Tensor-Derived Similarity Networks for Characterising Spatial Patterns in Colorectal Cancer

Spatial transcriptomics enables the study of gene expression within the spatial context of tissue architecture, offering new opportunities for understanding tumour heterogeneity. This study proposes a tensor-derived similarity network framework for analysing spatial organisation in colorectal cancer. Gene expression data from four patients are represented as spatially structured tensors and decomposed using a low-rank canonical polyadic model to extract latent spatial-molecular features. These features are used to construct similarity networks that characterise spatial relationships between tissue regions. Global network measures, including similarity, density, and spatial heterogeneity, reveal sparse but structured connectivity patterns across all patients. An embedding-permutation framework is introduced to generate randomised spatial configurations while preserving feature distributions. Comparative analysis shows that randomised networks exhibit higher similarity, density, and heterogeneity than real data, indicating that spatial organisation constrains network structure. The results demonstrate that the proposed framework captures meaningful spatial patterns in tumour tissue and provides quantitative measures of spatial heterogeneity. This approach offers a general methodology for analysing spatial transcriptomics data and has potential applications in spatial biomarker discovery and characterisation of tumour architecture.