Extended Data Fig. 6: Comprehensive benchmarking with additional methods.

A total of 12 methods are benchmarked here: CellLENS (our method). SpaGCN: Designed for spot-level spatial modalities (to identify spatial domains). StLearn: Designed for spatial modalities (to identify cell populations). SEDR: Designed for spatial modalities (to identify cell populations). MUSE: Designed for single-cell spatial modalities (to identify cell populations). SpiceMix: Designed for spatial modalities (to identify cell populations). BANKSY: Designed for spatial modalities (to identify cell populations or spatial domains). CellCharter: Designed for spatial modalities (to identify spatial domains). MOFA+: Designed for general modalities. CCA: General statistical procedure with canonical correlation analysis. Concatenation: Direct concatenation between feature and location matrix. Feature-only profile: Conventional way of cell type identification. We applied all 12 methods to five datasets presented in our manuscript (CODEX spleen, Xenium tonsil, CODEX tonsil, CODEX cHL, and CosMx HCC) and evaluated them using four different metrics (See Methods for details). Here we aggregated all the results across metrics and datasets into one summary figure. Each subpanel represents a specific metric (for example, Modularity score). The Y-axis indicates the average ranking of a method across benchmarking conditions (for example, K clusters or resolution numbers). On the X-axis, methods are arranged by their average ranking across all four metrics, such that methods on the left perform the best overall. In the summary figure, the rankings were averaged across all five datasets.