Fig. 5: Facilitating vertical integration for sample classification.

a,b, Bar plots of the ARI of vertically integrated multi-omics datasets of different quality (a; bad versus good) and different scenarios (b; confounded versus balanced) at the absolute level (blue) and ratio level (red) using SNF, iClusterBayes, MOFA+, MCIA and intNMF. The number of data sampling and integration instances (n) used to derive statistics was as follows: bad, n = 10; good, n = 10; confounded, n = 200; balanced, n = 100. Data are presented as mean values ± s.d. The P values were calculated using unpaired two-tailed Wilcoxon rank-sum tests with FDR correction. ****P < 0.0001, **P < 0.01, *P < 0.05; not significant, P ≥ 0.05. Specific P values are listed in Supplementary Data 3 and 4. c, Scatterplots of the degree of sample class-batch balance versus ARI with different data preprocessing methods. d, Scatterplots of the degree of sample class-batch balance versus SNR with different data preprocessing methods. SNR was calculated on the basis of a sample-to-sample similarity matrix. e, Curves of ARI and SNR with the degree of balance between sample classes and batches at the absolute level (blue, solid line), ratio level (red, solid line), absolute level combined with BECAs (blue, dotted line) and ratio level combined with BECAs (red, dotted line). Each point represents an instance of data sampling and integration. The solid lines correspond to fitted curves obtained from local regression, and the shading indicates the 95% confidence interval around the smoothing.