# Two-Mode Clustering via the E_ReMI Method Performs row-by-column clustering using the E-ReMI (Extended REMAXINT) algorithm. It estimates latent cluster structures in rows and columns of a data matrix with unequal row cluster proportions using a REMAXINT-like procedure. ```r E_ReMI(DC, P, Q, Nruns, initR, initC, initG) ``` ## Arguments - `DC`: A doubly centered numeric matrix of size `I x J` representing the input data to be clustered. - `P`: An integer indicating the number of clusters for rows. - `Q`: An integer indicating the number of clusters for columns. - `Nruns`: The number of random initializations (runs) to perform to avoid local maxima. The solution with the highest likelihood is returned. - `initR`: An initial binary matrix of size `I x P` indicating the initial row cluster assignments. - `initC`: An initial binary matrix of size `J x Q` indicating the initial column cluster assignments. - `initG`: A `P x Q` matrix representing the initial estimate of the latent interaction between row and column clusters. ## Details The `E_ReMI` function implements an EM-style algorithm for biclustering, based on maximizing the likelihood of a Gaussian interaction model with unequal row cluster sizes. Starting from user-provided initial values for cluster assignments and the interaction matrix, the algorithm iteratively updates row clusters, column clusters, the bi-cluster interaction matrix, and estimates the proportions of row clusters (`Omega`) and residual variance. Unlike REMAXINT clustering models, `E_ReMI` accounts for unequal cluster sizes in expectation, allowing for more flexible modeling of heterogeneous block-structured data. ## Returns A list containing: - **BestR**: Binary matrix (`I x P`) of row cluster assignments. - **BestC**: Binary matrix (`J x Q`) of column cluster assignments. - **BestG**: Estimated `P x Q` latent interaction matrix. - **LL**: Maximal log-likelihood of the fitted model. - **Best_O**: Estimated row cluster proportions (Omega), a vector of length `P`. ## References Ahmed, Z., van Breukelen, G. J. P., Schepers, J., & Cassese, A. (2025). Robustness study of normality-based likelihood ratio tests for testing maximal interaction two-mode clustering and a permutation-based alternative. **Available on OSF** (submitted to ADAC). Ahmed, Z., van Breukelen, G. J. P., Schepers, J., & Cassese, A. (2023). E-ReMI: extended maximal interaction two-mode clustering. **Journal of Classification, 40, 298-331.** Ahmed, Z., van Breukelen, G. J. P., Schepers, J., & Cassese, A. (2021). REMAXINT: a two-mode clustering-based method for statistical inference on two-way interaction. **Advances in Data Analysis and Classification, 15(4), 987-1013.** ## Author(s) Zaheer Ahmed (ahmed@ifado.de), Jan Schepers (jan.schepers@maastrichtuniversity.nl), Uwe Ligges (ligges@statistik.tu-dortmund.de), Alberto Cassese (alberto.cassese@unifi.it), Gerard van Breukelen (gerard.vbreukelen@maastrichtuniversity.nl), Katja Ickstadt (ickstadt@statistik.tu-dortmund.de), Edmund Wascher (wascher@ifado.de) ## Note This function is useful for clustering data with unequal row cluster sizes and estimating interaction structures between biclusters. ## See Also `Permutation_Function`, `Randompartition_function`, `Unequal_Randompartition_Function`, `Update_row_clusters_E_ReMI`, `Update_column_clusters`, `Update_G_Omega`, `Log_Likelihood_function_E_ReMI`, `pinv` ## Examples ```r I <- 10 P <- 4 J <- 5 Q <- 2 Nruns <- 5 DC <- matrix(rnorm(I * J), I, J) initR <- diag(1, nrow = I, ncol = P) initC <- diag(1, nrow = J, ncol = Q) R_inv <- pracma::pinv(t(initR) %*% initR) C_inv <- pracma::pinv(t(initC) %*% initC) initG <- R_inv %*% t(initR) %*% DC %*% initC %*% C_inv initG <- as.matrix(initG) result <- E_ReMI(DC, P, Q, Nruns, initR, initC, initG) result ```

E_ReMI function