Kernel Joint Non-Negative Matrix Factorization for Genomic Data

The multi-modal or multi-view integration of data has generated a wide range of applicability in pattern extraction, clustering, and data interpretation. Recently, variants of the Non-negative Matrix Factorization (NMF), such as joint NMF (jNMF), have allowed the integration of data from different sources and have facilitated the incorporation of prior knowledge such as the interactions between variables from different sources. However, in both NMF and jNMF, the factorization is carried out as a linear system, which does not identify non-linear patterns present in most real-world data. Therefore, we propose a new variant of jNMF called Kernel jNMF. This new method incorporates the factorization of the original matrices into a high-dimensional space. Applying our method to synthetic data and biological cancer data, we found that the method performed better in clustering and interpretation than the jNMF methods.