Choosing Between MNNs and Anchors

Why the Choice Is About More Than the Matching Algorithm

MNN correction and anchor-based integration both use correspondences between cells to estimate how datasets differ. Neither can determine from expression data alone whether a difference is technical or biological. Their usefulness therefore depends on the study design: which cell states are genuinely shared, which batches contain them, and whether the representation used for matching keeps those states distinguishable.

The central practical question is not simply which method finds more matches. It is whether its matches provide credible evidence about the technical displacement to be corrected. MNNs define matches by mutual nearest-neighbor relationships between batches. Anchor-based methods identify and assess cell correspondences in a shared representation, then use weighted anchor information to correct cells. Both can fail if biological differences are mistaken for batch effects, but their matching and reference strategies make some failure modes more likely than others.

What Each Method Assumes and Does

Both methods need cells in different batches that represent the same or sufficiently similar biological states. They also need a representation in which genuine shared states can be matched without systematically pairing biologically different cells. If a state occurs in only one batch, there is no direct cross-batch correspondence for that state. If a biological condition is present in just one batch, its effect may be indistinguishable from a batch effect without additional design information.

For MNN correction, reciprocal proximity is the evidence for a match. For a matched pair, the displacement from one cell to its partner estimates the local difference between batches. Nearby MNN pairs can be combined to estimate a correction for a cell. This is most credible when matched cells really share a state and the batch displacement varies smoothly enough that nearby matches inform the cell being corrected. It can be unreliable when a batch shift changes nearest-neighbor identities, when overlap is sparse, or when biologically distinct cells become mutual neighbors.

Anchor-based methods first find correspondences in a shared latent space; anchor filtering and scoring assess their consistency and reliability. A cell’s correction is then built from weighted anchor displacements, with nearby or more reliable anchors contributing more. This can accommodate a local correction that is informed by several correspondences rather than a single nearest pair. It still depends on the shared representation and the validity of the retained anchors. A high anchor score does not establish that two cells are biologically equivalent if the design or representation has confounded biology with batch.

The two methods are related in their correction logic: each uses cross-batch displacements to estimate a shift. They are not identical. Reciprocal nearest-neighbor status is the defining matching rule for MNNs; anchor-based integration uses a broader correspondence and reliability framework. An anchor workflow may be explicitly reference-based, mapping query cells to a chosen reference. MNN matches are pairwise, but a multi-batch MNN analysis can still depend on the order and reference choices used to combine batches. Neither method is universally reference-free or universally reference-dependent; the workflow determines that aspect.

Local Correction as a Weighted Displacement

Let a query cell have coordinates \(q\) in a reduced representation and let its matched reference cells have coordinates \(r_j\). Define the displacement from the query toward matched reference cell \(j\) as \(d_j=r_j-q_j\), where \(q_j\) denotes the query-side cell in correspondence \(j\). A local correction can be written as a weighted average of these displacements:

The corrected coordinate is the original query coordinate plus the estimated displacement. The weights may reflect local proximity and, in anchor workflows, anchor reliability. In an MNN illustration, the contributing displacements come from relevant reciprocal pairs; in an anchor illustration, they come from relevant anchors. These equations summarize the local correction idea, not every implementation detail of either method.

A simple justification shows why averaging is natural when the local displacements are noisy measurements of one shared shift. Suppose each observed displacement is \(d_j=\delta+\varepsilon_j\), where \(\delta\) is the local shift and the errors have mean zero. For fixed nonnegative weights summing to one, \(\hat{d}\) is unbiased for \(\delta\), because

This argument depends on the correspondences being valid and the local shift being sufficiently similar across them. If different biological states are mixed together, the average can be precise yet wrong: it estimates the average displacement of the incorrect matches. Weighting cannot repair a lack of genuine shared biology.

Reference Dependence and Study Design

A reference is valuable when it provides broad, well-characterized coverage of the states that query datasets are expected to share. Reference-based anchor mapping makes this choice explicit: query cells are related to the reference, so reference coverage and representation affect which correspondences are available. A query state absent from the reference cannot acquire a direct anchor to its true counterpart there. It may remain unmatched or be assigned misleadingly to a nearby reference state, depending on the workflow and data.

MNN analysis is often built from pairwise batch comparisons. Reciprocal matching itself is defined between a pair of datasets, but integrating many batches requires choices about how pairwise evidence is combined. A weakly overlapping batch can be difficult to align through a chain of other batches, and an early error can influence later alignments. Thus, choosing a reference is not exclusively an anchor concern. The difference is that reference-based mapping typically specifies a target dataset for query mapping, whereas MNN reference dependence can arise through the multi-batch integration strategy.

In either approach, reference selection should be based on biological coverage, data quality, and the intended target of alignment, not simply on which dataset has the most cells. If all batches have substantial overlap and comparable quality, pairwise or multi-batch strategies may be reasonable. If a high-quality reference covers the expected shared states and future queries should be mapped to it, reference-based anchors may offer a clearer operational choice. If the biological states are not shared, choosing a different reference cannot create the missing overlap.

How to Choose, Diagnose, and Avoid Overcorrection

A practical decision should be followed by diagnostics. For MNNs, examine whether reciprocal matches are numerous enough, concentrated in plausible shared states, and locally consistent in their displacement directions. For anchors, inspect coverage by cell state, the distribution and reliability of retained anchors, and whether correction is supported across the query rather than only in a few regions. For both, compare pre- and post-correction structure and check whether known biological distinctions remain interpretable.

Warning signs include abrupt changes in displacement across neighboring cells, matches crossing known state boundaries, large unmatched regions, and apparent disappearance of a condition-associated population after correction. These are not merely cosmetic problems in a visualization. They can indicate that the estimated correction is extrapolated, confounded, or removing biological structure. A method’s score or a visually mixed embedding cannot by itself establish that the integration is valid.

When the assumptions are weak, reasonable alternatives include analyzing batches separately, restricting alignment to well-supported shared states, or reporting unmatched states without forcing them into a reference. These choices may be preferable to a single integrated representation that obscures the uncertainty. Integration is a modeling decision about which differences to treat as technical; it is not a guarantee that all batch-associated variation should be removed.

Common Mistake