Park, K.; Sun, Z.; Liao, R.; Bresnick, E. H.; Keles, S.

Contrastive dimension reduction enhances the analysis of high-dimensional data by generating target-specific low-dimensional representations relative to a background. Emerging methods for contrastive dimension reduction have demonstrated their utility in extracting target-specific signals across domains involving high-dimensional observations, including genomics, transcriptomics, and pattern recognition. However, even though choosing an appropriate background is critical to the success of contrastive dimension reduction, no established criterion currently exists for selecting such backgrounds. To address this gap, we introduce BasCoD, a novel testing framework grounded in the spectral theory of subspace inclusion, to enable rigorous evaluation and optimal selection of backgrounds. Extensive application of BasCoD across diverse single-cell datasets demonstrates its effectiveness in systematically identifying suitable backgrounds, thereby significantly improving the contrast and interpretability of the derived target representations. We further illustrate how BasCoD can facilitate design of appropriate backgrounds in large-scale single cell experiments under heterogeneous conditions.