Multi-level quality control for lower-dimensional representations of spatial transtriptomics data

Low-dimensional representations have become a substantial step in data analysis, especially in the single-cell domain, with much research focused on method development. Howerver, quality control is equally important, as dimensionality reduction (DR) inevitably introduces distortions. In this work, we explore the utility of post-hoc unsupervised metrics, widely used in visual data exploration, for evaluating embeddings intended for downstream analysis. We focus specifically on spatial transcriptomics data, where gene expression and spatial organisation jointly shape the embedding. To this end, we introduce a unifying decomposition framework designed to improve embedding interpretability and facilitate the detection of distortions.