Rectified Factor Networks for Biclustering
Authors: Djork-Arné Clevert, Thomas Unterthiner, Sepp Hochreiter

Abstract: Biclustering is evolving into one of the major tools for analyzing large datasets given as matrix of samples times features. Biclustering has been successfully applied in life sciences, e.g. for drug design, in e-commerce, e.g. for internet retailing or recommender systems. 
FABIA is one of the most successful biclustering methods which excelled in different projects and is used by companies like Janssen, Bayer, or Zalando. FABIA 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. Sample membership is difficult to determine because vectors do not have exact zero entries and can have both large positive and large negative values. 
We propose to use the recently introduced unsupervised Deep Learning approach Rectified Factor Networks (RFNs) to overcome the drawbacks of FABIA. 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. 
On 400 benchmark datasets with artificially implanted biclusters, RFN significantly outperformed 13 other biclustering competitors including FABIA. In biclustering experiments on three gene expression datasets with known clusters that were determined by separate measurements, RFN biclustering was two times significantly better than the other 13 methods and once on second place.