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. An accurate ST clustering result can greatly benefit downstream biological analyses. As various ST clustering approaches are proposed in recent years, comparing their clustering accuracy becomes important in benchmarking studies. However, the widely used metric, adjusted Rand index (ARI), totally ignores the spatial information in ST data, which prevents ARI from fully evaluating spatial ST clustering methods. We propose a spatially aware Rand index (spRI) as well as spatially aware adjusted Rand index (spARI) that incorporate the spatial distance information. Specifically, when comparing two partitions, spRI provides a disagreement object pair with a weight relying on the distance of the two objects, whereas Rand index assigns a zero weight to it. This spatially aware feature of spRI adaptively differentiates disagreement object pairs based on their distinct distances, providing a useful evaluation metric that favors spatial coherence of clustering. The spARI is obtained by adjusting spRI for random chances such that its expectation takes zero under an appropriate null model. Statistical properties of spRI and spARI are discussed. The applications to simulation study and two ST datasets demonstrate the improved utilities of spARI compared to ARI in evaluating ST clustering methods.