat=False,
  271. dropout=0, add_self_loops=False, bias=False)
  273. self.mlp_classifier = nn.Sequential(
  274. nn.Linear(hidden_dims[-1], num_classes),
  275. nn.Softmax(dim=1)
  276. )
  277. def forward(self, features, featpsd, edge_index, edge_index_std, edge_index_psd, scale_factor):
  278. h1 = F.elu(self.conv1(features, edge_index))
  279. h2 = self.conv2(h1, edge_index)
  281. p1 = F.elu(self.conv_gene_psd1(featpsd, edge_index_psd))
  282. p2 = self.conv_gene_psd2(p1, edge_index_psd)
  283. cell_type_ratio = self.mlp_classifier(p2)
  285. s1 = F.elu(self.conv_gene_std1(features, edge_index_std))
  286. s2 = self.conv_gene_std2(s1, edge_index_std)
  288. h2s2 = torch.cat([h2,s2],dim=1)
  289. h3 = F.elu(self.conv3(h2s2, edge_index, attention=True,
  290. tied_attention=self.conv1.attentions))
  292. pi = pi_act(self.pi(h3, edge_index))
  293. disp = disp_act(self.disp(h3, edge_index))
  294. mean = mean_act(self.mean(h3, edge_index))
  295. mean = (mean.T * scale_factor).T
  297. return mean, disp, pi, h2, s2, p2, h2s2, cell_type_ratio

model.py, under CC-BY-4.0 · at the source

Overview

Authors: Md Istiaq Ansari1, Muhtasim Noor Alif1, Wei Zhang1
ORCID iDs: Wei Zhang
  1. Department of Computer Science, University of Central Florida, Orlando, FL 32816, United States
Institutions: University of Central Florida (United States)
Journal: Bioinformatics (Oxford, England), volume 42, issue Suppl 2, article btag430
Dates: published online 21 August 2026; in print August 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1093/bioinformatics/btag430 · PMID 42635216 · PMCID PMC13501285 · OpenAlex W7164005801
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: genetics / omics (modality), human (organism)
Methods: Spectral & time-frequency, Machine learning, Physiology & signal measures
MeSH: RNA-Seq*, Software*, Algorithms, Humans, Single-Cell Gene Expression Analysis, Spatial Transcriptomics (* major topic)
Journal subjects: Transcriptomics
Topic: Single-cell and spatial transcriptomics (Molecular Biology, Biochemistry, Genetics and Molecular Biology), according to OpenAlex
Funding: National Science Foundation (NSF-III2246796, NSF-III2152030)
Citations: not cited yet (Europe PMC); 24 references in the paper

Abstract

Motivation: Spatial transcriptomics (ST) technologies profile gene expression while preserving tissue architecture, enabling the study of spatial cellular organization and microenvironmental interactions. However, raw ST data are heavily affected by technical noise, sparsity, and dropout events, which obscure true biological signals and hinder downstream analyses. While recent denoising methods incorporate spatial neighborhood information, they lack explicit supervision due to missing cell-type annotations in ST data. To address this challenge, we introduce SPIDER, a semi-supervised framework that leverages independently generated, annotated single-cell RNA-seq (scRNA-seq) references to guide ST denoising. SPIDER synthesizes pseudo-ST data from scRNA-seq to inject cell-type information without requiring paired measurements. The method constructs three graphs capturing spatial proximity, transcriptional similarity in real-ST data, and transcriptional structure in pseudo-ST data. Graph encoders map these representations into a shared latent space, and a domain-alignment module transfers biologically meaningful structure from pseudo-ST to real-ST embeddings. A graph-attention decoder with a zero-inflated negative binomial objective reconstructs denoised ST expression profiles.

Results: We benchmark SPIDER on human dorsolateral prefrontal cortex and breast cancer datasets. SPIDER consistently enhances spatial gene expression patterns, recovers known tissue structures, and achieves superior clustering performance compared to existing approaches. Marker gene analyses demonstrate improved spatial continuity and clearer anatomical organization. By directly producing denoised expression matrices, SPIDER improves both accuracy and interpretability, providing a generalizable solution for robust ST data denoising.

Availability and implementation: The source code and dataset is available at: (https://github.com/compbiolabucf/SPIDER) and archived on Zenodo (https://doi.org/10.5281/zenodo.20613921).

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 7 matches between paragraphs and lines of code.

Zenodo 20613921

License: CC-BY-4.0
State: the link answers, verified on 26 September 2026
Evidence: files inventoried
Size: 2 files
Software Heritage: not checked
Found in: “Data availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: NumPy (6 files), pandas (5 files), PyTorch (4 files), Scanpy (4 files), PyTorch Geometric (3 files), scikit-learn (3 files), Matplotlib (2 files), rpy2 (2 files), SciPy (2 files), anndata (1 file)
Availability: 1 check, the latest on 26 September 2026: the link answers (HTTP 200)
  • 26 September 2026: the link answers (HTTP 200)
11 files
At the source:

Availability and implementation

The source code and dataset is available at: (https://github.com/compbiolabucf/SPIDER) and archived on Zenodo (https://doi.org/10.5281/zenodo.20613921).

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

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 9 scripts, each with its path and the digest of its content;
  • 7 matches between paragraphs of the paper and lines of the code (method lexical-v1);
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Data availability

The data underlying this article are available in Zenodo at DOI: 10.5281/zenodo.20613921. The source code used in this study is available in the SPIDER GitHub repository and is also archived in Zenodo at the same DOI.

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

Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 6 MeSH terms, 1 funder, 19 references.

Cite

This paper

Ansari, M. I., Alif, M. N., & Zhang, W. (2026). SPIDER: spatially integrated denoising via embedding regularization with single cell supervision. Bioinformatics (Oxford, England), 42(Suppl 2), btag430. https://doi.org/10.1093/bioinformatics/btag430

BibTeX

@article{ansari2026spider,
author = {Ansari, Md Istiaq and Alif, Muhtasim Noor and Zhang, Wei},
title = {{SPIDER: spatially integrated denoising via embedding regularization with single cell supervision}},
journal = {Bioinformatics (Oxford, England)},
year = {2026},
month = aug,
volume = {42},
number = {Suppl 2},
pages = {btag430},
publisher = {Oxford University Press},
issn = {1367-4803},
doi = {10.1093/bioinformatics/btag430},
url = {https://doi.org/10.1093/bioinformatics/btag430},
pmid = {42635216},
pmcid = {PMC13501285}
}

RIS

TY - JOUR
AU - Ansari, Md Istiaq
AU - Alif, Muhtasim Noor
AU - Zhang, Wei
TI - SPIDER: spatially integrated denoising via embedding regularization with single cell supervision
T2 - Bioinformatics (Oxford, England)
J2 - Bioinformatics
PY - 2026
DA - 2026/08/01
VL - 42
IS - Suppl 2
SP - btag430
SN - 1367-4803
PB - Oxford University Press
DO - 10.1093/bioinformatics/btag430
UR - https://doi.org/10.1093/bioinformatics/btag430
LA - en
ER -

CSL-JSON

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"PMID": "42635216",
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[5] doi:10.1093/bioinformatics/btag540 [code]
Deciphering spatial heterogeneity by multimodal spatial transcriptomics modelling with SpatialModal.
Journal: Bioinformatics (Oxford, England)
In common: rpy2, PyTorch Geometric, anndata, 7 other tools, genetics / omics, 5 references
[6] doi:10.1371/journal.pcbi.1014346 [code]
StPedf: Cell trajectory inference of spatial transcriptomics via spatial proximity embedding and spatial density-adaptive fusion.
Journal: PLoS computational biology
In common: rpy2, anndata, Scanpy, 6 other tools, genetics / omics, 5 references
[7] doi:10.1016/j.isci.2026.117206 [code]
ReliST: A model-agnostic risk layer for spatial transcriptomics deconvolution.
Journal: iScience
In common: anndata, Scanpy, PyTorch, 5 other tools, genetics / omics, 6 references
[8] doi:10.1093/bib/bbag404 [code]
Navigating cell maps by deep learning integration of single-cell and spatially resolved transcriptomics.
Journal: Briefings in bioinformatics
In common: PyTorch Geometric, anndata, Scanpy, 6 other tools, genetics / omics, 3 references
[9] doi:10.1002/advs.75969 [code]
Accurately Deciphering Tissue Heterogeneity From Spatial Multi-Modal and Multi-Omics With STransformer.
Journal: Advanced science (Weinheim, Baden-Wurttemberg, Germany)
In common: PyTorch Geometric, anndata, Scanpy, 6 other tools, genetics / omics, 3 references
[10] doi:10.1093/bioinformatics/btag578 [code]
NicheDeSig: niche-aware deconvolution and adaptive signature analysis for spatial transcriptomics.
Journal: Bioinformatics (Oxford, England)
In common: anndata, Scanpy, PyTorch, 4 other tools, genetics / omics, 5 references

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