PIntMF: Penalized Integrative Matrix Factorization Method for\n Multi-Omics Data

Abstract

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