Overview of ALPINE for disentangling the effects of conditions and batches. (A) Example of a data set with multiple condition and batch effects, creating challenges in cross-study analyses. (B) ALPINE's workflow incorporates an NMF-based approach with two main components: classic matrix decomposition and label-guided decomposition. The label-guided decomposition enables identification of condition- or batch-associated components. (C) ALPINE extends beyond standard single-cell analyses (e.g., clustering and cell embedding) by uncovering condition-associated genes and cells and addressing batch effects in a principled way, facilitating deeper insights across complex data sets.