Fig. 1

Illustrative of MHSNMF framework on human microbiome data. a Example representation of the phylogenetic profile and metabolic profile for the same cohort of samples. b Sample-sample similarity matrices obtained from each view. c Using MHSNMF, each similarity matrix is factorized into a low rank matrix and its transposition. Matrix fusion process iteratively updates each clustering with information from the other view. d The iterative fusion leads to convergence to the final consensus matrix H^∗. e Given a new sample x_new from the i ‐ th view, we can obtain its subspace representation h by H^∗ and the proposed mapping approach. Here, \( {V}_{tr}^i \) indicates the training samples from i ‐ th view, S denotes the similarity between x_new and \( {V}_{tr}^i \). α is the regularization parameter. f Once obtaining h, some applications such as classification, prediction and so on would be executed naturally