Fig. 2

Clustering procedure of the MVLBM method described in [52]. Step 1: The Latent Block Model (LBM) is applied independently to each view of the dataset, clustering rows (observations) and columns (features) into distinct groups specific to each view. Step 2: Perform hypothesis testing to assess the independence of row clusters across different views. If dependency is detected between views, they are incorporated into the multi-view analysis. Pairwise tests are performed, with adjustments for multiple comparisons applied when analyzing more than two views. Step 3: Use the co-clustering results from the single-view LBMs as the initialization for the multi-view analysis. The initial clustering assignments inform the joint row-cluster membership structure and the column-cluster parameters for each view. Step 4: Employ the stochastic Expectation-Maximization algorithm combined with Gibbs sampling for parameter estimation. This approach accounts for the dependency structure among views. The MVLBM algorithm iteratively updates (1) row and column cluster assignments, (2) cluster parameters within each view, and (3) the joint row-cluster membership matrix, which captures dependencies across views. Step 5: The iterative process terminates when the Integrated Completed Likelihood (ICL) criterion fails to increase between iterations. This ensures that the best-fitting model is identified