Recent advancements in microarray technology and data storage have led to easier access to high-quality biological expression data, in large quantities and from many different sources. As a result, there has been growing interest in finding ways to integrate different types of omics data (genomics, proteomics, metabolomics, etc.) in order to achieve higher power or to gain a better global perspective of the system. However, many of the current data integration approaches are only designed for the specific biological context at hand, and thus are difficult to extend to other settings. We elect to develop a more generalizable framework for multi-modal data analysis based on nonnegative matrix factorization (NMF). Recently, Zhang et al. (2012) developed the joint NMF (JNMF) model, which detects multi-dimensional modules representative of common signals across multiple data sets. We propose here joint-individual NMF (JINMF), a natural extension which is adaptive to source-specific variation. It is designed to handle the increased heterogeneity that comes with combining multiple data types or platforms. We derive an algorithm based on multiplicative updates with a sparsity option for high-dimensional settings. A simulation study and an application using biological omics data show that JINMF outperforms its predecessor in perturbed settings and achieves comparable performance in general settings.
