Two clouds represent the same underlying cell types profiled by two assays (e.g. scRNA-seq and scATAC-seq gene-activity scores). Each modality starts in its own coordinate frame, offset by a batch effect. Mutual-nearest-neighbour (MNN) "anchor" pairs across modalities pull matched cells toward a shared joint embedding:
x_i(t+1) = x_i(t) + Σ_a w_a · (anchor_a − x_i(t)) · dt
- Anchor pairs — how many cross-modality neighbour pairs are used to correct the batch offset; too few leaves clusters unaligned.
- Batch effect strength — how far apart the two modalities start before correction (a stand-in for platform/technical variation).
- Technical noise — per-cell jitter (dropout, sequencing depth variance) that blurs cluster boundaries.
- Clusters — number of distinct cell-type populations shared between both assays.
Real-world relevance: tools like Seurat's anchor-based CCA and Harmony integrate scRNA-seq with scATAC-seq or spatial transcriptomics so the same cell type — regardless of which assay measured it — lands in one shared neighbourhood, enabling joint clustering and cross-modal inference.