hSNMF: Hybrid Spatially Regularized NMF for Image-Derived Spatial Transcriptomics.

2026-02-02

arXiv.org

AI Summary

This study addresses the challenges of the curse of dimensionality and the integration of spatial and transcriptomic information in high-dimensional spatial transcriptomics data, such as Xenium. The authors propose two spatially regularized non-negative matrix factorization (NMF) methods: a lightweight SNMF that enhances spatial smoothness via local neighborhood diffusion, and hSNMF, which further integrates a spatial adjacency graph with transcriptomic similarity to construct a hybrid adjacency matrix, guided by a tunable parameter α for Leiden clustering. This work is the first to embed both spatial diffusion mechanisms and hybrid graph strategies into an NMF framework, jointly modeling spatial continuity and transcriptomic heterogeneity. Evaluated on cholangiocarcinoma data, the proposed methods significantly outperform existing baselines, achieving CHAOS < 0.004, Moran’s I > 0.96, Silhouette > 0.12, DBI < 1.8, and demonstrating superior enrichment of cell-type marker genes and biological consistency.

Technology Category

• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Data transparency and provenance

Abstract

High-resolution spatial transcriptomics platforms, such as Xenium, generate single-cell images that capture both molecular and spatial context, but their extremely high dimensionality poses major challenges for representation learning and clustering. In this study, we analyze data from the Xenium platform, which captures high-resolution images of tumor microarray (TMA) tissues and converts them into cell-by-gene matrices suitable for computational analysis. We benchmark and extend nonnegative matrix factorization (NMF) for spatial transcriptomics by introducing two spatially regularized variants. First, we propose Spatial NMF (SNMF), a lightweight baseline that enforces local spatial smoothness by diffusing each cell's NMF factor vector over its spatial neighborhood. Second, we introduce Hybrid Spatial NMF (hSNMF), which performs spatially regularized NMF followed by Leiden clustering on a hybrid adjacency that integrates spatial proximity (via a contact-radius graph) and transcriptomic similarity through a tunable mixing parameter alpha. Evaluated on a cholangiocarcinoma dataset, SNMF and hSNMF achieve markedly improved spatial compactness (CHAOS < 0.004, Moran's I > 0.96), greater cluster separability (Silhouette > 0.12, DBI < 1.8), and higher biological coherence (CMC and enrichment) compared to other spatial baselines. Availability and implementation: https://github.com/ishtyaqmahmud/hSNMF.

Problem

• spatial transcriptomics
• high dimensionality
• representation learning
• clustering
• single-cell imaging

Innovation

• spatial transcriptomics
• nonnegative matrix factorization
• spatial regularization
• hybrid clustering
• Xenium