This manuscript offers a mathematical framing of spot‑based spatial transcriptomics (ST) deconvolution as a non‑negative blind source separation (BSS) problem. The author argues that the identifiability theory developed for independent component analysis (ICA), non‑negative matrix factorisation (NMF), and hyperspectral unmixing transfers directly to ST because both domains share the same non‑negative linear mixture model. The review structures the landscape around three conditions: (i) full column rank of the signature matrix (reference completeness), (ii) the condition number κ(S) (noise amplification when sources are similar), and (iii) separability or minimum‑volume conditions in unsupervised regimes. It also points out that the negative‑binomial nature of count data makes squared‑error objectives a high‑count approximation, and concludes with guidance for algorithm selection and clinical/regulatory interpretation.
The manuscript is clearly written, conceptually coherent, and likely to be valuable to ST practitioners who lack a background in identifiability theory. However, from the perspective of chemometrics and NMF, the treatment of rotational ambiguity and uniqueness is too limited, and key developments—especially recent work on partial identifiability—are not integrated. The central claim that three conditions “organise the entire field” risks oversimplifying a richer body of identifiability theory. I recommend major revision.