# JGR-NMF: joint graph-regularized non-negative matrix factorization for spatial domain identification

## TL;DR

This paper introduces JGR-NMF, a new method for identifying spatial domains in spatial transcriptomics data, which improves accuracy and robustness compared to existing methods.

## Contribution

The novel contribution is the JGR-NMF framework with adaptive neighborhood graph construction and integration of spatial adjacency.

## Key findings

- JGR-NMF outperforms five baseline methods on breast cancer and mouse datasets for spatial domain identification.
- Ablation studies confirm the importance of graph regularization in improving model performance.

## Abstract

The spatial transcriptomics technique provides an unprecedented perspective for analyzing the distribution patterns of cells within tissues and their functional tissue structures. To enhance the accuracy and robustness of spatial domain identification, we propose Joint Graph-Regularized Non-negative Matrix Factorization (JGR-NMF). An adaptive neighborhood graph construction strategy is introduced by applying an nth-power transformation to the spot adjacency probability matrix, thereby automatically optimizing the neighborhood size for individual spots. Furthermore, a JGR-NMF framework is developed, integrating this adaptively constructed kNN graph with the spatial adjacency matrix. Evaluations conducted on two breast cancer datasets, one Mouse Kidney dataset and one Mouse Embryo dataset, demonstrate that JGR-NMF significantly outperforms five state-of-the-art baseline methods in spatial domain identification. Systematic ablation studies further confirm the critical role of graph regularization in enhancing model performance.