Mutual Nearest Neighbors (MNN)

A pair of cells from different batches forms an MNN pair when each cell is the other's nearest neighbor in a shared feature space. This reciprocity filters out spurious matches that arise from random sampling noise or batch-specific outliers. The logic is that if two cells are mutual best matches despite originating from different technical batches, they likely represent the same biological state. This concept originates from image alignment and manifold alignment theory, where MNN pairs serve as reliable landmarks for warping one distribution onto another.

Once MNN pairs are identified, a correction vector is computed for each pair as the difference in expression between the two cells. For cells not part of an MNN pair, a correction is estimated by taking a weighted average of the correction vectors from the nearest MNN pairs in the reference batch. This smoothing step ensures that the correction varies smoothly across the expression manifold. The method applies this vector to the query batch cells, effectively subtracting the estimated batch effect while preserving the within-batch biological structure.

MNN correction integrates batches sequentially rather than all at once. The process begins by selecting the largest batch as the reference. The next batch is corrected onto this reference, and the two are merged. This merged dataset then serves as the new reference for the subsequent batch. This hierarchical merging strategy is computationally efficient and ensures that the reference representation grows more robust with each step. The order of merging is typically determined by batch size, but can be guided by data quality metrics.

A key advantage of MNN is that it only corrects cells that have a mutual match, leaving batch-unique cell types untouched. If a cell population exists only in one batch, it will not form an MNN pair and will not receive a correction vector, preventing the overcorrection that plagues global alignment methods. This makes MNN particularly suitable for atlas-scale integration where batches may contain distinct cell types. The method explicitly assumes that batch effects are orthogonal to biological space, operating only along dimensions of technical variation.

MNN correction typically employs cosine normalization on the input expression matrix before identifying neighbors. This step divides each cell's expression profile by its L2 norm, projecting all cells onto a unit hypersphere. This normalization removes library size effects and focuses the neighbor search on relative expression patterns rather than absolute counts. On the hypersphere, Euclidean distance is equivalent to cosine dissimilarity, making the nearest neighbor search robust to differences in sequencing depth between batches.

MNN assumes that batch effects are constant across the expression space, which may not hold for complex, non-linear technical artifacts. The method also requires sufficient overlap in cell types between batches to find enough MNN pairs for robust correction. Diagnostic tools include examining the number of MNN pairs identified and the distribution of correction vector magnitudes. A low number of pairs or extremely large correction vectors may indicate poor batch overlap or severe technical variation that violates the method's assumptions.