NMF-Based Super-Level Analysis and ECMSMA

In msma: Multiblock Sparse Multivariable Analysis

knitr::opts_chunk$set(collapse = TRUE, comment = "#>", fig.width = 7, fig.height = 5)
library(msma)

Overview

Version 3.2 adds NMF and sparse NMF (sNMF) as super-level decomposition methods. They support clustering-oriented analyses of multiblock data while the default sprmethod = "PCA" preserves the version 3.1 computational path.

dat <- simdata(n = 45, rho = 0.8, Xps = c(5, 5, 5), Yps = 3, seed = 3)
X <- dat$X
names(X) <- paste0("block", seq_along(X))

Super-level methods

The principal options are:

• sprmethod = "PCA": conventional super-level PCA;
• sprmethod = "NMF": non-negative matrix factorization;
• sprmethod = "sNMF": sparse non-negative matrix factorization.

fit_pca <- msma(X, comp = c(2, 2), sprmethod = "PCA", intseed = 1)
fit_nmf <- msma(X, comp = c(2, 2), sprmethod = "NMF", intseed = 1)
fit_snmf <- msma(
  X, comp = c(2, 2),
  sprmethod = "sNMF",
  lambdaXsup = 0.05,
  intseed = 1
)

Non-negative transformations

NMF requires non-negative input. The nneg argument controls transformation of the block scores:

• "posneg": separates positive and negative parts;
• "absolute": uses absolute values;
• "min": shifts values to a non-negative range.

For a score vector (s), positive-negative decomposition is

[ s^+ = \max(s,0), \qquad s^- = \max(-s,0), \qquad s=s^+-s^-. ]

fit_posneg <- msma(X, comp = c(2, 2), sprmethod = "NMF", nneg = "posneg")
fit_absolute <- msma(X, comp = c(2, 2), sprmethod = "NMF", nneg = "absolute")
fit_min <- msma(X, comp = c(2, 2), sprmethod = "NMF", nneg = "min")

Non-negativity and reproducibility

all(unlist(fit_snmf$ssX) >= 0)
all(unlist(fit_snmf$wsX) >= 0)

fit_snmf_2 <- msma(
  X, comp = c(2, 2),
  sprmethod = "sNMF",
  lambdaXsup = 0.05,
  intseed = 1
)
all.equal(fit_snmf$ssX, fit_snmf_2$ssX)
all.equal(fit_snmf$wsX, fit_snmf_2$wsX)

Clustering solutions

A simple cluster assignment is obtained from the largest super-score value for each observation. Each root component supplies one clustering solution.

cluster_matrix <- vapply(
  fit_snmf$ssX,
  function(score) max.col(score, ties.method = "first"),
  integer(nrow(fit_snmf$ssX[[1]]))
)
colnames(cluster_matrix) <- names(fit_snmf$ssX)
head(cluster_matrix)
apply(cluster_matrix, 2, table)

The resulting matrix may be supplied to a separate consensus or ensemble clustering procedure. The consensus step is not performed automatically by msma().

Multiple supervision variables

Z may be a numeric matrix. con4spv specifies weights used to combine its columns. This is a composite-supervision model rather than a multi-task model with a separate loading for every outcome.

set.seed(3)
z1 <- rnorm(nrow(X[[1]]))
z2 <- 0.5 * z1 + rnorm(nrow(X[[1]]), sd = 0.5)
Z <- cbind(clinical = z1, biomarker = z2)

fit_multi_z <- msma(
  X = X, Z = Z,
  con4spv = c(0.7, 0.3),
  comp = 2,
  muX = 0.20,
  intseed = 1
)
fit_multi_z$predictiv

Conceptually, the combined supervision score is

[ z_c = Zc, ]

where the supplied weights are normalized internally as required by the implementation.

One-column matrix compatibility

A vector and a one-column matrix produce the same result.

fit_z_vector <- msma(X, Z = z1, comp = 1, muX = 0.20, intseed = 1)
fit_z_matrix <- msma(X, Z = cbind(z1), comp = 1, muX = 0.20, intseed = 1)
fit_z_vector$call <- NULL
fit_z_matrix$call <- NULL
isTRUE(all.equal(fit_z_vector, fit_z_matrix, tolerance = 1e-8))

Practical recommendations

• Fix intseed for reproducible NMF and sNMF results.
• Inspect both ssX and wsX when interpreting clusters.
• Compare several values of lambdaXsup for sNMF.
• Treat clustering from different root components as distinct candidate solutions before ensemble integration.

Session information

sessionInfo()

msma documentation built on Oct. 3, 2026, 9:07 a.m.