Enhanced Spatial Clustering of Single-Molecule Localizations with Graph Neural Networks

Single-molecule localization microscopy generates point clouds corresponding to fluorophore localizations. Spatial cluster identification and analysis of these point clouds are crucial for extracting insights about molecular organization. However, this task becomes challenging in the presence of localization noise, high point density, or complex biological structures. Here, we introduce MIRO (Multifunctional Integration through Relational Optimization), an algorithm that uses recurrent graph neural networks to transform the point clouds in order to improve clustering efficiency when applying conventional clustering techniques. We show that MIRO supports simultaneous processing of clusters of different shapes and at multiple scales, demonstrating improved performance across varied datasets. Our comprehensive evaluation demonstrates MIRO’s transformative potential for single-molecule localization applications, showcasing its capability to revolutionize cluster analysis and provide accurate, reliable details of molecular architecture. In addition, MIRO’s robust clustering capabilities hold promise for applications in various fields such as neuroscience, for the analysis of neural connectivity patterns, and environmental science, for studying spatial distributions of ecological data.

💡 Research Summary

The paper introduces MIRO (Multifunctional Integration through Relational Optimization), a novel preprocessing framework designed to improve clustering of single‑molecule localization microscopy (SMLM) data. SMLM generates massive point clouds—often millions of fluorophore localizations—where high density, stochastic blinking, and localization noise make conventional clustering difficult. While density‑based algorithms such as DBSCAN, HDBSCAN, and OPTICS are widely used, their performance heavily depends on the choice of parameters (ε and minPts) and they struggle with irregular, multi‑scale, or overlapping structures.

MIRO tackles these challenges by learning a geometric transformation of the point cloud using a recurrent graph neural network (rGNN). Each localization becomes a node in a graph; edges are constructed via Delaunay triangulation and filtered by a distance threshold to capture local spatial relationships. Node features are not raw coordinates but Laplacian positional embeddings, preserving relative geometry while discarding absolute location. Edge features include Euclidean distance and direction vectors.

The core of MIRO is a single‑layer rGNN block that is applied repeatedly (the number of recurrent steps defines the receptive field). At each step the input graph G is concatenated with a hidden graph G_kh (initially zero‑filled). Message passing updates only the hidden graph based on hidden edge features, emphasizing immediate structural context. A dense decoder maps hidden node features to displacement vectors in Cartesian space. These vectors are optimized to pull points belonging to the same biological cluster toward a common centroid while leaving background points essentially unchanged. The loss function can be composed of multiple terms (e.g., L_spot for compact clusters, L_ring for ring‑shaped structures), allowing different training objectives at different recurrent steps. This multi‑scale loss design enables MIRO to simultaneously learn to collapse clusters of varying sizes and shapes, even when trained on a very limited set of representative clusters (few‑shot or single‑shot training).

After transformation, the point cloud exhibits clearer separation between clusters and between clusters and background. Consequently, downstream clustering with DBSCAN becomes far more robust: the ε and minPts parameters can be set over a broader range, and the algorithm’s sensitivity to parameter tuning is dramatically reduced. The authors demonstrate this by comparing DBSCAN performance on raw versus MIRO‑processed data across 27 benchmark scenarios (derived from Ref.