Fig. 2

Samples representation with AFT. a Intra and inter datasets pBCd distributions are computed on the 9.9M genes for each cohort dataset and compared with pBCd distributions among all samples. Little discrepancies are observed except for the Metacardis and Mediterranean diet cohorts, where intra pBCd is shifted towards lower values, and the CD cohort, where the shift is towards higher values. b The dysbiosis index distribution of each dataset is displayed, together with the dysbiosis threshold (red dotted line). Dysbiotic samples are over-represented in the CD cohort. c Comparison of different aggregation levels. pBCd distributions are displayed for each dataset, computed both on the 9.9M gene counts, on the subset of SGs or on the AFT counts (see Fig. 1b). pBCd with AFT are strongly decreased. HMP2 and CD distributions are wider than other datasets for all aggregation levels. d PERMANOVA p-values after variance decomposition analysis of pBCd matrices respectively to structuring co-variables. The PERMANOVA was performed for the different levels of aggregation and for the WH reconstruction. We can see that significance tends to decrease for higher aggregation levels, but the same level of significance is kept between AFT and WH, indicating that the same level of structure is kept after NMF decomposition. e Qq-plots of AFT and reconstructed pBCd distributions. The dots indicate the distribution centiles. The reconstructed pBCd are computed on WH reconstructions including 1 \(\left(WH_1 = W^{(AFT)}_{1} H^{(AFT)}_1\right)\), 2 \(\left(WH_{12} = \sum _{i=1}^2 W^{(AFT)}_{i} H^{(AFT)}_i\right)\), 3 \(\left(WH_{123} = \sum _{i=1}^3 W^{(AFT)}_{i} H^{(AFT)}_i\right)\) or the 4 profiles \(\left(WH_{1234}=\sum _{i=1}^4 W^{(AFT)}_{i} H^{(AFT)}_i\right)\). The red line indicates the bisector line. We observe that profile 1 alone is not sufficient to reconstruct accurate pBCd but that profiles 1 and 2 together allow the reconstruction of the main part of the pBCd distribution, for the lowest pBCd values. We can see that higher pBCd are not correctly rendered by the 2 profiles, especially for the CD cohort where dysbiotic samples are over represented. Adding the third and the fourth profiles enables a correct reconstruction of the whole distribution but with a homogeneous bias among the whole distribution