Graph-Radiomic Learning (GrRAiL)

• Graph-Radiomic Learning (GrRAiL) is a framework that constructs graph representations from voxel-level radiomic maps to capture spatial heterogeneity in lesions.
• It employs both descriptor-based clustering and GNN pipelines to quantify spatial associations using metrics like modularity, clustering, and efficiency.
• Empirical results show GrRAiL improves classification accuracy in distinguishing tumor recurrence and high-risk lesions compared to conventional radiomics.

Searching arXiv for the cited GrRAiL and related graph-radiomics papers to ground the article in current literature. Graph-Radiomic Learning (GrRAiL) denotes a family of graph-based medical imaging methods in which radiomic information is represented, organized, or quantified through graph structure, rather than only through region-level aggregation. In the most specific usage, GrRAiL refers to a descriptor for characterizing intralesional heterogeneity (ILH) on clinical MRI scans by identifying clusters of sub-regions using per-voxel radiomic measurements and then computing graph-theoretic metrics that quantify spatial associations among those clusters (Battalapalli et al., 23 Sep 2025). More broadly, the term has also been used for graph neural network (GNN) pipelines in which radiomic features are encoded as node attributes in spatial or similarity graphs, especially in digital pathology and related image analysis settings (Monroy et al., 2023).

1. Conceptual scope and rationale

GrRAiL emerges from a limitation of conventional radiomics: many radiomics pipelines aggregate feature values across the region of interest (ROI) and thereby lose spatial context regarding how heterogeneity is organized within a lesion. The GrRAiL descriptor was introduced to address this problem by constructing weighted graphs that capture both per-voxel radiomic patterns and higher-order spatial interactions within the ROI, with the explicit goal of disambiguating confounding pathologies from malignancy on routine imaging (Battalapalli et al., 23 Sep 2025).

Within this literature, two related formulations are visible. One is a descriptor-centric formulation, in which voxelwise radiomic maps are clustered into sub-regions and summarized by graph-theoretic features. The other is a node-centric GNN formulation, in which radiomic descriptors become node attributes and graph connectivity encodes spatial adjacency or feature similarity. In histopathology, for example, segmented cells are treated as graph nodes and either radiomic descriptors or gene expression profiles are used as node features, with radiomic features—particularly when combined with UMAP—reported to significantly enhance classification performance for melanoma cell classification (Monroy et al., 2023).

A common misconception is that GrRAiL is synonymous with applying a GNN to medical images. The cited work supports a narrower interpretation. In the descriptor paper, the central object is not a neural network but a 195-dimensional vector formed from graph metrics computed on clustered radiomic maps, and this handcrafted graph descriptor outperformed several GNN baselines in the reported tasks (Battalapalli et al., 23 Sep 2025). This suggests that GrRAiL is better understood as a graph-radiomic representation framework whose implementation may be descriptor-based or neural.

2. Descriptor construction for intralesional heterogeneity

The GrRAiL descriptor introduced for MRI-based lesion characterization follows a staged workflow. First, for each subject ROI, 13 Gray-Level Co-occurrence Matrix (GLCM) feature maps are computed at every voxel: energy, entropy, contrast, correlation, homogeneity, sum average, sum variance, sum entropy, difference entropy, difference average, difference variance, information measure of correlation 1 (ICM1), and 2 (ICM2) (Battalapalli et al., 23 Sep 2025). This is performed in 3D, often with a $3 \times 3 \times 3$ sliding window.

Let $I=(K,f)$ denote a radiomic feature map, where $K$ is a set of spatial voxels and $f(k)$ is the radiomic value at voxel $k$. Each feature map is then clustered using a Gaussian Mixture Model (GMM) in radiomic value space. The number of clusters, denoted $u$, is automatically selected via the Bayesian Information Criterion (BIC), typically 1–5. For each voxel, the posterior probability of cluster membership is

$$P(u \mid x_k) = \frac{\pi_u \mathcal{N}(x_k \mid \mu_u, \Sigma_u)} {\sum_{i=1}^M \pi_i \mathcal{N}(x_k \mid \mu_i, \Sigma_i)}.$$

The clustering yields, for each feature map, a clustered map $\hat{I}=(K,g)$ in which $g(k)$ is the mean feature value of voxel $k$’s cluster. This step is central because it transforms voxelwise radiomic variation into a set of radiomically coherent sub-regions.

The graph construction stage represents each cluster by its centroid, defined as the center of mass of that cluster’s voxels in 3D space:

$I=(K,f)$0

Edges between node pairs are assigned weights using the Earth Mover’s Distance (EMD) between centroid distributions:

$I=(K,f)$1

The resulting graph $I=(K,f)$2 is a weighted region adjacency graph intended to encode higher-order spatial relationships among radiomically distinct sub-regions (Battalapalli et al., 23 Sep 2025).

3. Graph-theoretic quantification and the GrRAiL feature vector

For each clustered GLCM radiomic map, 15 global graph metrics are computed: Size, Density, Diameter, Avg. Shortest Path, Clustering Coefficient, Modularity, Small-worldness, Connected Components, Assortativity, Radius, Global Efficiency, Network Entropy, Number of Hubs, Randomness Value, and Network Resilience (Battalapalli et al., 23 Sep 2025). The GrRAiL descriptor for a subject is formed by concatenating these graph measurements across all 13 GLCM maps, yielding a 195-dimensional vector.

The graph metrics were introduced as a quantitative surrogate for ILH. In this formulation, lesion heterogeneity is not reduced to first-order summary statistics but is represented through network topology: community structure, path-length organization, degree correlation, connectedness, and resilience. The paper further reports that feature selection, such as Recursive Feature Elimination, is applied to reduce redundancy among the 195 GrRAiL features, and that Random Forest classifiers are trained to separate confounding pathologies using these graph-based features. SHAP (SHapley Additive exPlanations) is used for feature importance analysis (Battalapalli et al., 23 Sep 2025).

This design is significant because it treats radiomics as a generator of spatially organized phenotypes rather than as a final feature space. A plausible implication is that GrRAiL shifts the representational burden from “what values occur in the lesion” to “how radiomically defined sub-regions are arranged and related.” That distinction underlies the claimed capacity of the method to characterize confounding tumor pathologies.

4. Cell-level graph-radiomic learning in histopathology

A different but closely related line of work uses radiomic descriptors directly as node attributes in cell graphs. In melanoma classification using MELC pathology data, the workflow consists of cell segmentation via Cellpose, feature extraction from each segmented cell, dimensionality reduction, graph construction, and node classification with a GNN (Monroy et al., 2023). The extracted radiomic features include first-order intensity statistics, shape-based descriptors, and complex texture features, notably via GLCM and GLRLM matrices. Gene expression profiles are also considered, but the comparative design trains the GNN with either gene expression profiles or radiomic descriptors as node features rather than concatenating them.

In this setting, individual cells are nodes, and edges encode neighborhood relationships based on spatial proximity or feature similarity. UMAP is applied as a dimensionality reduction technique after feature extraction and before graph encoding. The reported finding is that radiomic features, particularly when combined with UMAP, significantly enhance classification performance and computational efficiency relative to gene expression profiles, and that the best performance is observed when integrating radiomic features, UMAP for dimension reduction, and spatial adjacency for edges (Monroy et al., 2023).

The GNN architecture used is GRAND (Graph Random Neural Network), which decouples feature propagation from transformation and adds stochastic regularization. Typical graphs used for training contain approximately 2,080 cells, with the full training graph comprising 40,500 nodes and 202,500 edges. Non-graph machine learning baselines, including XGBoost and Random Forest, are also reported (Monroy et al., 2023).

This cell-level formulation broadens the meaning of GrRAiL. Here, “radiomics” does not operate at lesion scale but at single-cell scale, and “graph” refers to tissue architecture or phenotypic neighborhood structure. The result is a graph-radiomic model of microanatomical context rather than a whole-lesion heterogeneity descriptor.

5. Relation to learned graph construction in medical diagnosis

Graph-radiomic learning depends not only on radiomic features but also on how graphs are built. In disease prediction with Graph Convolutional Networks (GCNs), a key issue is that population graphs have often been constructed with manually defined patient similarity metrics based on meta-features such as demographics or clinical scores. The paper on latent-graph learning addresses this problem by introducing an end-to-end trainable graph learning module that constructs an optimal population graph directly from patient features, rather than relying on hand-crafted similarity measures (Cosmo et al., 2020).

In that architecture, each patient feature vector $I=(K,f)$3 is mapped into a lower-dimensional Euclidean space using an MLP with parameters $I=(K,f)$4,

$I=(K,f)$5

and edge weights are then computed with a sigmoidal, soft-thresholded distance function,

$I=(K,f)$6

The resulting adjacency matrix is weighted and fully differentiable, enabling end-to-end backpropagation through graph structure. The downstream GCN is spatial rather than spectral, with update

$I=(K,f)$7

Unlike commonly employed spectral GCN approaches, this GCN is spatial and inductive, and can thus infer previously unseen patients as well (Cosmo et al., 2020).

Although this work is not framed as GrRAiL, it is methodologically adjacent. It shows that graph construction itself can be learned toward the downstream task of disease classification. This suggests a complementary direction for GrRAiL: combining radiomic feature design with learned graph topology rather than treating graph structure as fixed.

6. Reported applications and empirical results

The GrRAiL descriptor has been evaluated in three multi-institutional clinical use cases spanning n=947 subjects: differentiating tumor recurrence from radiation effects in glioblastoma (GBM; n=106), differentiating recurrence from radiation necrosis in brain metastasis (n=233), and stratifying pancreatic intraductal papillary mucinous neoplasms (IPMNs) into no+low vs high risk (n=608) (Battalapalli et al., 23 Sep 2025). The paper reports that GrRAiL consistently outperformed state-of-the-art baselines, including Graph Neural Networks (GNNs), textural radiomics, and intensity-graph analysis.

Task	Cohort	Reported GrRAiL performance
GBM: TuR vs PsP	n=106	CV 89% ± 7%; test 78%
Mets: TuR vs RN	n=233 studies (332 lesions)	CV 84% ± 6%; test 74%
IPMN: Hi vs Lo/No risk	n=608	CV 85% ± 4.5%; test 79%

The reported comparator results further sharpen the distinction between descriptor-based GrRAiL and end-to-end graph classifiers. In GBM, the best GNN test accuracy was 74% using GraphSAGE, while the best radiomic test accuracy was 69% and the best intensity-graph accuracy was 59%. In brain metastasis, the best GNN test accuracy was 73% using GCN-JK, versus 61% for radiomics and 55% for intensity-graph analysis. In IPMN risk stratification, the best GNN test accuracy was 73%, compared with 71% for radiomics and 61% for intensity-graph analysis (Battalapalli et al., 23 Sep 2025).

In histopathology, the melanoma study reports that radiomic features, especially when combined with UMAP, consistently outperform gene expression profiles for cell classification tasks, and that graphs based on spatial proximity yield better results than those based solely on feature similarity (Monroy et al., 2023). It also emphasizes computational efficiency, arguing that radiomics allows extraction of critical data from fewer stains, thereby reducing operational costs.

A separate MRI study proposes radiomic feature-based keypoint detection for enhancing graph applications. Its abstract states that the anatomical significance of the detected keypoints was demonstrated by improving registration processes guided by these keypoints, that these keypoints were subsequently employed as the ground truth for LK-SuperRetina, and that GNNs in image matching showed superior performance in terms of both the number of good matches and confidence scores (Nasser et al., 2023). This is not a GrRAiL descriptor in the narrow sense, but it extends the graph-radiomic idea into registration and matching.

7. Interpretability, misconceptions, and adjacent directions

Interpretability is a recurrent theme in GrRAiL-related work. In the descriptor paper, SHAP analysis highlighted that graph features such as assortativity, modularity, path length, diameter, and clustering coefficient were differentially expressed between confounding and malignant pathologies (Battalapalli et al., 23 Sep 2025). The same study reports a qualitative pattern: PsP, RN, and low-risk lesions had graphs that were smaller and more homogeneous, whereas true tumor recurrence or high-risk lesions formed larger, more complex, and less modular graphs. In the latent-graph learning paper, learned adjacency structures were visualized and shown to correlate with human- or domain-expert constructions, while still yielding improved classification performance (Cosmo et al., 2020).

These findings address another misconception: that graph-radiomic methods are necessarily less interpretable than standard radiomics because they introduce more complex structure. The reported literature argues the opposite in some settings. Graph features such as modularity, clustering, hubness, density, or efficiency provide explicit structural quantities, and the learned or constructed graphs themselves can be visualized.

At the same time, the literature does not converge on a single implementation strategy. One branch favors handcrafted global graph metrics derived from clustered radiomic maps (Battalapalli et al., 23 Sep 2025); another uses GNNs with radiomic node attributes and spatial graphs (Monroy et al., 2023); another learns graph topology end-to-end for disease prediction (Cosmo et al., 2020). A plausible implication is that “GrRAiL” is best regarded as a representational principle rather than a single algorithm.

Adjacent developments reinforce that interpretation. A 2025 study on latent graph representation (LGR) for structure-preserving medical image generation learns a graph representation that captures the intrinsic structure of X-ray images, reconstructs images from the LGR using a GCN, and reports performance increases of up to $I=(K,f)$8 for classification and $I=(K,f)$9 for segmentation (Arias et al., 21 Aug 2025). While that work is not radiomics-based, it indicates that graph-centric image representations can support synthesis, classification, and segmentation in ways that preserve anatomical structure. This suggests a possible convergence between radiomic graph descriptors, learned graph construction, and latent graph generative modeling in future medical imaging research.