MOTIVATION: Spatial clustering is a critical analytical task in spatial transcriptomics (ST) that aids in uncovering the spatial molecular mechanisms underlying biological phenotypes. Along with the numerous spatial clustering methods, there comes the imperative need for an effective metric to evaluate their performance. An ideal metric should consider three factors: label agreement, spatial organization, and error severity. However, existing evaluation metrics focus solely on either label agreement or spatial organization, leading to biased and misleading evaluations. RESULTS: To fill this gap, we propose CEMUSA, a novel graph-based metric that integrates these factors into a unified evaluation framework. Extensive testing on both simulated and real datasets demonstrate CEMUSA's superiority over conventional metrics in differentiating clustering results with subtle differences in topology and error severity, while maintaining computational efficiency. AVAILABILITY AND IMPLEMENTATION: The source code and data are freely available at https://github.com/YihDu/CEMUSA. CEMUSA is implemented as an R package at https://yihdu.github.io/CEMUSA.

Spatial labeling assigns labels to specific spatial locations to characterize their spatial properties and relationships, with broad applications in scientific research and practice. Measuring the similarity between two spatial labelings is essential for understanding their differences and the contributing factors, such as changes in location properties or labeling methods. An adequate and unbiased measurement of spatial labeling similarity should consider the number of matched labels (label agreement), the topology of spatial label distribution, and the heterogeneous impacts of mismatched labels. However, existing methods often fail to account for all these aspects. To address this gap, we propose a methodological framework to guide the development of methods that meet these requirements. Given two spatial labelings, the framework transforms them into graphs based on location organization, labels, and attributes (e.g., location significance). The distributions of their graph attributes are then extracted, enabling an efficient computation of distributional discrepancy to reflect the dissimilarity level between the two labelings. We further provide a concrete implementation of this framework, termed Spatial Labeling Analogy Metric (SLAM), along with an analysis of its theoretical foundation, for evaluating spatial labeling results in spatial transcriptomics (ST) as per their similarity with ground truth labeling. Through a series of carefully designed experimental cases involving both simulated and real ST data, we demonstrate that SLAM provides a comprehensive and accurate reflection of labeling quality compared to other well-established evaluation metrics. Our code is available at https://github.com/YihDu/ SLAM.