Marker Exclusion Rate (MER) in Transcriptomics

• Marker Exclusion Rate (MER) is a biologically driven error metric that measures the fraction of cells assigned to clusters whose marker genes they fail to express.
• It complements geometric clustering metrics by comparing marker gene expression sums between assigned clusters and the best marker-supported clusters.
• MER-guided reassignment refines clustering results by reassigning cells when an alternative cluster shows a significant improvement in expressed markers.

Searching arXiv for papers on "Marker Exclusion Rate" and related spatial transcriptomics benchmarking. Marker Exclusion Rate (MER) is a biologically motivated error metric for clustering in spatial transcriptomics. It was introduced to quantify “how often cells end up in clusters whose marker genes they do not express, or feebly express,” and, more explicitly, “the fraction of cells whose assigned cluster’s marker set they fail to express” (Mahmud et al., 12 Sep 2025). In the benchmark where it was proposed, MER serves as a complement to geometric clustering scores, because a cluster may appear compact in latent space yet remain biologically inconsistent if its members do not express the canonical markers of that cluster. The metric is therefore intended to capture marker mismatch, estimate the fraction of cells that would be better annotated elsewhere on biological grounds, and function as a direct readout of downstream annotation risk (Mahmud et al., 12 Sep 2025).

1. Origin and analytical motivation

MER was introduced in a unified framework for evaluating dimensionality reduction techniques in spatial transcriptomics beyond standard PCA approaches, on a cholangiocarcinoma Xenium dataset (Mahmud et al., 12 Sep 2025). The benchmark systematically varied latent dimensions $k=5\text{--}40$ and clustering resolutions $\rho=0.1\text{--}1.2$, and evaluated configurations with complementary metrics including reconstruction error, explained variance, cluster cohesion, Cluster Marker Coherence (CMC), and MER (Mahmud et al., 12 Sep 2025).

The central motivation for MER is that standard dimensionality-reduction-plus-clustering pipelines can score well by silhouette or Davies–Bouldin Index (DBI) while still producing biologically inconsistent clusters (Mahmud et al., 12 Sep 2025). In spatial transcriptomics, especially in a tissue such as cholangiocarcinoma, the relevant question is not only whether the embedding separates cells, but whether the resulting clusters correspond to real cell identities and microenvironments. MER operationalizes this concern by measuring whether the cluster assignment inferred from the embedding agrees with the cluster whose marker genes the cell actually expresses most strongly (Mahmud et al., 12 Sep 2025).

This framing places MER on the biological side of the tradeoff against purely geometric or reconstruction-oriented criteria. A plausible implication is that MER is most informative when clustering is intended to support annotation, atlas construction, or interpretation of microenvironmental structure, rather than exploratory geometry alone.

2. Formal definition and computation

The paper defines MER using the expression matrix $X\in\mathbb{R}^{n\times p}$ and cluster-specific marker-gene sets $\mathcal{M}_c\subset\{1,\dots,p\}$ (Mahmud et al., 12 Sep 2025). For each cell $i$, the best-matching cluster is determined by summed marker expression:

$$\hat c_i \;=\;\arg\max_{c}\;\sum_{g\in\mathcal{M}_c}X_{i,g}.$$

A cell is then “flagged $i$ as marker-positive if $\sum_{g\in\mathcal{M}_{\hat c_i}}X_{i,g}>0$.” The set of marker-positive cells is denoted $I^+$. MER is defined as

$$\mathrm{MER} \;=\; \frac{1}{n} \sum_{i\in I^+} \mathbf{1}\bigl(c_i \neq \hat c_i\bigr),$$

where $\rho=0.1\text{--}1.2$0 is the Leiden-predicted cluster label (Mahmud et al., 12 Sep 2025).

The paper also gives an equivalent interpretation: MER is “the fraction of all cells whose assigned cluster’s marker set they fail to express” (Mahmud et al., 12 Sep 2025). Cells with no expressed marker are excluded from the numerator by the definition of $\rho=0.1\text{--}1.2$1, and the benchmark separately reports

$\rho=0.1\text{--}1.2$2

Operationally, the implementation is straightforward: compute marker-set sums per cell over all clusters, choose the cluster with the largest sum, and count the cell as excluded if its assigned Leiden cluster differs from that best marker-supported cluster (Mahmud et al., 12 Sep 2025). The metric is thus determined by a comparison between an embedding-derived label and a marker-supported label.

The paper’s post-processing also introduces a threshold $\rho=0.1\text{--}1.2$3: reassignment occurs only if the alternative cluster improves marker expression by at least $\rho=0.1\text{--}1.2$4 and the alternative cluster has at least one expressed marker in that cell (Mahmud et al., 12 Sep 2025). That threshold belongs to the refinement procedure rather than to the basic MER definition, but it clarifies how the metric is used in practice.

3. Relation to Cluster Marker Coherence and other evaluation criteria

MER is tightly linked to Cluster Marker Coherence, but the two quantities capture different aspects of biological validity (Mahmud et al., 12 Sep 2025). CMC asks how well each cluster captures its own markers; MER asks how often cells are placed in the wrong marker-defined cluster. For cluster $\rho=0.1\text{--}1.2$5 with marker set $\rho=0.1\text{--}1.2$6, the benchmark defines

$\rho=0.1\text{--}1.2$7

with unweighted

$\rho=0.1\text{--}1.2$8

and size-weighted

$\rho=0.1\text{--}1.2$9

High CMC means that cells assigned to a cluster tend to express that cluster’s marker genes. Low MER means that few cells are assigned to a cluster whose markers they do not best express (Mahmud et al., 12 Sep 2025). In the benchmarking study, MER is reported to correlate inversely with CMC and enrichment: when CMC and enrichment are high, MER tends to be lower (Mahmud et al., 12 Sep 2025).

The benchmark therefore uses MER alongside CMC and gene-set enrichment analysis as the biological counterpart to silhouette and DBI (Mahmud et al., 12 Sep 2025). This division is analytically important. A clustering can be geometrically cohesive but biologically misassigned, or biologically coherent but less compact in latent space. MER was introduced specifically to expose that discrepancy.

A common misconception is to treat MER as interchangeable with cluster purity or with within-cluster marker enrichment. The benchmark does not support that equivalence. CMC and enrichment concern how well clusters capture their own markers; MER concerns disagreement between assigned cluster labels and marker-supported cluster identity (Mahmud et al., 12 Sep 2025).

4. MER-guided reassignment as post-processing

The paper extends MER from a diagnostic into a refinement procedure called MER-guided reassignment, or MER-guided cell reassignment (Mahmud et al., 12 Sep 2025). After clustering in latent space, the method revisits the original expression matrix and reassigns a cell to the cluster whose marker genes it expresses most strongly, but only if the improvement exceeds $X\in\mathbb{R}^{n\times p}$0 and the target cluster has at least one expressed marker in that cell (Mahmud et al., 12 Sep 2025).

Algorithmically, for each cell the marker-gene sums

$X\in\mathbb{R}^{n\times p}$1

are computed over all clusters, $X\in\mathbb{R}^{n\times p}$2 is found, and the label is updated only if

$X\in\mathbb{R}^{n\times p}$3

and $X\in\mathbb{R}^{n\times p}$4 (Mahmud et al., 12 Sep 2025). The authors describe this as a “lightweight post-processing step” that preserves the geometric cohesion of the original clustering while correcting biologically implausible assignments, and characterize it as marker-guided refinement rather than a new embedding method (Mahmud et al., 12 Sep 2025).

This makes MER unusual among benchmarking metrics in that it functions both as an evaluative criterion and as the basis for label correction. A plausible implication is that MER is not merely descriptive; it encodes an explicit biological preference over cluster assignments when marker annotations are trusted.

5. Empirical behavior across dimensionality reduction methods

In benchmarking, MER was used to compare PCA, NMF, AE, VAE, RAW clustering, and hybrid embeddings (Mahmud et al., 12 Sep 2025). The broad pattern reported in the paper is that PCA gave the strongest geometric clustering but relatively weaker biological agreement; NMF gave the best biological signal recovery; VAE often struck the best balance; AE sat in between; and hybrids could improve tradeoffs (Mahmud et al., 12 Sep 2025).

Method	Representative Pareto-optimal MER values	Reported characterization
PCA	$X\in\mathbb{R}^{n\times p}$5	Strongest geometric clustering; biological fidelity lags
NMF	$X\in\mathbb{R}^{n\times p}$6	Best biological signal recovery
AE	$X\in\mathbb{R}^{n\times p}$7	Middle ground
VAE	$X\in\mathbb{R}^{n\times p}$8	Best overall balance among single methods
RAW	$X\in\mathbb{R}^{n\times p}$9	Raw clustering baseline
PCA+NMF	$\mathcal{M}_c\subset\{1,\dots,p\}$0	Improved tradeoff substantially
VAE+NMF	$\mathcal{M}_c\subset\{1,\dots,p\}$1	Combined biological signal with cohesion

Lower MER means fewer cells whose cluster label disagrees with their marker profile (Mahmud et al., 12 Sep 2025). The paper gives a representative hybrid configuration for PCA+NMF with silhouette $\mathcal{M}_c\subset\{1,\dots,p\}$2, CMC $\mathcal{M}_c\subset\{1,\dots,p\}$3, and MER $\mathcal{M}_c\subset\{1,\dots,p\}$4, which is reported as better than PCA alone (Mahmud et al., 12 Sep 2025). VAE+NMF is described as combining NMF’s biological signal with VAE’s cohesion (Mahmud et al., 12 Sep 2025).

The post-processing results are especially notable. In Table 6, after MER-guided reassignment, PCA, NMF, VAE, AE, PCA+NMF, and VAE+NMF all have $\mathcal{M}_c\subset\{1,\dots,p\}$5 (Mahmud et al., 12 Sep 2025). The authors explicitly note that this comes with some silhouette decrease, which they consider expected because labels are intentionally changed to favor marker coherence over purely geometric proximity. They also report that CMC improves after reassignment, summarizing the effect in the abstract as “CMC scores improving by up to 12% on average” (Mahmud et al., 12 Sep 2025). Additional qualitative evidence includes marker-gene dot plots where mean expression for some markers increases by more than 20% after reassignment, and a case study in which MER collapses method-specific artifacts and clarifies major epithelial, macrophage, stromal, and lymphoid programs (Mahmud et al., 12 Sep 2025).

6. Interpretation, limitations, and acronym ambiguity

The benchmark states several caveats for interpreting MER (Mahmud et al., 12 Sep 2025). First, MER depends on the marker sets $\mathcal{M}_c\subset\{1,\dots,p\}$6, so its meaning is only as good as the chosen marker annotation. If marker sets are incomplete, overlapping, or noisy, MER can overstate or understate biological error. Second, MER is computed from summed raw expression over marker genes and uses a simple positive-expression criterion; this makes it intuitive, but also somewhat coarse. It does not account for expression magnitude beyond being positive, except in the reassignment step where summed marker expression matters. Third, MER is not a standalone quality metric: it should be read together with CMC, enrichment, silhouette, DBI, and reconstruction error. A low MER with poor geometric structure may still be undesirable if the embedding is unstable or overfragmented, and a higher MER may be tolerable if the goal is exploratory geometry rather than annotation. Fourth, MER-guided reassignment prioritizes biological coherence over geometric fidelity, so post-processed silhouette scores become less relevant because the cluster labels no longer reflect the original embedding-based partition (Mahmud et al., 12 Sep 2025).

For practical method selection, the paper’s message is that MER is especially useful when the downstream task is cell-type annotation or marker-based atlas construction (Mahmud et al., 12 Sep 2025). If a method gives low MER and high CMC or enrichment, its clusters are more likely to correspond to real biological identities. PCA may be attractive for speed and cohesion, NMF for interpretable marker recovery, VAE for a balanced compromise, and hybrids when one wants to combine strengths (Mahmud et al., 12 Sep 2025). In that sense, MER is best used as a diagnostic and refinement criterion: it detects marker-inconsistent clusters, supports comparison of methods on biological faithfulness, and helps determine whether marker-guided label cleanup is warranted (Mahmud et al., 12 Sep 2025).

On arXiv, the acronym “MER” is ambiguous. In the paper “MER 2026: From Discriminative Emotion Recognition to Generative Emotion Understanding,” MER refers to Multimodal Emotion Recognition and to the MER challenge series, not to Marker Exclusion Rate (Lian et al., 21 Apr 2026). The two usages are unrelated: one belongs to multimodal affective computing, while Marker Exclusion Rate is a clustering metric in spatial transcriptomics.