Rectified factor networks for biclustering of omics data

Biclustering has become a major tool for analyzing large datasets given as matrix of samples times features and has been successfully applied in life sciences and e-commerce for drug design and recommender systems, respectively. Factor Analysis for Bicluster Acquisition (FABIA), one of the most successful biclustering methods, is a generative model that represents each bicluster by two sparse membership vectors: one for the samples and one for the features. However, FABIA is restricted to about 20 code units because of the high computational complexity of computing the posterior. Furthermore, code units are sometimes insufficiently decorrelated and sample membership is difficult to determine. We propose to use the recently introduced unsupervised Deep Learning approach Rectified Factor Networks (RFNs) to overcome the drawbacks of existing biclustering methods. RFNs efficiently construct very sparse, non-linear, high-dimensional representations of the input via their posterior means. RFN learning is a generalized alternating minimization algorithm based on the posterior regularization method which enforces non-negative and normalized posterior means. Each code unit represents a bicluster, where samples for which the code unit is active belong to the bicluster and features that have activating weights to the code unit belong to the bicluster. Results: On 400 benchmark datasets and on three gene expression datasets with known clusters, RFN outperformed 13 other biclustering methods including FABIA. On data of the 1000 Genomes Project, RFN could identify DNA segments which indicate, that interbreeding with other hominins starting already before ancestors of modern humans left Africa.