Fig. 2: Performance for SVG idenfication and spatial omics feature imputation.

a SpaGFT considers a gene-spot expression count matrix (\(m\times n\)) and spatial locations as input data, with ENC1, MOBP, and GPS1 listed as examples. b Two known SVGs (MOBP and ENC1) and one non-SVG (GPS1) are shown as examples. The FMs can be separated into low-frequency (red) and high-frequency (blue) domains. c The SVG prediction evaluation was compared to five benchmarking tools. The running time is represented as red lines. In addition, the other evaluation scores of all parameter combinations for each tool are shown as heatmaps. The two-sided Wilcox rank-sum test was used to calculate the p-value for the highest two tools (i.e., N = 16 and N = 53 for SpaGFT and MERINGUE in HE_coronal data; N = 16 and N = 54 for SpaGFT and MERINGUE in 151673 data; N = 16 and N = 18 for SpaGFT and SPARK-X in Puck-200115-08 data). The methods are not able to identify SVG in a reasonable time, showing NA in this panel. d The box plot shows independent test results. The two-sided Wilcox rank-sum test is used to calculate the p-values for the highest two tools (N = 28). Each box showcases the minimum, first quartile, median, third quartile, and maximum Jaccard scores in panels c and d. e SVG examples that all tools can identify (left panel) are uniquely identified by SpaGFT (middle and right panel). Green genes are reported in the literature, while orange is not. Expression of Nsmf, Tbr1, Cartpt, Cbln2, Ttr, and Pmch in adult mouse brain. Allen Mouse Brain Atlas, mouse.brain-map.org/experiment/show/74821712, mouse.brain-map.org/experiment/show/79591351, mouse.brain-map.org/experiment/show/72077479, mouse.brain-map.org/experiment/show/68632172, and mouse.brain-map.org/experiment/show/55. f Comparison of the UMAPs of the HE-coronal data in Principle Component features space and Fourier space. g Boxplot showcases the performance of SVG signal enhancement for grid search (top) and independent test using 151509 (bottom), where the y-axis is the ARI value. The two-sided Wilcox rank-sum test is used to calculate the p-values for the highest two tools (N = 27). Each box showcases the minimum, first quartile, median, third quartile, and maximum ARI scores. h and i The spatial map shows the signals before and after enhancement and noise removal for spatial omics features. Source data are provided as a Source Data file.