Average Silhouette Width (ASW)

The metric is based on the classic Silhouette coefficient, which measures how similar a data point is to its own cluster compared to other clusters. For a single cell i, the score is calculated as (b_i - a_i) / max(a_i, b_i) , where a_i is the mean intra-cluster distance and b_i is the mean nearest-cluster distance. The score ranges from -1 (incorrect clustering) to +1 (perfectly compact and separated).

To assess biological conservation, the ASW is calculated using cell-type labels as the cluster identity. A high average score (approaching 1.0) indicates that cells of the same type remain tightly grouped after integration, regardless of which batch they originated from. This confirms that the correction algorithm did not erase true biological variance.

To assess batch mixing, the ASW is calculated using batch labels as the cluster identity. An ideal correction results in a score near 0 or negative, indicating that batch labels are randomly distributed and do not form distinct clusters. A score of 1.0 represents a complete failure where batches remain perfectly separated.

For intuitive scaling, the batch mixing score is often transformed to 1 - absolute(bASW) . This normalizes the metric so that 0 indicates pure batch separation and 1 indicates perfect mixing. This transformation allows for direct averaging with the cell-type ASW to produce a single, unified integration score.

Unlike global divergence metrics, ASW operates on the local neighborhood structure. It penalizes scenarios where batch effects create artificial sub-clusters within a true cell type. This makes it sensitive to the 'kissing cell' problem, where two batches form distinct but adjacent groups that global metrics might incorrectly classify as well-mixed.

Calculating the full pairwise distance matrix for ASW scales quadratically with cell count, making it computationally intensive for million-cell atlases. Common optimizations include:

• Using a random subsample of cells
• Calculating distances on a PCA or scVI latent space rather than the full gene expression matrix
• Using approximate nearest neighbors to estimate the nearest-cluster distance

A complementary diversity score computed for each cell's local neighborhood. Integration LISI (iLISI) measures the effective number of batches present, where a higher value indicates better mixing. Cell-type LISI (cLISI) measures the effective number of cell types, where a lower value indicates better biological signal preservation. Used alongside ASW to provide a dual perspective on integration quality.

A quantitative metric that evaluates batch mixing by comparing the local batch label distribution in a k-nearest neighbor graph to the global batch distribution. A perfect mix yields a chi-squared test acceptance rate near 1.0. Unlike ASW, kBET provides a formal statistical test with a p-value, making it suitable for regulatory submissions.

An information-theoretic metric that quantifies the randomness of batch labels within a defined local neighborhood of cells. High entropy indicates a well-mixed, successfully integrated dataset free of local batch clustering. This metric directly measures the uniformity of batch distribution without requiring cluster labels, unlike ASW.

The process of evaluating whether a batch correction method has removed true biological variation alongside technical noise. Key indicators include:

• Preservation of known cell-type clusters
• Variance explained by biological covariates
• Maintenance of marker gene expression patterns ASW is a primary tool for this assessment, with cell-type ASW measuring biological preservation.

A kernel-based statistical test used as a loss function in deep learning to measure the distance between two probability distributions. In batch correction, MMD enables the alignment of latent feature distributions from different batches. It provides a distribution-level metric that complements ASW's cluster-level assessment, particularly useful for evaluating deep learning integration methods like scVI and DANN.

A dimensionality reduction technique used to visually inspect batch correction results. By coloring cells by batch label and cell type in PCA space, researchers can qualitatively assess integration before computing quantitative metrics like ASW. Effective correction shows overlapping batch distributions while maintaining distinct cell-type clusters.