Spatially Aware Adjusted Rand Index for Evaluating Spatial Transcriptomics Clustering

The spatial transcriptomics (ST) clustering plays a crucial role in elucidating the tissue spatial heterogeneity, which is referred to as region segmentation for spot level ST data and spatial cell typing for single-cell ST data. An accurate ST clustering result can greatly benefit downstream biological analyses. As various ST clustering approaches are proposed in recent years, quantifying and comparing their clustering accuracy become important in the benchmarking study. However, the commonly used metric adjusted Rand index (ARI) totally ignores the invaluable spatial locations of objects (spots or cells) in ST data. To address this issue, we propose a spatially aware Rand index (spRI) as well as its adjusted version (spARI) that incorporate the spatial distance information into the clustering evaluation. Specifically, when comparing two partitions, spRI provides a pair of objects that are in the same cluster of one partition but are in different clusters of the other partition (called disagreement pair) with a weight relying on the distance of the two objects, while original Rand index offers this disagreement pair with an identical zero weight. This spatially aware feature of spRI successfully differentiates disagreement object pairs based on their distinct distances, which cannot be achieved by Rand index. The spRI is then adjusted to correct for random chances such that its expectation takes on the zero value under an appropriate random null model, resulting in spARI. Statistical properties of spRI and spARI are thoroughly discussed. The applications of spARI to simulation study and two ST datasets demonstrate its better utilities than ARI in evaluating ST clustering methods. The R package to compute spRI and spARI is available at https://github.com/yinqiaoyan/spARI .