Geometry-Constrained Residual Projection with Optimal Transport for scRNA Cell-State Analysis

Observed zeros in single-cell RNA sequencing (scRNA-seq) data couple two problems that are usually treated separately: expression imputation and cell-state progression inference. Imputation seeks to recover expression missed by the assay, whereas optimal transport (OT) infers progression from distributions of cell states. However, imputation changes the same cell-state geometry from which OT infers progression. To limit this change, we introduce Geometry-Constrained Residual Projection (GCRP), which treats existing imputers as generators of candidate residuals. GCRP accepts only corrections that are supported by neighboring cells, have a controlled amplitude, and satisfy cell-displacement and population-level OT limits. Per-cell displacement bounds induce Wasserstein bounds on population displacement and on the distortion of pairwise group distances. Candidate selection relies only on agreement with observed positive expression and on OT over clusters of raw expression. GCRP itself uses no biological labels or external measurements, which serve for evaluation. Across controlled-corruption, CITE-seq, disease-progression, and time-course experiments, GCRP and its support gate keep the population geometry used for progression inference. Under controlled corruption, full graph imputation triples the error of the relative state geometry against an uncorrupted reference, whereas GCRP keeps this error at the level of raw data and lowers held-out expression RMSE by 5%. Applied on top of each of five published imputers, GCRP lowers that imputer's distortion of the population geometry 3.7- to 8.2-fold. On CITE-seq cells, scVI and SAVER lower the correlation between RNA and surface-protein levels, and GCRP applied on top of them raises it in every seed, from 0.146 to 0.290 for scVI. At the default radius, the Wasserstein bounds certify that the displacement projection preserves 45% of the raw orderings of group distances. These results show that progression geometry can set how much uncertain expression correction is admitted.