Mixtures of spatial factor analyzers for tensor-variate data

A mixture of spatial factor analyzers (MSFA) is introduced to address the challenges of clustering high-dimensional spatial data. By leveraging the underlying coordinate system, the proposed framework incorporates a flexible, spline-based spatial decay covariance structure that prevents parameter inflation as dimensionality increases. To model non-spatial dependence, matrix variate factor analyzers are employed for further dimensionality reduction. Parameter estimation is conducted via a variant of the expectation-maximization algorithm combined with a generalized least squares estimator. The proposed models are explored in the context of tensor-variate data analysis, where simulation studies and applications to Raman spectroscopy and hyperspectral texture databases demonstrate their capacity to accurately infer and differentiate distinct spatial patterns.

Building artificial intelligence virtual tissue (AIVT) for tissue state representation, feature prediction, and dynamic simulation

Modeling tissue states and their transitions is essential for understanding tissue homeostasis in health and pathological remodeling in disease. However, conventional computational modeling approaches are inadequate to capture the complexity of tissues as spatially organized, multiscale biological systems. Artificial intelligence (AI) has shown a remarkable ability for representing intricate systems, creating new opportunities to characterize tissue states and their transitions. Here, we propose the concept of AI virtual tissue (AIVT), an AI framework grounded in spatial multimodal data for modeling tissues in health and disease. AIVT is designed to learn unified, spatially resolved, and dynamically manipulatable representations of tissue state, enabling tissue state representation and analysis, molecular and morphological feature prediction, and simulation of spatiotemporal tissue dynamics. We outline the fundamental assumptions, core capabilities, architectural components, as well as data and algorithm foundations of AIVT as a framework for AI-driven tissue modeling.

Magnitude-Based Features for Multispecies Spatial Data

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.