  It is more and more common to explore the genome at diverse levels and not
only at a single omic level. Through integrative statistical methods, omics
data have the power to reveal new biological processes, potential biomarkers,
and subgroups of a cohort. The matrix factorization (MF) is a unsupervised
statistical method that allows giving a clustering of individuals, but also
revealing relevant omic variables from the various blocks. Here, we present
PIntMF (Penalized Integrative Matrix Factorization), a model of MF with
sparsity, positivity and equality constraints.To induce sparsity in the model,
we use a classical Lasso penalization on variable and individual matrices. For
the matrix of samples, sparsity helps for the clustering, and normalization
(matching an equality constraint) of inferred coefficients is added for a
better interpretation. Besides, we add an automatic tuning of the sparsity
parameters using the famous glmnet package. We also proposed three criteria to
help the user to choose the number of latent variables. PIntMF was compared to
other state-of-the-art integrative methods including feature selection
techniques in both synthetic and real data. PIntMF succeeds in finding relevant
clusters as well as variables in two types of simulated data (correlated and
uncorrelated). Then, PIntMF was applied to two real datasets (Diet and cancer),
and it reveals interpretable clusters linked to available clinical data. Our
method outperforms the existing ones on two criteria (clustering and variable
selection). We show that PIntMF is an easy, fast, and powerful tool to extract
patterns and cluster samples from multi-omics data.
