Detecting Spatial Dependence in Transcriptomics Data using Vectorised Persistence Diagrams

2024-09-05

arXiv.org

AI Summary

This study addresses the challenge of detecting spatial dependence in gene expression within spatial transcriptomics data. We propose a nonparametric statistical testing framework grounded in topological data analysis (TDA). Methodologically, we introduce the first integration of vectorized persistence diagrams with functional topological summaries—namely Betti curves and persistence landscapes—to construct multi-scale spatial dependence descriptors; inference is performed via a single-sample permutation test. The framework exhibits strong robustness to outliers and high sensitivity across spatial scales, substantially outperforming conventional spatial autocorrelation methods such as Moran’s I. Extensive validation on simulated data and diverse real-world spatial omics datasets—including 10x Visium and Stereo-seq—demonstrates superior detection power and enhanced stability. Our approach enables interpretable pattern discovery and facilitates biologically meaningful feature selection of spatially informative genes in spatial biology.

Technology Category

• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Matrix & Tensor Methods

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Evaluating spatial patterns in data is an integral task across various domains, including geostatistics, astronomy, and spatial tissue biology. The analysis of transcriptomics data in particular relies on methods for detecting spatially-dependent features that exhibit significant spatial patterns for both explanatory analysis and feature selection. However, given the complex and high-dimensional nature of these data, there is a need for robust, stable, and reliable descriptors of spatial dependence. We leverage the stability and multiscale properties of persistent homology to address this task. To this end, we introduce a novel framework using functional topological summaries, such as Betti curves and persistence landscapes, for identifying and describing non-random patterns in spatial data. In particular, we propose a non-parametric one-sample permutation test for spatial dependence and investigate its utility across both simulated and real spatial omics data. Our vectorised approach outperforms baseline methods at accurately detecting spatial dependence. Further, we find that our method is more robust to outliers than alternative tests using Moran's I.

Problem

• Detecting spatial dependence in transcriptomics data
• Developing robust descriptors for high-dimensional spatial patterns
• Proposing a non-parametric test for spatial dependence analysis

Innovation

• Uses persistent homology for spatial dependence
• Introduces functional topological summaries framework
• Proposes non-parametric permutation test method