ResNMTF

Welcome to the landing page for the resnmtf package implementing Restrictive Non-Negative Matrix Tri-Factorisation (ResNMTF) from the paper “Multi-view biclustering via non-negative matrix tri-factorisation”.

ResNMTF is a flexible method which allows for any combination of shared rows and/or columns between views. For example, if view 1 and 2 share columns and views 1, 3 and 4 share rows, as in the following figure, this can be incorporated.

It does this by approximating the data matrix for each view $X^{(v)}$ by the factorisation $F^{(v)}S^{(v)}{(G^{(v)})}^T$, as in the following image (for 3 views with shared rows):

Installation

You can install this R package using the following line of code:

devtools::install_github("eso28599/resnmtf") # requires devtools package to be installed

Usage

To demonstrate the use of resnmtf we generate toy data with 2 views and 3 biclusters, assuming biclusters share rows across views, but do not share columns. View 1 has dimensions $100 \times 50$ and view 2, $100 \times 30$.

row_clusters <- cbind(
  rbinom(100, 1, 0.5),
  rbinom(100, 1, 0.5),
  rbinom(100, 1, 0.5)
)
col_clusters_v1 <- cbind(
  rbinom(50, 1, 0.4),
  rbinom(50, 1, 0.4),
  rbinom(50, 1, 0.4)
)
col_clusters_v2 <- cbind(
  rbinom(30, 1, 0.4),
  rbinom(30, 1, 0.4),
  rbinom(30, 1, 0.4)
)
data <- list(
  row_clusters %*% diag(c(5, 5, 5)) %*% t(col_clusters_v2) +
    abs(matrix(rnorm(100 * 50), 100, 50)),
  row_clusters %*% diag(c(5, 5, 5)) %*% t(col_clusters_v2) +
    abs(0.01 * matrix(rnorm(100 * 30), 100, 30))
)

Application

The apply_resnmtf function is used to obtain biclusters. It takes as input multi-view data in the form of a list i.e. the data $X =\{X^{(1)}, \dots,X^{(n_v)}\}$ should be inputted as a list list(x_1, x_2, \dots, x_n_v).

The desired restrictions are imposed via restriction matrices phi, psi and xi which enforce shared row clusters, column clusters and row-column matching respectively.

phi <- matrix(0, 2, 2)
phi[1, 2] <- 1 # regularises towards shared rows between view 1 and view 2
phi_val <- 200 # hyperparameter chosen to enforce regularisation
results <- apply_resnmtf(data, phi = phi_val * phi)

If the number of biclusters present in each view are known, this can be supplied via k_vec:

results <- apply_resnmtf(data, k_vec = rep(3, 2), phi = phi_val * phi)

If instead you would like to change the range of biclusters considered initially ($3\leq k \leq 8$ by default), this can be implented via the k_min and k_max inputs:

results <- apply_resnmtf(data, k_min = 4, k_max = 10, phi = phi_val * phi)

Notes:

• a non-zero xi restriction matrix also enforces the assumption that the scale of the biclusters is equal across views.
• the number of biclusters does not need to be specified, but will be determined by the bisilhouette score.

Results

The multi-view biclustering is contained within two lists defining the row and column clusters associated with the biclusters. For a specific view, both are represented via binary logic matrices, with the $(i,j)^{th}$ element equal to $1$ if row/column $i$ belongs to bicluster $j$, and $0$ otherwise.

results$row_clusters
results$col_clusters

I.e. for the given example, results$row_clusters is a list of length 2, the first element of which is a binary matrix of size $100 \times k$ where $k$ is the number of biclusters found.

Single-view data

The method can also be applied on single-view data, inputted either as a list containing the matrix of the single-view:

data <- list(
  row_clusters %*% diag(c(5, 5, 5)) %*% t(col_clusters_v2) +
    abs(matrix(rnorm(100 * 50), 100, 50))
    )
results <- apply_resnmtf(data)

Or as a matrix:

data <- row_clusters %*% diag(c(5, 5, 5)) %*% t(col_clusters_v2) +
          abs(matrix(rnorm(100 * 50), 100, 50))
results <- apply_resnmtf(data)

Citation

If you use our model in your work, please cite us with:

Orme, E.S.C., Rodosthenous, T. and Evangelou, M., 2025. Multi-view biclustering via non-negative matrix tri-factorisation. arXiv preprint arXiv:2502.13698.

Or with the following bibtex entry:

@misc{resnmtf,
      title={Multi-view biclustering via non-negative matrix tri-factorisation},
      author={Ella S. C. Orme and Theodoulos Rodosthenous and Marina Evangelou},
      year={2025},
      eprint={2502.13698},
      archivePrefix={arXiv},
      primaryClass={stat.ME},
      url={https://arxiv.org/abs/2502.13698},
}