Spatial transcriptomics is a technology that measures gene activity across thousands of locations within a tissue slice simultaneously, preserving information about where each gene is expressed in the tissue rather than averaging it across all cells.
This approach is transforming cancer research because tumors are not molecularly uniform. Identifying which regions of a tumor express which genes helps researchers map cancer architecture, distinguish tumor from stromal tissue, and uncover spatially restricted signals that bulk sequencing would miss.
To analyze spatial transcriptomics data computationally, researchers use deep learning models that convert gene expression and spatial position data into compact numerical summaries called embeddings. These embeddings are then used for tasks such as clustering tissue regions and segmenting tissue architecture.
The quality of these embeddings varies substantially depending on how the model was configured, creating a practical challenge: with no reliable way to evaluate embedding quality before running the analysis, researchers either pick hyperparameters by trial and error or accept inconsistent results across datasets.
Deep learning models used for spatial transcriptomics analysis, such as SpaGCN and RESEPT, generate data representations called embeddings by learning from both gene expression values and the spatial coordinates of each tissue spot. The quality of these embeddings directly determines how accurately tissue architecture is identified.
Graph neural networks (GNNs) are particularly popular for this task because they can model the spatial neighborhood structure of tissue spots, aggregating information from surrounding spots to enrich each embedding with local context. A specific type called the graph convolutional network (GCN) is used in both SpaGCN and RESEPT.
The same deep learning model can produce dozens of different embeddings by varying its hyperparameters, and performance differs widely from one embedding to the next and from one tissue sample to another. Currently, researchers must run the full analysis pipeline with each candidate embedding and compare results manually, which is computationally expensive and impractical for large studies.
The key insight driving this work is that spatial autocorrelation, the degree to which nearby tissue spots have similar embedding values, can serve as a proxy for embedding quality without requiring the full downstream analysis to be run first.
The authors developed a method called MP-MIM (message passing-Moran's I with maximum filtering) that evaluates embedding quality in two stages: first transforming the embedding using message passing to make spatial patterns more explicit, then measuring the spatial coherence of the result using Moran's I.
Message passing is a graph computation technique in which each tissue spot aggregates feature information from neighboring spots. This smoothing operation propagates spatial information through the graph, making long-distance tissue relationships visible in the embedding that short-range methods would miss. The process uses a k-nearest neighbor (KNN) graph built from the spatial coordinates of tissue spots.
Moran's I is a statistical index that measures how strongly neighboring locations share similar values, a property called spatial autocorrelation. A Moran's I value near 1 indicates that similar values cluster together spatially, meaning the embedding reflects genuine biological tissue organization rather than random noise.
MP-MIM takes the maximum Moran's I value across all dimensions of a transformed embedding as its final quality score. The embedding with the highest score is selected for downstream clustering or segmentation. This maximum filtering step is key because different embedding dimensions capture different biological patterns, and the most informative dimension should drive embedding selection.
The method was validated on 16 spatial transcriptomics tissue samples from the human brain, including 12 published samples and four additional samples from postmortem brain tissue at various disease stages, ranging from healthy Braak stage I to early Alzheimer's disease at Braak stage IV.
For each of the 16 brain samples, the team generated 56 different RESEPT embeddings by systematically varying two hyperparameters: the number of latent space dimensions and the weight given to spatial location information. For the SpaGCN model, 36 embeddings were generated across six samples using three varied hyperparameters.
The ground-truth quality of each embedding was determined by running K-means clustering and measuring the Adjusted Rand Index (ARI), which compares the clustering result against expert-labeled ground-truth tissue architecture. The higher the ARI, the more accurately the embedding captures the true tissue organization.
Comparison methods included using raw Moran's I or Geary's C directly on individual embedding dimensions without the message-passing transformation step, allowing a direct test of whether the message-passing enhancement was necessary for accurate quality ranking.
In the top-5 ranking evaluation, MP-MIM correctly identified high-quality embeddings within its top 5 selections on 10 out of 16 samples for the RESEPT model, outperforming the baseline method that used raw Moran's I without message passing. The transformed embeddings also produced clearer, more organized RGB tissue images compared with non-transformed embeddings.
On the Spearman correlation metric, which measures how well the ranking produced by MP-MIM matches the true quality ranking, 13 out of 16 samples showed improvement over the baseline. In most samples, the Spearman correlation exceeded 0.5, indicating a strong and statistically significant agreement with the ground truth. On sample 151671, MP-MIM achieved twice the Spearman correlation of the baseline.
Hyperparameter sensitivity analysis revealed that performance improved consistently as the number of message-passing neighbors (k_num) and layers (l_num) increased, with the best results obtained at k_num = 90 and l_num = 15. This plateau effect confirmed that sufficient information aggregation is critical for accurate embedding evaluation.
Among different filtering strategies, maximum filtering on Moran's I consistently outperformed both minimum and average filtering. The analysis also showed that Moran's I is better suited than Geary's C for measuring spatial autocorrelation quality in this context, performing better on the majority of tested samples.
Integrating MP-MIM into the SpaGCN model improved tissue architecture identification on 9 out of 16 samples compared with the original model using default hyperparameters. The improvement was especially pronounced on samples 151669 and 151673, where the refined embedding substantially clarified the spatial tissue map.
When integrated into the RESEPT model, MP-MIM improved architecture identification on 15 out of 16 samples, with the top-5 ARI values exceeding the baseline median ARI on nearly all samples tested. On three samples (151509, 151670, and 2-5), all five top-ranked embeddings selected by MP-MIM surpassed the baseline.
The only limitation observed was computational cost: each sample required several hours of processing when MP-MIM was integrated into SpaGCN or RESEPT on a desktop machine. The method's scalability depends on the number of cells, genes, and tissue types in the dataset.
A publicly available software tool was released on GitHub, designed for easy integration with existing spatial transcriptomics analysis pipelines. The tool works as a plug-in for methods like SpaGCN that generate embeddings directly during training, as well as for methods like RESEPT that generate multiple embeddings for comparison.
MP-MIM addresses a key bottleneck in spatial transcriptomics analysis by providing an automated, computationally efficient way to select the best deep learning embedding without running the full downstream analysis for every candidate configuration.
The combination of message passing and Moran's I maximum filtering works because message passing reveals the spatial structure embedded in gene expression data, and Moran's I quantifies how much spatial structure is present, creating a reliable signal for quality ranking.
The main limitation is sample dependency: when a dataset contains a high proportion of low-quality embeddings, the statistical signal becomes noisy and ranking accuracy decreases. Expanding the method to larger and more diverse tissue datasets, including cancer tissues, will be important for establishing its generalizability.
In the context of cancer research, the ability to reliably extract high-quality tissue architecture embeddings from spatial transcriptomics data is a prerequisite for mapping tumor heterogeneity, identifying cancer cell subpopulations, and discovering spatially restricted biomarkers that could guide targeted therapy.