SpaCoEx: Sparse Gene Selection for Spatially Varying Co-expression in Spatial Transcriptomics

Spatial transcriptomics enables gene expression to be measured while preserving tissue location, but most existing analyses focus on spatial variation in individual genes or expression-defined domains. Here, we introduce SpaCoEx, a sparse spatial representation framework that integrates gene-expression levels with spatially varying gene-gene co-expression. SpaCoEx first estimates local co-expression matrices from neighboring spatial spots, maps them into a log-Euclidean representation, and performs structured gene selection by retaining or removing the full row and column associated with each gene. The selected genes are then used to construct both expression-level features and local co-expression features, which are combined through an -weighted joint representation for downstream spatial analysis. We applied SpaCoEx to human cutaneous squamous cell carcinoma and annotated human breast cancer spatial transcriptomics datasets. In the cutaneous squamous cell carcinoma dataset, SpaCoEx selected 29 of 45 keratinocyte-related genes while preserving 96.74% of the spatial co-expression variation. In the breast cancer dataset, SpaCoEx identified spatially varying co-expression between B2M and HLA-C, a biologically meaningful major histocompatibility complex (MHC) class I antigen-presentation gene pair. Their local correlation was significantly higher in cancer-associated regions than in non-cancer regions (mean difference = 0.30, spatially adjusted SE = 0.045, P<1.0x10^(-10)), whereas B2M and HLA-C expression individually did not differ significantly between cancer and non-cancer. In benchmarking against manual tissue annotations, co-expression-only SpaCoEx achieved the strongest spatial coherence (percentage of abnormal spots [PAS] = 0.076), while the joint expression/co-expression representation achieved the highest annotation agreement, with an adjusted Rand Index (ARI) of 0.584 at = 0.60 and and normalized mutual information (NMI) of 0.663 at = 0.40. By integrating marginal gene-expression information with local gene-gene co-expression structure, SpaCoEx provides a sparse, low-dimensional, and interpretable representation of spatial transcriptomics data that captures complementary aspects of tissue organization beyond expression-based variation alone.