Magnitude-Based Features for Multispecies Spatial Data

2026-06-10

AI Summary

Existing approaches struggle to effectively quantify interactions among entities in multispecies spatial data. This work introduces, for the first time, the metric space invariant known as “magnitude” into this domain, proposing a global and local feature vector method that simultaneously captures spatial configuration and scale. Grounded in magnitude theory for finite metric spaces, the method extracts structural features from both synthetic and real tissue microarray data. Applied to tumor microenvironment analysis, it successfully identifies radial distribution patterns correlated with clinical outcomes and reveals the discriminative roles of B/T cell interactions and CD4⁺ T cell–CD163⁺ macrophage associations in determining immune response types in colorectal cancer.

Abstract

Multispecies spatial data arise in many applications where interactions between different entities are central to system behaviour, including biomedical imaging, geospatial analysis, and species ecology. Despite their importance, relatively few quantitative tools exist to capture such interactions. In this work, we propose magnitude-based features for the analysis of multispecies spatial data. Magnitude is a real-valued invariant of finite metric spaces that can be interpreted as an effective number of points, incorporating both spatial configuration and scale. We develop global and local magnitude feature vectors and demonstrate their utility on synthetic tumour microenvironment data, and in tissue microarray data from human colorectal cancer samples. Locally, the method identifies distinct neighbourhood types and reveals spatial heterogeneity; in the model, this includes radial patterns associated with different qualitative outcomes of the simulations, while in the real-world data it reflects the importance of tertiary lymphoid structure-like interactions between B and T cell populations. Globally, the approach recovers known classifications of long-term simulation outcomes across parameter regimes in synthetic data, and suggests important roles for CD4+ T cells and CD163+ macrophages in distinguishing patients with favourable Crohn's like reactions from unfavourable diffuse immune infiltration. Together, these results suggest that magnitude-based features provide a powerful and flexible tool for the analysis of multispecies spatial data.

Problem

• multispecies spatial data
• spatial interactions
• quantitative analysis
• spatial heterogeneity
• tumour microenvironment

Innovation

• magnitude
• multispecies spatial data
• spatial heterogeneity
• tumour microenvironment
• metric space invariant