Disentangling Shared and Target-Enriched Topics via Background-Contrastive Non-negative Matrix Factorization

Biological signals of interest in high-dimensional data are often masked by dominant variation shared across conditions. This variation, arising from baseline biological structure or technical effects, can prevent standard dimensionality reduction methods from resolving condition-specific structure. The challenge is that these confounding topics are often unknown and mixed with biological signals. Existing background correction methods are either unscalable to high dimensions or not interpretable. We introduce background contrastive Non-negative Matrix Factorization (\model), which extracts target-enriched latent topics by jointly factorizing a target dataset and a matched background using shared non-negative bases under a contrastive objective that suppresses background-expressed structure. This approach yields non-negative components that are directly interpretable at the feature level, and explicitly isolates target-specific variation. \model is learned by an efficient multiplicative update algorithm via matrix multiplication such that it is highly efficient on GPU hardware and scalable to big data via minibatch training akin to deep learning approach. Across simulations and diverse biological datasets, \model reveals signals obscured by conventional methods, including disease-associated programs in postmortem depressive brain single-cell RNA-seq, genotype-linked protein expression patterns in mice, treatment-specific transcriptional changes in leukemia, and TP53-dependent drug responses in cancer cell lines.