Multimodal single-cell technologies profile multiple modalities for each cell simultaneously, enabling a more thorough characterization of cell populations. Existing dimension-reduction methods for multimodal data capture the "union of information," producing a lower-dimensional embedding that combines the information across modalities. While these tools are useful, we focus on a fundamentally different task of separating and quantifying the information among cells that is shared between the two modalities as well as unique to only one modality. Hence, we develop Tilted Canonical Correlation Analysis (Tilted-CCA), a method that decomposes a paired multimodal dataset into three lower-dimensional embeddings-one embedding captures the "intersection of information," representing the geometric relations among the cells that is common to both modalities, while the remaining two embeddings capture the "distinct information for a modality," representing the modality-specific geometric relations. We analyze single-cell multimodal datasets sequencing RNA along surface antibodies (i.e., CITE-seq) as well as RNA alongside chromatin accessibility (i.e., 10x) for blood cells and developing neurons via Tilted-CCA. These analyses show that Tilted-CCA enables meaningful visualization and quantification of the cross-modal information. Finally, Tilted-CCA's framework allows us to perform two specific downstream analyses. First, for single-cell datasets that simultaneously profile transcriptome and surface antibody markers, we show that Tilted-CCA helps design the target antibody panel to complement the transcriptome best. Second, for developmental single-cell datasets that simultaneously profile transcriptome and chromatin accessibility, we show that Tilted-CCA helps identify development-informative genes and distinguish between transient versus terminal cell types.
Keywords: canonical correlation analysis; matrix factorization; multimodal data; multiview data; single-cell genomics.